From 2fb6708a4622573b77d8f9b2900fba4550f55092 Mon Sep 17 00:00:00 2001 From: ChrisRackauckas-Claude Date: Mon, 31 Aug 2026 20:22:34 -0400 Subject: [PATCH] Publish refreshed Jumps benchmarks Co-Authored-By: Chris Rackauckas Co-Authored-By: Claude Claude-Session: https://chatgpt.com/codex/tasks/01a03a17-ad6f-7131-82fc-d0fd57ea6512 --- markdown/Jumps/Diffusion_CTRW.md | 685 ++++---- markdown/Jumps/EGFR_Benchmark.md | 658 ++++---- markdown/Jumps/Mendes_multistate_example.md | 663 ++++---- markdown/Jumps/MultivariateHawkes.md | 1411 ----------------- markdown/Jumps/NegFeedback_GeneExpr.md | 650 ++++---- .../Jumps/NegFeedback_GeneExpr_Marchetti.md | 650 ++++---- markdown/Jumps/Spatial_Signaling_Sanft.md | 689 ++++---- markdown/Jumps/figures/Diffusion_CTRW_2_1.png | Bin 134268 -> 130877 bytes markdown/Jumps/figures/Diffusion_CTRW_3_1.png | Bin 124217 -> 0 bytes markdown/Jumps/figures/Diffusion_CTRW_6_1.png | Bin 38524 -> 38116 bytes markdown/Jumps/figures/Diffusion_CTRW_7_1.png | Bin 33160 -> 0 bytes markdown/Jumps/figures/EGFR_Benchmark_2_1.png | Bin 33962 -> 33810 bytes markdown/Jumps/figures/EGFR_Benchmark_4_1.png | Bin 18342 -> 17618 bytes .../figures/Mendes_multistate_example_3_1.png | Bin 131014 -> 0 bytes .../figures/Mendes_multistate_example_4_1.png | Bin 100446 -> 101343 bytes .../figures/Mendes_multistate_example_6_1.png | Bin 29906 -> 0 bytes .../figures/Mendes_multistate_example_7_1.png | Bin 33133 -> 33569 bytes .../Jumps/figures/MultivariateHawkes_13_1.png | Bin 23350 -> 0 bytes .../Jumps/figures/MultivariateHawkes_16_1.png | Bin 59094 -> 0 bytes .../Jumps/figures/MultivariateHawkes_20_1.png | Bin 38115 -> 0 bytes .../Jumps/figures/MultivariateHawkes_21_1.png | Bin 71441 -> 0 bytes .../Jumps/figures/MultivariateHawkes_23_1.png | Bin 46880 -> 0 bytes .../Jumps/figures/MultivariateHawkes_8_1.png | Bin 69098 -> 0 bytes .../figures/NegFeedback_GeneExpr_2_1.png | Bin 49873 -> 0 bytes .../figures/NegFeedback_GeneExpr_3_1.png | Bin 60845 -> 60203 bytes .../figures/NegFeedback_GeneExpr_7_1.png | Bin 37669 -> 37248 bytes .../NegFeedback_GeneExpr_Marchetti_3_1.png | Bin 19749 -> 19750 bytes .../NegFeedback_GeneExpr_Marchetti_4_1.png | Bin 50746 -> 49649 bytes .../NegFeedback_GeneExpr_Marchetti_5_1.png | Bin 24653 -> 26743 bytes .../NegFeedback_GeneExpr_Marchetti_8_1.png | Bin 35740 -> 35408 bytes .../figures/Spatial_Signaling_Sanft_11_1.png | Bin 82553 -> 78364 bytes .../figures/Spatial_Signaling_Sanft_13_1.png | Bin 82338 -> 81012 bytes .../figures/Spatial_Signaling_Sanft_6_1.png | Bin 33309 -> 32762 bytes script/Jumps/Diffusion_CTRW.jl | 55 +- script/Jumps/EGFR_Benchmark.jl | 44 +- script/Jumps/Mendes_multistate_example.jl | 72 +- script/Jumps/MultivariateHawkes.jl | 719 --------- script/Jumps/NegFeedback_GeneExpr.jl | 54 +- .../Jumps/NegFeedback_GeneExpr_Marchetti.jl | 58 +- script/Jumps/Spatial_Signaling_Sanft.jl | 104 +- script/Jumps/Synapse.jl | 120 -- 41 files changed, 2074 insertions(+), 4558 deletions(-) delete mode 100644 markdown/Jumps/MultivariateHawkes.md delete mode 100644 markdown/Jumps/figures/Diffusion_CTRW_3_1.png delete mode 100644 markdown/Jumps/figures/Diffusion_CTRW_7_1.png delete mode 100644 markdown/Jumps/figures/Mendes_multistate_example_3_1.png delete mode 100644 markdown/Jumps/figures/Mendes_multistate_example_6_1.png delete mode 100644 markdown/Jumps/figures/MultivariateHawkes_13_1.png delete mode 100644 markdown/Jumps/figures/MultivariateHawkes_16_1.png delete mode 100644 markdown/Jumps/figures/MultivariateHawkes_20_1.png delete mode 100644 markdown/Jumps/figures/MultivariateHawkes_21_1.png delete mode 100644 markdown/Jumps/figures/MultivariateHawkes_23_1.png delete mode 100644 markdown/Jumps/figures/MultivariateHawkes_8_1.png delete mode 100644 markdown/Jumps/figures/NegFeedback_GeneExpr_2_1.png delete mode 100644 script/Jumps/MultivariateHawkes.jl delete mode 100644 script/Jumps/Synapse.jl diff --git a/markdown/Jumps/Diffusion_CTRW.md b/markdown/Jumps/Diffusion_CTRW.md index ec362fb6f..c4928048b 100644 --- a/markdown/Jumps/Diffusion_CTRW.md +++ b/markdown/Jumps/Diffusion_CTRW.md @@ -10,6 +10,7 @@ using Catalyst, JumpProcesses, JumpProblemLibrary, Plots, Statistics, DataFrames # Model and example solutions + Here we implement a 1D continuous time random walk approximation of diffusion for $N$ lattice sites on $\left[0,1\right]$, with reflecting boundary conditions at $x=0$ and $x=1$. Note that our goal is to benchmark the non-spatial @@ -19,21 +20,24 @@ spatial SSAs too here. ```julia N = 256 h = 1 / N -u0 = 10 * ones(Int64, N) -tf = .01 -methods = (Direct(), FRM(), SortingDirect(), NRM(), DirectCR(), RSSA(), RSSACR(), Coevolve(), RDirect()) -shortlabels = [string(leg)[15:end-2] for leg in methods] +tf = 0.01 +methods = (Direct(), FRM(), SortingDirect(), NRM(), DirectCR(), + RSSA(), RSSACR(), Coevolve(), RDirect()) +shortlabels = [string(leg)[15:(end - 2)] for leg in methods] jprob = JumpProblemLibrary.prob_jump_diffnetwork rn = jprob.network(N) -prob = DiscreteProblem(rn, u0, (0.0, tf), [1 / (h*h)]) -ploth = plot(reuse=false) -for (i,method) in enumerate(methods) +u0 = jprob.u0(rn, N) +rates = [:K => 1 / (h * h)] +ploth = plot(reuse = false) +for (i, method) in enumerate(methods) println("Benchmarking method: ", method) - jump_prob = JumpProblem(rn, prob, method, save_positions=(false, false)) - sol = solve(jump_prob, SSAStepper(); saveat=tf/1000.) - plot!(ploth, sol.t, sol[Int(N//2),:], label=shortlabels[i]) + jump_prob = JumpProblem( + rn, u0, (0.0, tf), rates; aggregator = method, save_positions = (false, false) + ) + sol = solve(jump_prob, SSAStepper(); saveat = tf/1000.0) + plot!(ploth, sol.t, sol[Int(N//2), :], label = shortlabels[i]) end -plot!(ploth, title="Population at middle lattice site", xlabel="time") +plot!(ploth, title = "Population at middle lattice site", xlabel = "time") ``` ``` @@ -74,7 +78,9 @@ run_benchmark! (generic function with 1 method) nsims = 50 benchmarks = Vector{Vector{Float64}}() for method in methods - jump_prob = JumpProblem(rn, prob, method, save_positions=(false, false)) + jump_prob = JumpProblem( + rn, u0, (0.0, tf), rates; aggregator = method, save_positions = (false, false) + ) stepper = SSAStepper() t = Vector{Float64}(undef, nsims) run_benchmark!(t, jump_prob, stepper) @@ -84,17 +90,18 @@ end ```julia -medtimes = Vector{Float64}(undef,length(methods)) -stdtimes = Vector{Float64}(undef,length(methods)) -avgtimes = Vector{Float64}(undef,length(methods)) +medtimes = Vector{Float64}(undef, length(methods)) +stdtimes = Vector{Float64}(undef, length(methods)) +avgtimes = Vector{Float64}(undef, length(methods)) for i in 1:length(methods) medtimes[i] = median(benchmarks[i]) avgtimes[i] = mean(benchmarks[i]) stdtimes[i] = std(benchmarks[i]) end -df = DataFrame(names=shortlabels, medtimes=medtimes, relmedtimes=(medtimes/medtimes[1]), - avgtimes=avgtimes, std=stdtimes, cv=stdtimes./avgtimes) +df = DataFrame( + names = shortlabels, medtimes = medtimes, relmedtimes = (medtimes/medtimes[1]), + avgtimes = avgtimes, std = stdtimes, cv = stdtimes ./ avgtimes) ``` ``` @@ -105,24 +112,24 @@ df = DataFrame(names=shortlabels, medtimes=medtimes, relmedtimes=(medtimes/medti 4 ⋯ ─────┼───────────────────────────────────────────────────────────────────── ───── - 1 │ Direct 7.04995 1.0 7.04973 0.00515773 0.0007 -316 ⋯ - 2 │ FRM 15.9036 2.25584 15.9138 0.0643626 0.0040 -444 - 3 │ SortingDirect 1.06543 0.151126 1.06522 0.00426768 0.0040 -063 - 4 │ NRM 0.743135 0.10541 0.743926 0.00313082 0.0042 -085 - 5 │ DirectCR 0.475098 0.0673902 0.475005 0.00141176 0.0029 -720 ⋯ - 6 │ RSSA 1.41678 0.200963 1.41675 0.00319636 0.0022 -561 - 7 │ RSSACR 0.393641 0.0558361 0.393271 0.00235362 0.0059 -847 - 8 │ Coevolve 0.865318 0.122741 0.866045 0.00273446 0.0031 -574 - 9 │ RDirect 0.408486 0.0579417 0.409129 0.00222711 0.0054 -435 ⋯ + 1 │ Direct 9.45822 1.0 9.45868 0.00757127 0.0008 +004 ⋯ + 2 │ FRM 22.1954 2.34668 22.2194 0.0715947 0.0032 +221 + 3 │ SortingDirect 1.43655 0.151884 1.43663 0.00523339 0.0036 +428 + 4 │ NRM 1.01202 0.106998 1.0134 0.00590352 0.0058 +254 + 5 │ DirectCR 0.663292 0.0701286 0.663935 0.00194931 0.0029 +36 ⋯ + 6 │ RSSA 1.91481 0.202449 1.91528 0.00546598 0.0028 +538 + 7 │ RSSACR 0.551969 0.0583586 0.553364 0.00457602 0.0082 +694 + 8 │ Coevolve 1.29751 0.137184 1.29903 0.00864847 0.0066 +576 + 9 │ RDirect 0.567072 0.0599555 0.567832 0.00390389 0.0068 +750 ⋯ 1 column om itted ``` @@ -132,10 +139,11 @@ itted # Plotting + ```julia -sa = [string(round(mt,digits=4),"s") for mt in df.medtimes] -bar(df.names, df.relmedtimes, legend=:false) -scatter!(df.names, .05 .+ df.relmedtimes, markeralpha=0, series_annotations=sa) +sa = [string(round(mt, digits = 4), "s") for mt in df.medtimes] +bar(df.names, df.relmedtimes, legend = :false) +scatter!(df.names, 0.05 .+ df.relmedtimes, markeralpha = 0, series_annotations = sa) ylabel!("median relative to Direct") title!("256 Site 1D Diffusion CTRW") ``` @@ -148,7 +156,6 @@ title!("256 Site 1D Diffusion CTRW") These benchmarks are a part of the SciMLBenchmarks.jl repository, found at: [https://github.com/SciML/SciMLBenchmarks.jl](https://github.com/SciML/SciMLBenchmarks.jl). For more information on high-performance scientific machine learning, check out the SciML Open Source Software Organization [https://sciml.ai](https://sciml.ai). To locally run this benchmark, do the following commands: - ``` using SciMLBenchmarks SciMLBenchmarks.weave_file("benchmarks/Jumps","Diffusion_CTRW.jmd") @@ -157,8 +164,8 @@ SciMLBenchmarks.weave_file("benchmarks/Jumps","Diffusion_CTRW.jmd") Computer Information: ``` -Julia Version 1.10.9 -Commit 5595d20a287 (2025-03-10 12:51 UTC) +Julia Version 1.10.12 +Commit d93beab124c (2026-08-15 10:29 UTC) Build Info: Official https://julialang.org/ release Platform Info: @@ -167,432 +174,372 @@ Platform Info: WORD_SIZE: 64 LIBM: libopenlibm LLVM: libLLVM-15.0.7 (ORCJIT, znver2) -Threads: 1 default, 0 interactive, 1 GC (on 128 virtual cores) +Threads: 128 default, 0 interactive, 64 GC (on 128 virtual cores) Environment: - JULIA_CPU_THREADS = 128 - JULIA_DEPOT_PATH = /cache/julia-buildkite-plugin/depots/5b300254-1738-4989-ae0a-f4d2d937f953 + JULIA_NUM_THREADS = auto ``` Package Information: ``` -Status `/cache/build/exclusive-amdci1-0/julialang/scimlbenchmarks-dot-jl/benchmarks/Jumps/Project.toml` - [6e4b80f9] BenchmarkTools v1.6.0 - [479239e8] Catalyst v15.0.8 - [8f4d0f93] Conda v1.10.2 - [a93c6f00] DataFrames v1.7.0 - [0c46a032] DifferentialEquations v7.16.1 - [31c24e10] Distributions v0.25.120 - [86223c79] Graphs v1.12.1 - [faf0f6d7] JumpProblemLibrary v1.1.0 - [ccbc3e58] JumpProcesses v9.15.0 -⌅ [961ee093] ModelingToolkit v9.80.2 - [1dea7af3] OrdinaryDiffEq v6.98.0 - [86206cdf] PiecewiseDeterministicMarkovProcesses v0.0.10 - [91a5bcdd] Plots v1.40.13 +Status `/julia/github-runners/amdci1-1/_work/SciMLBenchmarks.jl/SciMLBenchmarks.jl/benchmarks/Jumps/Project.toml` + [6e4b80f9] BenchmarkTools v1.8.0 + [479239e8] Catalyst v16.4.0 + [8f4d0f93] Conda v1.10.3 + [a93c6f00] DataFrames v1.8.2 + [0c46a032] DifferentialEquations v8.1.1 + [31c24e10] Distributions v0.25.131 + [86223c79] Graphs v1.14.0 + [faf0f6d7] JumpProblemLibrary v2.0.3 + [ccbc3e58] JumpProcesses v9.30.1 + [961ee093] ModelingToolkit v11.40.0 + [1dea7af3] OrdinaryDiffEq v7.8.1 + [86206cdf] PiecewiseDeterministicMarkovProcesses v0.0.12 + [91a5bcdd] Plots v1.41.7 [438e738f] PyCall v1.96.4 - [b4db0fb7] ReactionNetworkImporters v0.16.1 - [31c91b34] SciMLBenchmarks v0.1.3 - [860ef19b] StableRNGs v1.0.3 - [f3b207a7] StatsPlots v0.15.7 - [c3572dad] Sundials v4.28.0 + [b4db0fb7] ReactionNetworkImporters v1.5.0 +⌃ [31c91b34] SciMLBenchmarks v0.1.3 + [860ef19b] StableRNGs v1.0.4 + [f3b207a7] StatsPlots v0.15.8 + [c3572dad] Sundials v6.6.0 + [2efcf032] SymbolicIndexingInterface v0.3.55 [37e2e46d] LinearAlgebra [9a3f8284] Random [10745b16] Statistics v1.10.0 -Info Packages marked with ⌅ have new versions available but compatibility constraints restrict them from upgrading. To see why use `status --outdated` +Info Packages marked with ⌃ have new versions available and may be upgradable. ``` And the full manifest: ``` -Status `/cache/build/exclusive-amdci1-0/julialang/scimlbenchmarks-dot-jl/benchmarks/Jumps/Manifest.toml` - [47edcb42] ADTypes v1.14.0 +Status `/julia/github-runners/amdci1-1/_work/SciMLBenchmarks.jl/SciMLBenchmarks.jl/benchmarks/Jumps/Manifest.toml` + [47edcb42] ADTypes v1.24.0 + [14f7f29c] AMD v0.5.3 [621f4979] AbstractFFTs v1.5.0 + [6e696c72] AbstractPlutoDingetjes v1.4.0 [1520ce14] AbstractTrees v0.4.5 - [7d9f7c33] Accessors v0.1.42 - [79e6a3ab] Adapt v4.3.0 + [7d9f7c33] Accessors v0.1.45 + [79e6a3ab] Adapt v4.7.0 [66dad0bd] AliasTables v1.1.3 - [a95523ee] AlmostBlockDiagonals v0.1.10 [ec485272] ArnoldiMethod v0.4.0 [7d9fca2a] Arpack v0.5.4 - [4fba245c] ArrayInterface v7.19.0 - [4c555306] ArrayLayouts v1.11.1 + [4fba245c] ArrayInterface v7.30.0 + [4c555306] ArrayLayouts v1.12.2 [13072b0f] AxisAlgorithms v1.1.0 - [aae01518] BandedMatrices v1.9.4 - 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Let's plot the dimer concentration as a function of time using each of the different stochastic simulation algorithms. ```julia -tf = 12. +tf = 12.0 rng = StableRNG(53124) algs = [NRM(), CCNRM(), DirectCR(), RSSACR()] -egfr_net = loadrxnetwork(BNGNetwork(), joinpath(@__DIR__, "Data/egfr_net.net")); -dprob = DiscreteProblem(complete(egfr_net.rn), egfr_net.u0, (0., tf), egfr_net.p) -dprob = remake(dprob,u0=Int64.(dprob.u0)) +egfr_net = complete(loadrxnetwork(BNGNetwork(), joinpath(@__DIR__, "Data/egfr_net.net"))) +egfr_u0 = Catalyst.get_u0_map(egfr_net) +egfr_parameters = Catalyst.get_parameter_map(egfr_net) -plt = plot(title="Dimer concentrations") +plt = plot(title = "Dimer concentrations") for alg in algs - jprob = JumpProblem(complete(egfr_net.rn), dprob, alg) + jprob = JumpProblem( + egfr_net, egfr_u0, (0.0, tf), egfr_parameters; + aggregator = alg, u0_eltype = Int64 + ) sol = solve(jprob, SSAStepper(), saveat = tf/200) - plot!(plt, sol, idxs = :Dimers, label="$alg") + plot!(plt, sol, idxs = :Dimers, label = "$alg") end plot!(plt) ``` ``` +Scanning blocks...done Parsing parameters...done Creating parameters...done Parsing species...done -Creating species...done -Creating species and parameters for evaluating expressions...done -Parsing and adding reactions...done +Creating variables...done +Setting up expression bindings...done Parsing groups...done +Parsing functions...done +Parsing and adding reactions...done ``` ![](figures/EGFR_Benchmark_2_1.png) + These results seem pretty reasonable - it seems like we're getting the same dimer concentration curve for each method. - # Model Benchmark -We define a function to benchmark the model and then plot the results in a benchmark. The goal is to see how the SSAs perform relative to each other. + +We define a function to benchmark the model and then plot the results in a benchmark. The goal is to see how the SSAs perform relative to each other. ```julia function benchmark_and_bar_plot(model, end_time, algs) times = Vector{Float64}() - alg_names = ["$s"[15:end-2] for s in algs] + alg_names = ["$s"[15:(end - 2)] for s in algs] + u0 = Catalyst.get_u0_map(model) + parameters = Catalyst.get_parameter_map(model) benchmarks = Vector{BenchmarkTools.Trial}(undef, length(algs)) for (i, alg) in enumerate(algs) alg_name = alg_names[i] println("Benchmarking $alg_name") - dprob = DiscreteProblem(complete(model.rn), model.u0, (0., end_time), model.p) - dprob = remake(dprob,u0 = Int64.(dprob.u0)) - jprob = JumpProblem(complete(model.rn), dprob, alg; rng, save_positions = (false, false)) + jprob = JumpProblem( + model, u0, (0.0, end_time), parameters; + aggregator = alg, rng, save_positions = (false, false), u0_eltype = Int64 + ) - b = @benchmarkable solve($jprob; saveat = $end_time) samples = 5 seconds = 7200 + b = @benchmarkable solve($jprob; saveat = $end_time) samples=5 seconds=7200 bm = run(b) push!(times, median(bm).time/1e9) end - bar(alg_names, times, xlabel = "Algorithm", ylabel = "Average Time (s)", title = "SSA Runtime for EGFR network", legend = false) + bar(alg_names, times, xlabel = "Algorithm", ylabel = "Average Time (s)", + title = "SSA Runtime for EGFR network", legend = false) end ``` @@ -81,9 +92,10 @@ benchmark_and_bar_plot (generic function with 1 method) -Now we benchmark the EGFR network on the four algorithms and plot the results. +Now we benchmark the EGFR network on the four algorithms and plot the results. + ```julia -tf = 12. +tf = 12.0 rng = StableRNG(53124) algs = [NRM(), CCNRM(), DirectCR(), RSSACR()] @@ -104,17 +116,15 @@ Benchmarking RSSACR ### References + [^1]: Blinov ML, Faeder JR, Goldstein B, Hlavacek WS. A network model of early events in epidermal growth factor receptor signaling that accounts for combinatorial complexity. [^2]: Loman TE, Ma Y, Ilin V, et al. Catalyst: Fast and flexible modeling of reaction networks. - - ## Appendix These benchmarks are a part of the SciMLBenchmarks.jl repository, found at: [https://github.com/SciML/SciMLBenchmarks.jl](https://github.com/SciML/SciMLBenchmarks.jl). For more information on high-performance scientific machine learning, check out the SciML Open Source Software Organization [https://sciml.ai](https://sciml.ai). To locally run this benchmark, do the following commands: - ``` using SciMLBenchmarks SciMLBenchmarks.weave_file("benchmarks/Jumps","EGFR_Benchmark.jmd") @@ -123,8 +133,8 @@ SciMLBenchmarks.weave_file("benchmarks/Jumps","EGFR_Benchmark.jmd") Computer Information: ``` -Julia Version 1.10.9 -Commit 5595d20a287 (2025-03-10 12:51 UTC) +Julia Version 1.10.12 +Commit d93beab124c (2026-08-15 10:29 UTC) Build Info: Official https://julialang.org/ release Platform Info: @@ -133,432 +143,372 @@ Platform Info: WORD_SIZE: 64 LIBM: libopenlibm LLVM: libLLVM-15.0.7 (ORCJIT, znver2) -Threads: 1 default, 0 interactive, 1 GC (on 128 virtual cores) +Threads: 128 default, 0 interactive, 64 GC (on 128 virtual cores) Environment: - JULIA_CPU_THREADS = 128 - JULIA_DEPOT_PATH = /cache/julia-buildkite-plugin/depots/5b300254-1738-4989-ae0a-f4d2d937f953 + JULIA_NUM_THREADS = auto ``` Package Information: ``` -Status `/cache/build/exclusive-amdci1-0/julialang/scimlbenchmarks-dot-jl/benchmarks/Jumps/Project.toml` - [6e4b80f9] BenchmarkTools v1.6.0 - [479239e8] Catalyst v15.0.8 - [8f4d0f93] Conda v1.10.2 - [a93c6f00] DataFrames v1.7.0 - [0c46a032] DifferentialEquations v7.16.1 - [31c24e10] Distributions v0.25.120 - [86223c79] Graphs v1.12.1 - [faf0f6d7] JumpProblemLibrary v1.1.0 - [ccbc3e58] JumpProcesses v9.15.0 -⌅ [961ee093] ModelingToolkit v9.80.2 - [1dea7af3] OrdinaryDiffEq v6.98.0 - [86206cdf] PiecewiseDeterministicMarkovProcesses v0.0.10 - [91a5bcdd] Plots v1.40.13 +Status `/julia/github-runners/amdci1-1/_work/SciMLBenchmarks.jl/SciMLBenchmarks.jl/benchmarks/Jumps/Project.toml` + [6e4b80f9] BenchmarkTools v1.8.0 + [479239e8] Catalyst v16.4.0 + [8f4d0f93] Conda v1.10.3 + [a93c6f00] DataFrames v1.8.2 + [0c46a032] DifferentialEquations v8.1.1 + [31c24e10] Distributions v0.25.131 + [86223c79] Graphs v1.14.0 + [faf0f6d7] JumpProblemLibrary v2.0.3 + [ccbc3e58] JumpProcesses v9.30.1 + [961ee093] ModelingToolkit v11.40.0 + [1dea7af3] OrdinaryDiffEq v7.8.1 + [86206cdf] PiecewiseDeterministicMarkovProcesses v0.0.12 + [91a5bcdd] Plots v1.41.7 [438e738f] PyCall v1.96.4 - [b4db0fb7] ReactionNetworkImporters v0.16.1 - [31c91b34] SciMLBenchmarks v0.1.3 - [860ef19b] StableRNGs v1.0.3 - [f3b207a7] StatsPlots v0.15.7 - [c3572dad] Sundials v4.28.0 + [b4db0fb7] ReactionNetworkImporters v1.5.0 +⌃ [31c91b34] SciMLBenchmarks v0.1.3 + [860ef19b] StableRNGs v1.0.4 + [f3b207a7] StatsPlots v0.15.8 + [c3572dad] Sundials v6.6.0 + [2efcf032] SymbolicIndexingInterface v0.3.55 [37e2e46d] LinearAlgebra [9a3f8284] Random [10745b16] Statistics v1.10.0 -Info Packages marked with ⌅ have new versions available but compatibility constraints restrict them from upgrading. To see why use `status --outdated` +Info Packages marked with ⌃ have new versions available and may be upgradable. ``` And the full manifest: ``` -Status `/cache/build/exclusive-amdci1-0/julialang/scimlbenchmarks-dot-jl/benchmarks/Jumps/Manifest.toml` - [47edcb42] ADTypes v1.14.0 +Status `/julia/github-runners/amdci1-1/_work/SciMLBenchmarks.jl/SciMLBenchmarks.jl/benchmarks/Jumps/Manifest.toml` + [47edcb42] ADTypes v1.24.0 + [14f7f29c] AMD v0.5.3 [621f4979] AbstractFFTs v1.5.0 + [6e696c72] AbstractPlutoDingetjes v1.4.0 [1520ce14] AbstractTrees v0.4.5 - [7d9f7c33] Accessors v0.1.42 - [79e6a3ab] Adapt v4.3.0 + [7d9f7c33] Accessors v0.1.45 + [79e6a3ab] Adapt v4.7.0 [66dad0bd] AliasTables v1.1.3 - [a95523ee] AlmostBlockDiagonals v0.1.10 [ec485272] ArnoldiMethod v0.4.0 [7d9fca2a] Arpack v0.5.4 - [4fba245c] ArrayInterface v7.19.0 - [4c555306] ArrayLayouts v1.11.1 + [4fba245c] ArrayInterface v7.30.0 + [4c555306] ArrayLayouts v1.12.2 [13072b0f] AxisAlgorithms v1.1.0 - [aae01518] BandedMatrices v1.9.4 - 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2)] for leg in methods] +tf = 10.0 * jprob.tstop varlegs = ["A_P" "A_bound_P" "A_unbound_P" "RLA_P"] @variables t S7(t) S8(t) S9(t) varsyms = [ - [S7,S8,S9], + [S7, S8, S9], [S9], - [S7,S8], + [S7, S8], [S7] ] varidxs = [] for vars in varsyms - push!(varidxs, [findfirst(isequal(sym),unknowns(rn)) for sym in vars]) + push!(varidxs, [findfirst(isequal(sym), unknowns(rn)) for sym in vars]) end ``` ```julia p = [] -for (i,method) in enumerate(methods) - jump_prob = JumpProblem(rn, prob, method, save_positions=(false, false)) - sol = solve(jump_prob, SSAStepper(), saveat=tf/1000.) +for (i, method) in enumerate(methods) + jump_prob = JumpProblem( + rn, jprob.u0, (0.0, tf), jprob.rates; + aggregator = method, save_positions = (false, false) + ) + sol = solve(jump_prob, SSAStepper(), saveat = tf/1000.0) solv = zeros(1001, 4) - for (i,varidx) in enumerate(varidxs) - solv[:,i] = sum(sol[varidx,:], dims=1) + for (i, varidx) in enumerate(varidxs) + solv[:, i] = sum(sol[varidx, :], dims = 1) end if i < length(methods) - push!(p, plot(sol.t, solv, title=shortlabels[i], legend=false, format=fmt)) + push!(p, plot(sol.t, solv, title = shortlabels[i], legend = false, format = fmt)) else - push!(p, plot(sol.t, solv, title=shortlabels[i], legend=false, format=fmt)) + push!(p, plot(sol.t, solv, title = shortlabels[i], legend = false, format = fmt)) end end -push!(p, plot((1:4)', framestyle = :none, legend=:inside, labels=varlegs)) -plot(p..., layout=(6,2), format=fmt) +push!(p, plot((1:4)', framestyle = :none, legend = :inside, labels = varlegs)) +plot(p..., layout = (6, 2), format = fmt) ``` ![](figures/Mendes_multistate_example_4_1.png) @@ -117,7 +122,10 @@ run_benchmark! (generic function with 1 method) nsims = 100 benchmarks = Vector{Vector{Float64}}() for method in methods - jump_prob = JumpProblem(rn, prob, method, save_positions=(false, false)) + jump_prob = JumpProblem( + rn, jprob.u0, (0.0, tf), jprob.rates; + aggregator = method, save_positions = (false, false) + ) stepper = SSAStepper() time = Vector{Float64}(undef, nsims) run_benchmark!(time, jump_prob, stepper) @@ -127,9 +135,9 @@ end ```julia -medtimes = Vector{Float64}(undef,length(methods)) -stdtimes = Vector{Float64}(undef,length(methods)) -avgtimes = Vector{Float64}(undef,length(methods)) +medtimes = Vector{Float64}(undef, length(methods)) +stdtimes = Vector{Float64}(undef, length(methods)) +avgtimes = Vector{Float64}(undef, length(methods)) for i in 1:length(methods) medtimes[i] = median(benchmarks[i]) avgtimes[i] = mean(benchmarks[i]) @@ -137,12 +145,14 @@ for i in 1:length(methods) end using DataFrames -df = DataFrame(names=shortlabels, medtimes=medtimes, relmedtimes=(medtimes/medtimes[1]), - avgtimes=avgtimes, std=stdtimes, cv=stdtimes./avgtimes) +df = DataFrame( + names = shortlabels, medtimes = medtimes, relmedtimes = (medtimes/medtimes[1]), + avgtimes = avgtimes, std = stdtimes, cv = stdtimes ./ avgtimes) -sa = [text(string(round(mt,digits=3),"s"),:center,12) for mt in df.medtimes] -bar(df.names,df.relmedtimes,legend=:false, fmt=fmt) -scatter!(df.names, .05 .+ df.relmedtimes, markeralpha=0, series_annotations=sa, fmt=fmt) +sa = [text(string(round(mt, digits = 3), "s"), :center, 12) for mt in df.medtimes] +bar(df.names, df.relmedtimes, legend = :false, fmt = fmt) +scatter!( + df.names, 0.05 .+ df.relmedtimes, markeralpha = 0, series_annotations = sa, fmt = fmt) ylabel!("median relative to Direct") title!("Multistate Model") ``` @@ -155,7 +165,6 @@ title!("Multistate Model") These benchmarks are a part of the SciMLBenchmarks.jl repository, found at: [https://github.com/SciML/SciMLBenchmarks.jl](https://github.com/SciML/SciMLBenchmarks.jl). For more information on high-performance scientific machine learning, check out the SciML Open Source Software Organization [https://sciml.ai](https://sciml.ai). To locally run this benchmark, do the following commands: - ``` using SciMLBenchmarks SciMLBenchmarks.weave_file("benchmarks/Jumps","Mendes_multistate_example.jmd") @@ -164,8 +173,8 @@ SciMLBenchmarks.weave_file("benchmarks/Jumps","Mendes_multistate_example.jmd") Computer Information: ``` -Julia Version 1.10.9 -Commit 5595d20a287 (2025-03-10 12:51 UTC) +Julia Version 1.10.12 +Commit d93beab124c (2026-08-15 10:29 UTC) Build Info: Official https://julialang.org/ release Platform Info: @@ -174,432 +183,372 @@ Platform Info: WORD_SIZE: 64 LIBM: libopenlibm LLVM: libLLVM-15.0.7 (ORCJIT, znver2) -Threads: 1 default, 0 interactive, 1 GC (on 128 virtual cores) +Threads: 128 default, 0 interactive, 64 GC (on 128 virtual cores) Environment: - JULIA_CPU_THREADS = 128 - JULIA_DEPOT_PATH = /cache/julia-buildkite-plugin/depots/5b300254-1738-4989-ae0a-f4d2d937f953 + JULIA_NUM_THREADS = auto ``` Package Information: ``` -Status `/cache/build/exclusive-amdci1-0/julialang/scimlbenchmarks-dot-jl/benchmarks/Jumps/Project.toml` - [6e4b80f9] BenchmarkTools v1.6.0 - [479239e8] Catalyst v15.0.8 - [8f4d0f93] Conda v1.10.2 - [a93c6f00] DataFrames v1.7.0 - [0c46a032] DifferentialEquations v7.16.1 - [31c24e10] Distributions v0.25.120 - [86223c79] Graphs v1.12.1 - [faf0f6d7] JumpProblemLibrary v1.1.0 - [ccbc3e58] JumpProcesses v9.15.0 -⌅ [961ee093] ModelingToolkit v9.80.2 - [1dea7af3] OrdinaryDiffEq v6.98.0 - [86206cdf] PiecewiseDeterministicMarkovProcesses v0.0.10 - [91a5bcdd] Plots v1.40.13 +Status `/julia/github-runners/amdci1-1/_work/SciMLBenchmarks.jl/SciMLBenchmarks.jl/benchmarks/Jumps/Project.toml` + [6e4b80f9] BenchmarkTools v1.8.0 + [479239e8] Catalyst v16.4.0 + [8f4d0f93] Conda v1.10.3 + [a93c6f00] DataFrames v1.8.2 + [0c46a032] DifferentialEquations v8.1.1 + [31c24e10] Distributions v0.25.131 + [86223c79] Graphs v1.14.0 + [faf0f6d7] JumpProblemLibrary v2.0.3 + [ccbc3e58] JumpProcesses v9.30.1 + [961ee093] ModelingToolkit v11.40.0 + [1dea7af3] OrdinaryDiffEq v7.8.1 + [86206cdf] PiecewiseDeterministicMarkovProcesses v0.0.12 + [91a5bcdd] Plots v1.41.7 [438e738f] PyCall v1.96.4 - [b4db0fb7] ReactionNetworkImporters v0.16.1 - [31c91b34] SciMLBenchmarks v0.1.3 - [860ef19b] StableRNGs v1.0.3 - [f3b207a7] StatsPlots v0.15.7 - [c3572dad] Sundials v4.28.0 + [b4db0fb7] ReactionNetworkImporters v1.5.0 +⌃ [31c91b34] SciMLBenchmarks v0.1.3 + [860ef19b] StableRNGs v1.0.4 + [f3b207a7] StatsPlots v0.15.8 + [c3572dad] Sundials v6.6.0 + [2efcf032] SymbolicIndexingInterface v0.3.55 [37e2e46d] LinearAlgebra [9a3f8284] Random [10745b16] Statistics v1.10.0 -Info Packages marked with ⌅ have new versions available but compatibility constraints restrict them from upgrading. To see why use `status --outdated` +Info Packages marked with ⌃ have new versions available and may be upgradable. ``` And the full manifest: ``` -Status `/cache/build/exclusive-amdci1-0/julialang/scimlbenchmarks-dot-jl/benchmarks/Jumps/Manifest.toml` - [47edcb42] ADTypes v1.14.0 +Status `/julia/github-runners/amdci1-1/_work/SciMLBenchmarks.jl/SciMLBenchmarks.jl/benchmarks/Jumps/Manifest.toml` + [47edcb42] ADTypes v1.24.0 + [14f7f29c] AMD v0.5.3 [621f4979] AbstractFFTs v1.5.0 + [6e696c72] AbstractPlutoDingetjes v1.4.0 [1520ce14] AbstractTrees v0.4.5 - [7d9f7c33] Accessors v0.1.42 - [79e6a3ab] Adapt v4.3.0 + [7d9f7c33] Accessors v0.1.45 + [79e6a3ab] Adapt v4.7.0 [66dad0bd] AliasTables v1.1.3 - [a95523ee] AlmostBlockDiagonals v0.1.10 [ec485272] ArnoldiMethod v0.4.0 [7d9fca2a] Arpack v0.5.4 - [4fba245c] ArrayInterface v7.19.0 - [4c555306] ArrayLayouts v1.11.1 + [4fba245c] ArrayInterface v7.30.0 + [4c555306] ArrayLayouts v1.12.2 [13072b0f] AxisAlgorithms v1.1.0 - [aae01518] BandedMatrices v1.9.4 - 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- - - -# Model and example solutions - -Let a graph with ``V`` nodes, then the multivariate Hawkes process is characterized by ``V`` point processes such that the conditional intensity rate of node ``i`` connected to a set of nodes ``E_i`` in the graph is given by: -```math - \lambda_i^\ast (t) = \lambda + \sum_{j \in E_i} \sum_{t_{n_j} < t} \alpha \exp \left[-\beta (t - t_{n_j}) \right] -``` -This process is known as self-exciting, because the occurrence of an event ``j`` at ``t_{n_j}`` will increase the conditional intensity of all the processes connected to it by ``\alpha``. The excited intensity then decreases at a rate proportional to ``\beta``. - -The conditional intensity of this process has a recursive formulation which can significantly speed the simulation. The recursive formulation for the univariate case is derived in Laub et al. [2]. We derive the compound case here. Let ``t_{N_i} = \max \{ t_{n_j} < t \mid j \in E_i \}`` and -```math -\begin{split} - \phi_i^\ast (t) - &= \sum_{j \in E_i} \sum_{t_{n_j} < t} \alpha \exp \left[-\beta (t - t_{N_i} + t_{N_i} - t_{n_j}) \right] \\ - &= \exp \left[ -\beta (t - t_{N_i}) \right] \sum_{j \in E_i} \sum_{t_{n_j} \leq t_{N_i}} \alpha \exp \left[-\beta (t_{N_i} - t_{n_j}) \right] \\ - &= \exp \left[ -\beta (t - t_{N_i}) \right] \left( \alpha + \phi^\ast (t_{N_i}) \right) -\end{split} -``` -Then the conditional intensity can be re-written in terms of ``\phi_i^\ast (t_{N_i})`` -```math - \lambda_i^\ast (t) = \lambda + \phi_i^\ast (t) = \lambda + \exp \left[ -\beta (t - t_{N_i}) \right] \left( \alpha + \phi_i^\ast (t_{N_i}) \right) -``` - -In Julia, we define a factory for the conditional intensity ``\lambda_i`` which returns the brute-force or recursive versions of the intensity given node ``i`` and network ``g``. - -```julia -function hawkes_rate(i::Int, g; use_recursion = false) - - @inline @inbounds function rate_recursion(u, p, t) - λ, α, β, h, urate, ϕ = p - urate[i] = λ + exp(-β*(t - h[i]))*ϕ[i] - return urate[i] - end - - @inline @inbounds function rate_brute(u, p, t) - λ, α, β, h, urate = p - x = zero(typeof(t)) - for j in g[i] - for _t in reverse(h[j]) - ϕij = α * exp(-β * (t - _t)) - if ϕij ≈ 0 - break - end - x += ϕij - end - end - urate[i] = λ + x - return urate[i] - end - - if use_recursion - return rate_recursion - else - return rate_brute - end - -end -``` - -``` -hawkes_rate (generic function with 1 method) -``` - - - - - -Given the rate factory, we can create a jump factory which will create all the jumps in our model. - -```julia -function hawkes_jump(i::Int, g; use_recursion = false) - rate = hawkes_rate(i, g; use_recursion) - urate = rate - @inbounds rateinterval(u, p, t) = p[5][i] == p[1] ? typemax(t) : 2 / p[5][i] - @inbounds lrate(u, p, t) = p[1] - @inbounds function affect_recursion!(integrator) - λ, α, β, h, _, ϕ = integrator.p - for j in g[i] - ϕ[j] *= exp(-β*(integrator.t - h[j])) - ϕ[j] += α - h[j] = integrator.t - end - integrator.u[i] += 1 - end - @inbounds function affect_brute!(integrator) - push!(integrator.p[4][i], integrator.t) - integrator.u[i] += 1 - end - return VariableRateJump( - rate, - use_recursion ? affect_recursion! : affect_brute!; - lrate, - urate, - rateinterval, - ) -end - -function hawkes_jump(u, g; use_recursion = false) - return [hawkes_jump(i, g; use_recursion) for i = 1:length(u)] -end -``` - -``` -hawkes_jump (generic function with 2 methods) -``` - - - - - -We can then create a factory for Multivariate Hawkes `JumpProblem`s. We can define two types of `JumpProblem`s depending on the aggregator. The `Direct()` aggregator expects an `ODEProblem` since it cannot handle the `SSAStepper` with `VariableRateJump`s. - - -```julia -function f!(du, u, p, t) - du .= 0 - nothing -end - -function hawkes_problem( - p, - agg; - u = [0.0], - tspan = (0.0, 50.0), - save_positions = (false, true), - g = [[1]], - use_recursion = false, -) - oprob = ODEProblem(f!, u, tspan, p) - jumps = hawkes_jump(u, g; use_recursion) - jprob = JumpProblem(oprob, agg, jumps...; save_positions = save_positions) - return jprob -end -``` - -``` -hawkes_problem (generic function with 1 method) -``` - - - - - -The `Coevolve()` aggregator knows how to handle the `SSAStepper`, so it accepts a `DiscreteProblem`. - -```julia -function hawkes_problem( - p, - agg::Coevolve; - u = [0.0], - tspan = (0.0, 50.0), - save_positions = (false, true), - g = [[1]], - use_recursion = false, -) - dprob = DiscreteProblem(u, tspan, p) - jumps = hawkes_jump(u, g; use_recursion) - jprob = - JumpProblem(dprob, agg, jumps...; dep_graph = g, save_positions = save_positions) - return jprob -end -``` - -``` -hawkes_problem (generic function with 2 methods) -``` - - - - - -Lets solve the problems defined so far. We sample a random graph sampled from the Erdős-Rényi model. This model assumes that the probability of an edge between two nodes is independent of other edges, which we fix at ``0.2``. For illustration purposes, we fix ``V = 10``. - -```julia -V = 10 -G = erdos_renyi(V, 0.2, seed = 9103) -g = [neighbors(G, i) for i = 1:nv(G)] -``` - -``` -10-element Vector{Vector{Int64}}: - [4, 7] - [8, 9] - [4, 5] - [1, 3] - [3] - [] - [1, 8, 9] - [2, 7] - [2, 7, 10] - [9] -``` - - - - - -We fix the Hawkes parameters at ``\lambda = 0.5 , \alpha = 0.1 , \beta = 2.0`` which ensures the process does not explode. - -```julia -tspan = (0.0, 50.0) -u = [0.0 for i = 1:nv(G)] -p = (0.5, 0.1, 2.0) -``` - -``` -(0.5, 0.1, 2.0) -``` - - - - - -Now, we instantiate the problems, find their solutions and plot the results. - - -```julia -algorithms = Tuple{Any, Any, Bool, String}[ - (Direct(), Tsit5(), false, "Direct (brute-force)"), - (Coevolve(), SSAStepper(), false, "Coevolve (brute-force)"), - (Direct(), Tsit5(), true, "Direct (recursive)"), - (Coevolve(), SSAStepper(), true, "Coevolve (recursive)"), -] - -let fig = [] - for (i, (algo, stepper, use_recursion, label)) in enumerate(algorithms) - @info label - if use_recursion - h = zeros(eltype(tspan), nv(G)) - urate = zeros(eltype(tspan), nv(G)) - ϕ = zeros(eltype(tspan), nv(G)) - _p = (p[1], p[2], p[3], h, ϕ, urate) - else - h = [eltype(tspan)[] for _ = 1:nv(G)] - urate = zeros(eltype(tspan), nv(G)) - _p = (p[1], p[2], p[3], h, urate) - end - jump_prob = hawkes_problem(_p, algo; u, tspan, g, use_recursion) - sol = solve(jump_prob, stepper) - push!(fig, plot(sol.t, sol[1:V, :]', title=label, legend=false, format=fmt)) - end - fig = plot(fig..., layout=(2,2), format=fmt, size=(width_px, 2*height_px/2)) -end -``` - -![](figures/MultivariateHawkes_8_1.png) - - - -## Alternative libraries - -We benchmark `JumpProcesses.jl` against `PiecewiseDeterministicMarkovProcesses.jl` and Python `Tick` library. - -In order to compare with the `PiecewiseDeterministicMarkovProcesses.jl`, we need to reformulate our jump problem as a Piecewise Deterministic Markov Process (PDMP). In this setting, we have two options. - -The simple version only requires the conditional intensity. Like above, we define a brute-force and recursive approach. Following the library's specification we define the following functions. - -```julia -function hawkes_rate_simple_recursion(rate, xc, xd, p, t, issum::Bool) - λ, _, β, h, ϕ, g = p - for i in 1:length(g) - rate[i] = λ + exp(-β * (t - h[i])) * ϕ[i] - end - if issum - return sum(rate) - end - return 0.0 -end - -function hawkes_rate_simple_brute(rate, xc, xd, p, t, issum::Bool) - λ, α, β, h, g = p - for i in 1:length(g) - x = zero(typeof(t)) - for j in g[i] - for _t in reverse(h[j]) - ϕij = α * exp(-β * (t - _t)) - if ϕij ≈ 0 - break - end - x += ϕij - end - end - rate[i] = λ + x - end - if issum - return sum(rate) - end - return 0.0 -end - -function hawkes_affect_simple_recursion!(xc, xd, p, t, i::Int64) - _, α, β, h, ϕ, g = p - for j in g[i] - ϕ[j] *= exp(-β * (t - h[j])) - ϕ[j] += α - h[j] = t - end -end - -function hawkes_affect_simple_brute!(xc, xd, p, t, i::Int64) - push!(p[4][i], t) -end -``` - -``` -hawkes_affect_simple_brute! (generic function with 1 method) -``` - - - - - -Since this is a library for PDMP, we also need to define the ODE problem. In the simple version, we simply set it to zero. - -```julia -function hawkes_drate_simple(dxc, xc, xd, p, t) - dxc .= 0 -end -``` - -``` -hawkes_drate_simple (generic function with 1 method) -``` - - - - - -Next, we create a factory for the Multivariate Hawkes `PDMPCHVSimple` problem. - -```julia -import LinearAlgebra: I -using PiecewiseDeterministicMarkovProcesses -const PDMP = PiecewiseDeterministicMarkovProcesses - -struct PDMPCHVSimple end - -function hawkes_problem(p, - agg::PDMPCHVSimple; - u = [0.0], - tspan = (0.0, 50.0), - save_positions = (false, true), - g = [[1]], - use_recursion = true) - xd0 = Array{Int}(u) - xc0 = copy(u) - nu = one(eltype(xd0)) * I(length(xd0)) - if use_recursion - jprob = PDMPProblem(hawkes_drate_simple, hawkes_rate_simple_recursion, - hawkes_affect_simple_recursion!, nu, xc0, xd0, p, tspan) - else - jprob = PDMPProblem(hawkes_drate_simple, hawkes_rate_simple_brute, - hawkes_affect_simple_brute!, nu, xc0, xd0, p, tspan) - end - return jprob -end - -push!(algorithms, (PDMPCHVSimple(), CHV(Tsit5()), false, "PDMPCHVSimple (brute-force)")); -push!(algorithms, (PDMPCHVSimple(), CHV(Tsit5()), true, "PDMPCHVSimple (recursive)")); -``` - - - - -The full version requires that we describe how the conditional intensity changes with time which we derive below: -```math -\begin{split} - \frac{d \lambda_i^\ast (t)}{d t} - &= -\beta \sum_{j \in E_i} \sum_{t_{n_j} < t} \alpha \exp \left[-\beta (t - t_{n_j}) \right] \\ - &= -\beta \left( \lambda_i^\ast (t) - \lambda \right) -\end{split} -``` - -```julia -function hawkes_drate_full(dxc, xc, xd, p, t) - λ, α, β, _, _, g = p - for i = 1:length(g) - dxc[i] = -β * (xc[i] - λ) - end -end -``` - -``` -hawkes_drate_full (generic function with 1 method) -``` - - - - - -Next, we need to define the intensity rate and the jumps according to library's specification. - -```julia -function hawkes_rate_full(rate, xc, xd, p, t, issum::Bool) - λ, α, β, _, _, g = p - if issum - return sum(@view(xc[1:length(g)])) - end - rate[1:length(g)] .= @view xc[1:length(g)] - return 0.0 -end - -function hawkes_affect_full!(xc, xd, p, t, i::Int64) - λ, α, β, _, _, g = p - for j in g[i] - xc[i] += α - end -end -``` - -``` -hawkes_affect_full! (generic function with 1 method) -``` - - - - - -Finally, we create a factory for the Multivariate Hawkes `PDMPCHVFull` problem. - -```julia -struct PDMPCHVFull end - -function hawkes_problem( - p, - agg::PDMPCHVFull; - u = [0.0], - tspan = (0.0, 50.0), - save_positions = (false, true), - g = [[1]], - use_recursion = true, -) - xd0 = Array{Int}(u) - xc0 = [p[1] for i = 1:length(u)] - nu = one(eltype(xd0)) * I(length(xd0)) - jprob = PDMPProblem(hawkes_drate_full, hawkes_rate_full, hawkes_affect_full!, nu, xc0, xd0, p, tspan) - return jprob -end - -push!(algorithms, (PDMPCHVFull(), CHV(Tsit5()), true, "PDMPCHVFull")); -``` - - - - -The Python `Tick` library can be accessed with the `PyCall.jl`. We install the required Python dependencies with `Conda.jl` and define a factory for the Multivariate Hawkes `PyTick` problem. - -```julia -const BENCHMARK_PYTHON::Bool = tryparse(Bool, get(ENV, "SCIMLBENCHMARK_PYTHON", "true")) -const REBUILD_PYCALL::Bool = tryparse(Bool, get(ENV, "SCIMLBENCHMARK_REBUILD_PYCALL", "true")) - -struct PyTick end - -if BENCHMARK_PYTHON - if REBUILD_PYCALL - using Pkg, Conda - - # PyCall only works with Conda.ROOTENV - # tick requires python=3.8 - Conda.add("python=3.8", Conda.ROOTENV) - Conda.add("numpy", Conda.ROOTENV) - Conda.pip_interop(true, Conda.ROOTENV) - Conda.pip("install", "tick", Conda.ROOTENV) - - # rebuild PyCall to ensure it links to the python provided by Conda.jl - ENV["PYTHON"] = "" - Pkg.build("PyCall") - end - - ENV["PYTHON"] = "" - using PyCall - @info "PyCall" PyCall.libpython PyCall.pyversion PyCall.conda - - function hawkes_problem( - p, - agg::PyTick; - u = [0.0], - tspan = (0.0, 50.0), - save_positions = (false, true), - g = [[1]], - use_recursion = true, - ) - λ, α, β = p - SimuHawkesSumExpKernels = pyimport("tick.hawkes")[:SimuHawkesSumExpKernels] - jprob = SimuHawkesSumExpKernels( - baseline = fill(λ, length(u)), - adjacency = [i in j ? α / β : 0.0 for j in g, i = 1:length(u), u = 1:1], - decays = [β], - end_time = tspan[2], - verbose = false, - force_simulation = true, - ) - return jprob - end - - push!(algorithms, (PyTick(), nothing, true, "PyTick")); -end -``` - -``` -Channels: - - conda-forge -Platform: linux-64 -Collecting package metadata (repodata.json): ...working... done -Solving environment: ...working... failed -Error: failed process: Process(setenv(`/cache/julia-buildkite-plugin/depots -/5b300254-1738-4989-ae0a-f4d2d937f953/conda/3/x86_64/bin/conda install -q - -y python=3.8`,["BUILDKITE_UNBLOCKER_TEAMS=juliagpu-full-access:sciml-full-a -ccess", "DBUS_SESSION_BUS_ADDRESS=unix:path=/run/user/21581/bus", "BUILDKIT -E_PULL_REQUEST_REPO=", "BUILDKITE_SOURCE=webhook", "BUILDKITE_PLUGIN_COPPER 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-4/bin/../lib/julia:/cache/julia-buildkite-plugin/julia_installs/bin/linux/x -64/1.10/julia-1.10-latest-linux-x86_64/bin/../lib /cache/julia-buildkite-pl -ugin/depots/5b300254-1738-4989-ae0a-f4d2d937f953/artifacts/9d01ece285704bef -6238fd8461f65f1b63aeaece/bin/gksqt"]), ProcessExited(1)) [1] -``` - - - - - -Now, we instantiate the problems, find their solutions and plot the results. - -```julia -let fig = [] - for (i, (algo, stepper, use_recursion, label)) in enumerate(algorithms[5:end]) - @info label - if algo isa PyTick - _p = (p[1], p[2], p[3]) - jump_prob = hawkes_problem(_p, algo; u, tspan, g, use_recursion) - jump_prob.reset() - jump_prob.simulate() - t = tspan[1]:0.1:tspan[2] - N = [[sum(jumps .< _t) for _t in t] for jumps in jump_prob.timestamps] - push!(fig, plot(t, N, title=label, legend=false, format=fmt)) - elseif algo isa PDMPCHVSimple - if use_recursion - h = zeros(eltype(tspan), nv(G)) - ϕ = zeros(eltype(tspan), nv(G)) - _p = (p[1], p[2], p[3], h, ϕ, g) - else - h = [eltype(tspan)[] for _ in 1:nv(G)] - _p = (p[1], p[2], p[3], h, g) - end - jump_prob = hawkes_problem(_p, algo; u, tspan, g, use_recursion) - sol = solve(jump_prob, stepper) - push!(fig, plot(sol.time, sol.xd[1:V, :]', title=label, legend=false, format=fmt)) - elseif algo isa PDMPCHVFull - _p = (p[1], p[2], p[3], nothing, nothing, g) - jump_prob = hawkes_problem(_p, algo; u, tspan, g, use_recursion) - sol = solve(jump_prob, stepper) - push!(fig, plot(sol.time, sol.xd[1:V, :]', title=label, legend=false, format=fmt)) - end - end - fig = plot(fig..., layout=(2,2), format=fmt, size=(width_px, 2*height_px/2)) -end -``` - -![](figures/MultivariateHawkes_16_1.png) - - - -# Correctness: QQ-Plots - -We check that the algorithms produce correct simulation by inspecting their QQ-plots. Point process theory says that transforming the simulated points using the compensator should produce points whose inter-arrival duration is distributed according to the exponential distribution (see Section 7.4 [1]). - -The compensator of any point process is the integral of the conditional intensity ``\Lambda_i^\ast(t) = \int_0^t \lambda_i^\ast(u) du``. The compensator for the Multivariate Hawkes process is defined below. -```math - \Lambda_i^\ast(t) = \lambda t + \frac{\alpha}{\beta} \sum_{j \in E_i} \sum_{t_{n_j} < t} ( 1 - \exp \left[-\beta (t - t_{n_j}) \right]) -``` - -```julia -function hawkes_Λ(i::Int, g, p) - @inline @inbounds function Λ(t, h) - λ, α, β = p - x = λ * t - for j in g[i] - for _t in h[j] - if _t >= t - break - end - x += (α / β) * (1 - exp(-β * (t - _t))) - end - end - return x - end - return Λ -end - -function hawkes_Λ(g, p) - return [hawkes_Λ(i, g, p) for i = 1:length(g)] -end - -Λ = hawkes_Λ(g, p) -``` - -``` -10-element Vector{Main.var"##WeaveSandBox#225".var"#Λ#33"{Int64, Vector{Vec -tor{Int64}}, Tuple{Float64, Float64, Float64}}}: - (::Main.var"##WeaveSandBox#225".var"#Λ#33"{Int64, Vector{Vector{Int64}}, T -uple{Float64, Float64, Float64}}) (generic function with 1 method) - (::Main.var"##WeaveSandBox#225".var"#Λ#33"{Int64, Vector{Vector{Int64}}, T -uple{Float64, Float64, Float64}}) (generic function with 1 method) - (::Main.var"##WeaveSandBox#225".var"#Λ#33"{Int64, Vector{Vector{Int64}}, T -uple{Float64, Float64, Float64}}) (generic function with 1 method) - (::Main.var"##WeaveSandBox#225".var"#Λ#33"{Int64, Vector{Vector{Int64}}, T -uple{Float64, Float64, Float64}}) (generic function with 1 method) - (::Main.var"##WeaveSandBox#225".var"#Λ#33"{Int64, Vector{Vector{Int64}}, T -uple{Float64, Float64, Float64}}) (generic function with 1 method) - (::Main.var"##WeaveSandBox#225".var"#Λ#33"{Int64, Vector{Vector{Int64}}, T -uple{Float64, Float64, Float64}}) (generic function with 1 method) - (::Main.var"##WeaveSandBox#225".var"#Λ#33"{Int64, Vector{Vector{Int64}}, T -uple{Float64, Float64, Float64}}) (generic function with 1 method) - (::Main.var"##WeaveSandBox#225".var"#Λ#33"{Int64, Vector{Vector{Int64}}, T -uple{Float64, Float64, Float64}}) (generic function with 1 method) - (::Main.var"##WeaveSandBox#225".var"#Λ#33"{Int64, Vector{Vector{Int64}}, T -uple{Float64, Float64, Float64}}) (generic function with 1 method) - (::Main.var"##WeaveSandBox#225".var"#Λ#33"{Int64, Vector{Vector{Int64}}, T -uple{Float64, Float64, Float64}}) (generic function with 1 method) -``` - - - - - -We need a method for extracting the history from a simulation run. Below, we define such functions for each type of algorithm. - -```julia -""" -Given an ODE solution `sol`, recover the timestamp in which events occurred. It -returns a vector with the history of each process in `sol`. - -It assumes that `JumpProblem` was initialized with `save_positions` equal to -`(true, false)`, `(false, true)` or `(true, true)` such the system's state is -saved before and/or after the jump occurs; and, that `sol.u` is a -non-decreasing series that counts the total number of events observed as a -function of time. -""" -function histories(u, t) - _u = permutedims(reduce(hcat, u)) - k = size(_u)[2] - # computes a mask that show when total counts change - mask = cat(fill(0.0, 1, k), _u[2:end, :] .- _u[1:end-1, :], dims = 1) .≈ 1 - h = Vector{typeof(t)}(undef, k) - @inbounds for i = 1:k - h[i] = t[mask[:, i]] - end - return h -end - -function histories(sol::S) where {S<:ODESolution} - # get u and permute the dimensions to get a matrix n x k with n obsevations and k processes. - if sol.u[1] isa ExtendedJumpArray - u = map((u) -> u.u, sol.u) - else - u = sol.u - end - return histories(u, sol.t) -end - -function histories(sol::S) where {S<:PDMP.PDMPResult} - return histories(sol.xd.u, sol.time) -end - -function histories(sols) - map(histories, sols) -end -``` - -``` -histories (generic function with 4 methods) -``` - - - - - -We also need to compute the quantiles of the empirical distribution given a history of events `hs`, the compensator `Λ` and the target quantiles `quant`. - -```julia -import Distributions: Exponential - -""" -Computes the empirical and expected quantiles given a history of events `hs`, -the compensator `Λ` and the target quantiles `quant`. - -The history `hs` is a vector with the history of each process. Alternatively, -the function also takes a vector of histories containing the histories from -multiple runs. - -The compensator `Λ` can either be an homogeneous compensator function that -equally applies to all the processes in `hs`. Alternatively, it accepts a -vector of compensator that applies to each process. -""" -function qq(hs, Λ, quant = 0.01:0.01:0.99) - _hs = apply_Λ(hs, Λ) - T = typeof(hs[1][1][1]) - Δs = Vector{Vector{T}}(undef, length(hs[1])) - for k = 1:length(Δs) - _Δs = Vector{Vector{T}}(undef, length(hs)) - for i = 1:length(_Δs) - _Δs[i] = _hs[i][k][2:end] .- _hs[i][k][1:end-1] - end - Δs[k] = reduce(vcat, _Δs) - end - empirical_quant = map((_Δs) -> quantile(_Δs, quant), Δs) - expected_quant = quantile(Exponential(1.0), quant) - return empirical_quant, expected_quant -end - -""" -Compute the compensator `Λ` value for each timestamp recorded in history `hs`. - -The history `hs` is a vector with the history of each process. Alternatively, -the function also takes a vector of histories containing the histories from -multiple runs. - -The compensator `Λ` can either be an homogeneous compensator function that -equally applies to all the processes in `hs`. Alternatively, it accepts a -vector of compensator that applies to each process. -""" -function apply_Λ(hs::V, Λ) where {V<:Vector{<:Number}} - _hs = similar(hs) - @inbounds for n = 1:length(hs) - _hs[n] = Λ(hs[n], hs) - end - return _hs -end - -function apply_Λ(k::Int, hs::V, Λ::A) where {V<:Vector{<:Vector{<:Number}},A<:Array} - @inbounds hsk = hs[k] - @inbounds Λk = Λ[k] - _hs = similar(hsk) - @inbounds for n = 1:length(hsk) - _hs[n] = Λk(hsk[n], hs) - end - return _hs -end - -function apply_Λ(hs::V, Λ) where {V<:Vector{<:Vector{<:Number}}} - _hs = similar(hs) - @inbounds for k = 1:length(_hs) - _hs[k] = apply_Λ(hs[k], Λ) - end - return _hs -end - -function apply_Λ(hs::V, Λ::A) where {V<:Vector{<:Vector{<:Number}},A<:Array} - _hs = similar(hs) - @inbounds for k = 1:length(_hs) - _hs[k] = apply_Λ(k, hs, Λ) - end - return _hs -end - -function apply_Λ(hs::V, Λ) where {V<:Vector{<:Vector{<:Vector{<:Number}}}} - return map((_hs) -> apply_Λ(_hs, Λ), hs) -end -``` - -``` -apply_Λ (generic function with 5 methods) -``` - - - - - -We can construct QQ-plots with a Plot recipe as following. - -```julia -@userplot QQPlot -@recipe function f(x::QQPlot) - empirical_quant, expected_quant = x.args - max_empirical_quant = maximum(maximum, empirical_quant) - max_expected_quant = maximum(expected_quant) - upperlim = ceil(maximum([max_empirical_quant, max_expected_quant])) - @series begin - seriestype := :line - linecolor := :lightgray - label --> "" - (x) -> x - end - @series begin - seriestype := :scatter - aspect_ratio := :equal - xlims := (0.0, upperlim) - ylims := (0.0, upperlim) - xaxis --> "Expected" - yaxis --> "Empirical" - markerstrokewidth --> 0 - markerstrokealpha --> 0 - markersize --> 1.5 - size --> (400, 500) - label --> permutedims(["quantiles $i" for i = 1:length(empirical_quant)]) - expected_quant, empirical_quant - end -end -``` - - - - -Now, we simulate all of the algorithms we defined in the previous Section ``250`` times to produce their QQ-plots. - -```julia -let fig = [] - for (i, (algo, stepper, use_recursion, label)) in enumerate(algorithms) - @info label - if algo isa PyTick - _p = (p[1], p[2], p[3]) - elseif algo isa PDMPCHVSimple - if use_recursion - h = zeros(eltype(tspan), nv(G)) - ϕ = zeros(eltype(tspan), nv(G)) - _p = (p[1], p[2], p[3], h, ϕ, g) - else - h = [eltype(tspan)[] for _ in 1:nv(G)] - _p = (p[1], p[2], p[3], h, g) - end - elseif algo isa PDMPCHVFull - _p = (p[1], p[2], p[3], nothing, nothing, g) - else - if use_recursion - h = zeros(eltype(tspan), nv(G)) - ϕ = zeros(eltype(tspan), nv(G)) - urate = zeros(eltype(tspan), nv(G)) - _p = (p[1], p[2], p[3], h, urate, ϕ) - else - h = [eltype(tspan)[] for _ = 1:nv(G)] - urate = zeros(eltype(tspan), nv(G)) - _p = (p[1], p[2], p[3], h, urate) - end - end - jump_prob = hawkes_problem(_p, algo; u, tspan, g, use_recursion) - runs = Vector{Vector{Vector{Number}}}(undef, 250) - for n = 1:length(runs) - if algo isa PyTick - jump_prob.reset() - jump_prob.simulate() - runs[n] = jump_prob.timestamps - else - if ~(algo isa PDMPCHVFull) - if use_recursion - h .= 0 - ϕ .= 0 - else - for _h in h empty!(_h) end - end - if ~(algo isa PDMPCHVSimple) - urate .= 0 - end - end - runs[n] = histories(solve(jump_prob, stepper)) - end - end - qqs = qq(runs, Λ) - push!(fig, qqplot(qqs..., legend = false, aspect_ratio = :equal, title=label, fmt=fmt)) - end - fig = plot(fig..., layout = (4, 2), fmt=fmt, size=(width_px, 4*height_px/2)) -end -``` - -![](figures/MultivariateHawkes_21_1.png) - - - -# Benchmarking performance - -In this Section we benchmark all the algorithms introduced in the first Section. - -We generate networks in the range from ``1`` to ``95`` nodes and simulate the Multivariate Hawkes process ``25`` units of time. - - and simulate models in the range from ``1`` to ``95`` nodes for ``25`` units of time. We fix the Hawkes parameters at ``\lambda = 0.5 , \alpha = 0.1 , \beta = 5.0`` which ensures the process does not explode. We simulate ``50`` trajectories with a limit of ten seconds to complete execution for each configuration. - -```julia -tspan = (0.0, 25.0) -p = (0.5, 0.1, 5.0) -Vs = append!([1], 5:5:95) -Gs = [erdos_renyi(V, 0.2, seed = 6221) for V in Vs] - -bs = Vector{Vector{BenchmarkTools.Trial}}() - -for (algo, stepper, use_recursion, label) in algorithms - @info label - global _stepper = stepper - push!(bs, Vector{BenchmarkTools.Trial}()) - _bs = bs[end] - for (i, G) in enumerate(Gs) - local g = [neighbors(G, i) for i = 1:nv(G)] - local u = [0.0 for i = 1:nv(G)] - if algo isa PyTick - _p = (p[1], p[2], p[3]) - elseif algo isa PDMPCHVSimple - if use_recursion - global h = zeros(eltype(tspan), nv(G)) - global ϕ = zeros(eltype(tspan), nv(G)) - _p = (p[1], p[2], p[3], h, ϕ, g) - else - global h = [eltype(tspan)[] for _ in 1:nv(G)] - _p = (p[1], p[2], p[3], h, g) - end - elseif algo isa PDMPCHVFull - _p = (p[1], p[2], p[3], nothing, nothing, g) - else - if use_recursion - global h = zeros(eltype(tspan), nv(G)) - global urate = zeros(eltype(tspan), nv(G)) - global ϕ = zeros(eltype(tspan), nv(G)) - _p = (p[1], p[2], p[3], h, urate, ϕ) - else - global h = [eltype(tspan)[] for _ = 1:nv(G)] - global urate = zeros(eltype(tspan), nv(G)) - _p = (p[1], p[2], p[3], h, urate) - end - end - global jump_prob = hawkes_problem(_p, algo; u, tspan, g, use_recursion) - trial = try - if algo isa PyTick - @benchmark( - jump_prob.simulate(), - setup = (jump_prob.reset()), - samples = 50, - evals = 1, - seconds = 10, - ) - else - if algo isa PDMPCHVFull - @benchmark( - solve(jump_prob, _stepper), - setup = (), - samples = 50, - evals = 1, - seconds = 10, - ) - elseif algo isa PDMPCHVSimple - if use_recursion - @benchmark(solve(jump_prob, _stepper), - setup=(h .= 0; ϕ .= 0), - samples=50, - evals=1, - seconds=10,) - else - @benchmark(solve(jump_prob, _stepper), - setup=([empty!(_h) for _h in h]), - samples=50, - evals=1, - seconds=10,) - end - else - if use_recursion - @benchmark( - solve(jump_prob, _stepper), - setup = (h .= 0; urate .= 0; ϕ .= 0), - samples = 50, - evals = 1, - seconds = 10, - ) - else - @benchmark( - solve(jump_prob, _stepper), - setup = ([empty!(_h) for _h in h]; urate .= 0), - samples = 50, - evals = 1, - seconds = 10, - ) - end - end - end - catch e - BenchmarkTools.Trial( - BenchmarkTools.Parameters(samples = 50, evals = 1, seconds = 10), - ) - end - push!(_bs, trial) - if (nv(G) == 1 || nv(G) % 10 == 0) - median_time = - length(trial) > 0 ? "$(BenchmarkTools.prettytime(median(trial.times)))" : - "nan" - println("algo=$(label), V = $(nv(G)), length = $(length(trial.times)), median time = $median_time") - end - end -end -``` - -``` -algo=Direct (brute-force), V = 1, length = 50, median time = 98.719 μs -algo=Direct (brute-force), V = 10, length = 50, median time = 10.733 ms -algo=Direct (brute-force), V = 20, length = 50, median time = 84.722 ms -algo=Direct (brute-force), V = 30, length = 37, median time = 275.204 ms -algo=Direct (brute-force), V = 40, length = 7, median time = 1.551 s -algo=Direct (brute-force), V = 50, length = 4, median time = 3.240 s -algo=Direct (brute-force), V = 60, length = 2, median time = 5.686 s -algo=Direct (brute-force), V = 70, length = 1, median time = 10.190 s -algo=Direct (brute-force), V = 80, length = 1, median time = 15.298 s -algo=Direct (brute-force), V = 90, length = 1, median time = 20.870 s -algo=Coevolve (brute-force), V = 1, length = 50, median time = 3.340 μs -algo=Coevolve (brute-force), V = 10, length = 50, median time = 207.068 μs -algo=Coevolve (brute-force), V = 20, length = 50, median time = 1.310 ms -algo=Coevolve (brute-force), V = 30, length = 50, median time = 3.151 ms -algo=Coevolve (brute-force), V = 40, length = 50, median time = 8.119 ms -algo=Coevolve (brute-force), V = 50, length = 50, median time = 17.098 ms -algo=Coevolve (brute-force), V = 60, length = 50, median time = 29.820 ms -algo=Coevolve (brute-force), V = 70, length = 50, median time = 50.014 ms -algo=Coevolve (brute-force), V = 80, length = 50, median time = 73.230 ms -algo=Coevolve (brute-force), V = 90, length = 50, median time = 122.305 ms -algo=Direct (recursive), V = 1, length = 50, median time = 92.914 μs -algo=Direct (recursive), V = 10, length = 50, median time = 4.804 ms -algo=Direct (recursive), V = 20, length = 50, median time = 24.125 ms -algo=Direct (recursive), V = 30, length = 50, median time = 69.895 ms -algo=Direct (recursive), V = 40, length = 11, median time = 979.790 ms -algo=Direct (recursive), V = 50, length = 6, median time = 1.800 s -algo=Direct (recursive), V = 60, length = 4, median time = 3.087 s -algo=Direct (recursive), V = 70, length = 2, median time = 5.412 s -algo=Direct (recursive), V = 80, length = 2, median time = 8.048 s -algo=Direct (recursive), V = 90, length = 1, median time = 11.911 s -algo=Coevolve (recursive), V = 1, length = 50, median time = 3.830 μs -algo=Coevolve (recursive), V = 10, length = 50, median time = 74.740 μs -algo=Coevolve (recursive), V = 20, length = 50, median time = 263.803 μs -algo=Coevolve (recursive), V = 30, length = 50, median time = 493.786 μs -algo=Coevolve (recursive), V = 40, length = 50, median time = 899.168 μs -algo=Coevolve (recursive), V = 50, length = 50, median time = 1.485 ms -algo=Coevolve (recursive), V = 60, length = 50, median time = 2.202 ms -algo=Coevolve (recursive), V = 70, length = 50, median time = 3.112 ms -algo=Coevolve (recursive), V = 80, length = 50, median time = 4.023 ms -algo=Coevolve (recursive), V = 90, length = 50, median time = 5.461 ms -algo=PDMPCHVSimple (brute-force), V = 1, length = 50, median time = 71.079 -μs -algo=PDMPCHVSimple (brute-force), V = 10, length = 50, median time = 5.005 -ms -algo=PDMPCHVSimple (brute-force), V = 20, length = 50, median time = 41.739 - ms -algo=PDMPCHVSimple (brute-force), V = 30, length = 50, median time = 113.93 -7 ms -algo=PDMPCHVSimple (brute-force), V = 40, length = 35, median time = 285.70 -5 ms -algo=PDMPCHVSimple (brute-force), V = 50, length = 17, median time = 602.09 -8 ms -algo=PDMPCHVSimple (brute-force), V = 60, length = 10, median time = 1.083 -s -algo=PDMPCHVSimple (brute-force), V = 70, length = 6, median time = 1.898 s -algo=PDMPCHVSimple (brute-force), V = 80, length = 4, median time = 2.879 s -algo=PDMPCHVSimple (brute-force), V = 90, length = 3, median time = 4.524 s -algo=PDMPCHVSimple (recursive), V = 1, length = 50, median time = 71.570 μs -algo=PDMPCHVSimple (recursive), V = 10, length = 50, median time = 343.667 -μs -algo=PDMPCHVSimple (recursive), V = 20, length = 50, median time = 800.223 -μs -algo=PDMPCHVSimple (recursive), V = 30, length = 50, median time = 1.507 ms -algo=PDMPCHVSimple (recursive), V = 40, length = 50, median time = 2.474 ms -algo=PDMPCHVSimple (recursive), V = 50, length = 50, median time = 3.620 ms -algo=PDMPCHVSimple (recursive), V = 60, length = 50, median time = 5.083 ms -algo=PDMPCHVSimple (recursive), V = 70, length = 50, median time = 7.069 ms -algo=PDMPCHVSimple (recursive), V = 80, length = 50, median time = 9.347 ms -algo=PDMPCHVSimple (recursive), V = 90, length = 50, median time = 12.089 m -s -algo=PDMPCHVFull, V = 1, length = 50, median time = 70.070 μs -algo=PDMPCHVFull, V = 10, length = 50, median time = 482.171 μs -algo=PDMPCHVFull, V = 20, length = 50, median time = 739.314 μs -algo=PDMPCHVFull, V = 30, length = 50, median time = 1.216 ms -algo=PDMPCHVFull, V = 40, length = 50, median time = 1.531 ms -algo=PDMPCHVFull, V = 50, length = 50, median time = 1.891 ms -algo=PDMPCHVFull, V = 60, length = 50, median time = 2.557 ms -algo=PDMPCHVFull, V = 70, length = 50, median time = 3.099 ms -algo=PDMPCHVFull, V = 80, length = 50, median time = 3.716 ms -algo=PDMPCHVFull, V = 90, length = 50, median time = 4.443 ms -``` - - - -```julia -let fig = plot( - yscale = :log10, - xlabel = "V", - ylabel = "Time (ns)", - legend_position = :outertopright, -) - for (i, (algo, stepper, use_recursion, label)) in enumerate(algorithms) - _bs, _Vs = [], [] - for (j, b) in enumerate(bs[i]) - if length(b) == 50 - push!(_bs, median(b.times)) - push!(_Vs, Vs[j]) - end - end - plot!(_Vs, _bs, label=label) - end - title!("Simulations, 50 samples: nodes × time") -end -``` - -![](figures/MultivariateHawkes_23_1.png) - - - -# References - -[1] D. J. Daley and D. Vere-Jones. An Introduction to the Theory of Point Processes: Volume I: Elementary Theory and Methods. Probability and Its Applications, An Introduction to the Theory of Point Processes. Springer-Verlag, 2 edition. doi:10.1007/b97277. - -[2] Patrick J. Laub, Young Lee, and Thomas Taimre. The Elements of Hawkes Processes. Springer International Publishing. doi:10.1007/978-3-030-84639-8. diff --git a/markdown/Jumps/NegFeedback_GeneExpr.md b/markdown/Jumps/NegFeedback_GeneExpr.md index 2df7f704a..4145dbea1 100644 --- a/markdown/Jumps/NegFeedback_GeneExpr.md +++ b/markdown/Jumps/NegFeedback_GeneExpr.md @@ -17,6 +17,7 @@ fmt = :png Our model is + ```julia rn = prob_jump_dnarepressor.network reactions(rn) @@ -39,17 +40,20 @@ reactions(rn) # Plot solutions by each method ```julia -methods = (Direct(), FRM(), SortingDirect(), NRM(), DirectCR(), RSSA(), RSSACR(), Coevolve(), RDirect()) -shortlabels = [string(leg)[15:end-2] for leg in methods] -prob = prob_jump_dnarepressor.discrete_prob -tf = prob_jump_dnarepressor.tstop -ploth = plot(reuse=false) -for (i,method) in enumerate(methods) - jump_prob = JumpProblem(rn, prob, method, save_positions=(false, false)) - sol = solve(jump_prob, SSAStepper(), saveat=tf/1000.) - plot!(ploth,sol.t, sol[3,:], label=shortlabels[i], format=fmt) +methods = (Direct(), FRM(), SortingDirect(), NRM(), DirectCR(), + RSSA(), RSSACR(), Coevolve(), RDirect()) +shortlabels = [string(leg)[15:(end - 2)] for leg in methods] +tf = prob_jump_dnarepressor.tstop +ploth = plot(reuse = false) +for (i, method) in enumerate(methods) + jump_prob = JumpProblem( + rn, prob_jump_dnarepressor.u0, (0.0, tf), prob_jump_dnarepressor.rates; + aggregator = method, save_positions = (false, false) + ) + sol = solve(jump_prob, SSAStepper(), saveat = tf/1000.0) + plot!(ploth, sol.t, sol[3, :], label = shortlabels[i], format = fmt) end -plot(ploth, title="Protein level", xlabel="time", format=fmt) +plot(ploth, title = "Protein level", xlabel = "time", format = fmt) ``` ![](figures/NegFeedback_GeneExpr_3_1.png) @@ -77,9 +81,12 @@ run_benchmark! (generic function with 1 method) nsims = 2000 benchmarks = Vector{Vector{Float64}}() for method in methods - jump_prob = JumpProblem(rn, prob, method, save_positions=(false, false)) + jump_prob = JumpProblem( + rn, prob_jump_dnarepressor.u0, (0.0, tf), prob_jump_dnarepressor.rates; + aggregator = method, save_positions = (false, false) + ) stepper = SSAStepper() - t = Vector{Float64}(undef,nsims) + t = Vector{Float64}(undef, nsims) run_benchmark!(t, jump_prob, stepper) push!(benchmarks, t) end @@ -99,20 +106,22 @@ println(medtimes/medtimes[1]) ``` ``` -[1.0, 1.168571579808871, 0.8909985219448436, 1.6444116892582443, 1.72871783 -804913, 1.771105039638752, 3.3619565704234238, 2.4499456417731778, 1.874385 -6706013606] +[1.0, 1.2665766032258163, 0.9578719615024534, 1.7313847711463575, 1.8682014 +04623731, 1.8700326607037758, 3.4663832616180317, 2.741449818094213, 1.9279 +726272196929] ``` ```julia using DataFrames -df = DataFrame(names=shortlabels, medtimes=medtimes, relmedtimes=(medtimes/medtimes[1]), - avgtimes=avgtimes, std=stdtimes, cv=stdtimes./avgtimes) -sa = [text(string(round(mt,sigdigits=2),"s"),:center,10) for mt in df.medtimes] -bar(df.names,df.relmedtimes,legend=:false, fmt=fmt) -scatter!(df.names, .05 .+ df.relmedtimes, markeralpha=0, series_annotations=sa, fmt=fmt) +df = DataFrame( + names = shortlabels, medtimes = medtimes, relmedtimes = (medtimes/medtimes[1]), + avgtimes = avgtimes, std = stdtimes, cv = stdtimes ./ avgtimes) +sa = [text(string(round(mt, sigdigits = 2), "s"), :center, 10) for mt in df.medtimes] +bar(df.names, df.relmedtimes, legend = :false, fmt = fmt) +scatter!( + df.names, 0.05 .+ df.relmedtimes, markeralpha = 0, series_annotations = sa, fmt = fmt) ylabel!("median relative to Direct") title!("Negative Feedback Gene Expression Model") ``` @@ -125,7 +134,6 @@ title!("Negative Feedback Gene Expression Model") These benchmarks are a part of the SciMLBenchmarks.jl repository, found at: [https://github.com/SciML/SciMLBenchmarks.jl](https://github.com/SciML/SciMLBenchmarks.jl). For more information on high-performance scientific machine learning, check out the SciML Open Source Software Organization [https://sciml.ai](https://sciml.ai). To locally run this benchmark, do the following commands: - ``` using SciMLBenchmarks SciMLBenchmarks.weave_file("benchmarks/Jumps","NegFeedback_GeneExpr.jmd") @@ -134,8 +142,8 @@ SciMLBenchmarks.weave_file("benchmarks/Jumps","NegFeedback_GeneExpr.jmd") Computer Information: ``` -Julia Version 1.10.9 -Commit 5595d20a287 (2025-03-10 12:51 UTC) +Julia Version 1.10.12 +Commit d93beab124c (2026-08-15 10:29 UTC) Build Info: Official https://julialang.org/ release Platform Info: @@ -144,432 +152,372 @@ Platform Info: WORD_SIZE: 64 LIBM: libopenlibm LLVM: libLLVM-15.0.7 (ORCJIT, znver2) -Threads: 1 default, 0 interactive, 1 GC (on 128 virtual cores) +Threads: 128 default, 0 interactive, 64 GC (on 128 virtual cores) Environment: - JULIA_CPU_THREADS = 128 - JULIA_DEPOT_PATH = /cache/julia-buildkite-plugin/depots/5b300254-1738-4989-ae0a-f4d2d937f953 + JULIA_NUM_THREADS = auto ``` Package Information: ``` -Status `/cache/build/exclusive-amdci1-0/julialang/scimlbenchmarks-dot-jl/benchmarks/Jumps/Project.toml` - [6e4b80f9] BenchmarkTools v1.6.0 - [479239e8] Catalyst v15.0.8 - [8f4d0f93] Conda v1.10.2 - [a93c6f00] DataFrames v1.7.0 - [0c46a032] DifferentialEquations v7.16.1 - [31c24e10] Distributions v0.25.120 - [86223c79] Graphs v1.12.1 - [faf0f6d7] JumpProblemLibrary v1.1.0 - [ccbc3e58] JumpProcesses v9.15.0 -⌅ [961ee093] ModelingToolkit v9.80.2 - [1dea7af3] OrdinaryDiffEq v6.98.0 - [86206cdf] PiecewiseDeterministicMarkovProcesses v0.0.10 - [91a5bcdd] Plots v1.40.13 +Status `/julia/github-runners/amdci1-1/_work/SciMLBenchmarks.jl/SciMLBenchmarks.jl/benchmarks/Jumps/Project.toml` + [6e4b80f9] BenchmarkTools v1.8.0 + [479239e8] Catalyst v16.4.0 + [8f4d0f93] Conda v1.10.3 + [a93c6f00] DataFrames v1.8.2 + [0c46a032] DifferentialEquations v8.1.1 + [31c24e10] Distributions v0.25.131 + [86223c79] Graphs v1.14.0 + [faf0f6d7] JumpProblemLibrary v2.0.3 + [ccbc3e58] JumpProcesses v9.30.1 + [961ee093] ModelingToolkit v11.40.0 + [1dea7af3] OrdinaryDiffEq v7.8.1 + [86206cdf] PiecewiseDeterministicMarkovProcesses v0.0.12 + [91a5bcdd] Plots v1.41.7 [438e738f] PyCall v1.96.4 - [b4db0fb7] ReactionNetworkImporters v0.16.1 - [31c91b34] SciMLBenchmarks v0.1.3 - [860ef19b] StableRNGs v1.0.3 - [f3b207a7] StatsPlots v0.15.7 - [c3572dad] Sundials v4.28.0 + [b4db0fb7] ReactionNetworkImporters v1.5.0 +⌃ [31c91b34] SciMLBenchmarks v0.1.3 + [860ef19b] StableRNGs v1.0.4 + [f3b207a7] StatsPlots v0.15.8 + [c3572dad] Sundials v6.6.0 + [2efcf032] SymbolicIndexingInterface v0.3.55 [37e2e46d] LinearAlgebra [9a3f8284] Random [10745b16] Statistics v1.10.0 -Info Packages marked with ⌅ have new versions available but compatibility constraints restrict them from upgrading. To see why use `status --outdated` +Info Packages marked with ⌃ have new versions available and may be upgradable. ``` And the full manifest: ``` -Status `/cache/build/exclusive-amdci1-0/julialang/scimlbenchmarks-dot-jl/benchmarks/Jumps/Manifest.toml` - [47edcb42] ADTypes v1.14.0 +Status `/julia/github-runners/amdci1-1/_work/SciMLBenchmarks.jl/SciMLBenchmarks.jl/benchmarks/Jumps/Manifest.toml` + [47edcb42] ADTypes v1.24.0 + [14f7f29c] AMD v0.5.3 [621f4979] AbstractFFTs v1.5.0 + [6e696c72] AbstractPlutoDingetjes v1.4.0 [1520ce14] AbstractTrees v0.4.5 - [7d9f7c33] Accessors v0.1.42 - [79e6a3ab] Adapt v4.3.0 + [7d9f7c33] Accessors v0.1.45 + [79e6a3ab] Adapt v4.7.0 [66dad0bd] AliasTables v1.1.3 - [a95523ee] AlmostBlockDiagonals v0.1.10 [ec485272] ArnoldiMethod v0.4.0 [7d9fca2a] Arpack v0.5.4 - [4fba245c] ArrayInterface v7.19.0 - [4c555306] ArrayLayouts v1.11.1 + [4fba245c] ArrayInterface v7.30.0 + [4c555306] ArrayLayouts v1.12.2 [13072b0f] AxisAlgorithms v1.1.0 - [aae01518] BandedMatrices v1.9.4 - 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2)] for leg in methods] +ploth = plot(reuse = false) p = [] -for (i,method) in enumerate(methods) - jump_prob = JumpProblem(rn, prob, method, save_positions=(false, false)) - sol = solve(jump_prob, SSAStepper(), saveat=tf/1000.) - plot!(ploth, sol.t, sol[3,:], label=shortlabels[i], format=fmt) - push!(p, plot(sol, title=shortlabels[i], format=fmt)) +for (i, method) in enumerate(methods) + jump_prob = JumpProblem( + rn, u0, (0.0, tf), rnpar; + aggregator = method, save_positions = (false, false) + ) + sol = solve(jump_prob, SSAStepper(), saveat = tf/1000.0) + plot!(ploth, sol.t, sol[3, :], label = shortlabels[i], format = fmt) + push!(p, plot(sol, title = shortlabels[i], format = fmt)) end -plot(ploth, title="Protein level", xlabel="time", format=fmt) +plot(ploth, title = "Protein level", xlabel = "time", format = fmt) ``` ![](figures/NegFeedback_GeneExpr_Marchetti_4_1.png) @@ -99,7 +103,10 @@ run_benchmark! (generic function with 1 method) nsims = 200 benchmarks = Vector{Vector{Float64}}() for method in methods - jump_prob = JumpProblem(rn, prob, method, save_positions=(false, false)) + jump_prob = JumpProblem( + rn, u0, (0.0, tf), rnpar; + aggregator = method, save_positions = (false, false) + ) stepper = SSAStepper() t = Vector{Float64}(undef, nsims) run_benchmark!(t, jump_prob, stepper) @@ -119,11 +126,13 @@ for i in 1:length(methods) end using DataFrames -df = DataFrame(names=shortlabels, medtimes=medtimes, relmedtimes=(medtimes/medtimes[1]), - avgtimes=avgtimes, std=stdtimes, cv=stdtimes./avgtimes) -sa = [text(string(round(mt,digits=3),"s"),:center,12) for mt in df.medtimes] -bar(df.names,df.relmedtimes,legend=:false, fmt=fmt) -scatter!(df.names, .05 .+ df.relmedtimes, markeralpha=0, series_annotations=sa, fmt=fmt) +df = DataFrame( + names = shortlabels, medtimes = medtimes, relmedtimes = (medtimes/medtimes[1]), + avgtimes = avgtimes, std = stdtimes, cv = stdtimes ./ avgtimes) +sa = [text(string(round(mt, digits = 3), "s"), :center, 12) for mt in df.medtimes] +bar(df.names, df.relmedtimes, legend = :false, fmt = fmt) +scatter!( + df.names, 0.05 .+ df.relmedtimes, markeralpha = 0, series_annotations = sa, fmt = fmt) ylabel!("median relative to Direct") title!("Marchetti Gene Expression Model") ``` @@ -136,7 +145,6 @@ title!("Marchetti Gene Expression Model") These benchmarks are a part of the SciMLBenchmarks.jl repository, found at: [https://github.com/SciML/SciMLBenchmarks.jl](https://github.com/SciML/SciMLBenchmarks.jl). For more information on high-performance scientific machine learning, check out the SciML Open Source Software Organization [https://sciml.ai](https://sciml.ai). To locally run this benchmark, do the following commands: - ``` using SciMLBenchmarks SciMLBenchmarks.weave_file("benchmarks/Jumps","NegFeedback_GeneExpr_Marchetti.jmd") @@ -145,8 +153,8 @@ SciMLBenchmarks.weave_file("benchmarks/Jumps","NegFeedback_GeneExpr_Marchetti.jm Computer Information: ``` -Julia Version 1.10.9 -Commit 5595d20a287 (2025-03-10 12:51 UTC) +Julia Version 1.10.12 +Commit d93beab124c (2026-08-15 10:29 UTC) Build Info: Official https://julialang.org/ release Platform Info: @@ -155,432 +163,372 @@ Platform Info: WORD_SIZE: 64 LIBM: libopenlibm LLVM: libLLVM-15.0.7 (ORCJIT, znver2) -Threads: 1 default, 0 interactive, 1 GC (on 128 virtual cores) +Threads: 128 default, 0 interactive, 64 GC (on 128 virtual cores) Environment: - JULIA_CPU_THREADS = 128 - JULIA_DEPOT_PATH = /cache/julia-buildkite-plugin/depots/5b300254-1738-4989-ae0a-f4d2d937f953 + JULIA_NUM_THREADS = auto ``` Package Information: ``` -Status `/cache/build/exclusive-amdci1-0/julialang/scimlbenchmarks-dot-jl/benchmarks/Jumps/Project.toml` - [6e4b80f9] BenchmarkTools v1.6.0 - [479239e8] Catalyst v15.0.8 - [8f4d0f93] Conda v1.10.2 - [a93c6f00] DataFrames v1.7.0 - [0c46a032] DifferentialEquations v7.16.1 - [31c24e10] Distributions v0.25.120 - [86223c79] Graphs v1.12.1 - [faf0f6d7] JumpProblemLibrary v1.1.0 - [ccbc3e58] JumpProcesses v9.15.0 -⌅ [961ee093] ModelingToolkit v9.80.2 - [1dea7af3] OrdinaryDiffEq v6.98.0 - [86206cdf] PiecewiseDeterministicMarkovProcesses v0.0.10 - [91a5bcdd] Plots v1.40.13 +Status `/julia/github-runners/amdci1-1/_work/SciMLBenchmarks.jl/SciMLBenchmarks.jl/benchmarks/Jumps/Project.toml` + [6e4b80f9] BenchmarkTools v1.8.0 + [479239e8] Catalyst v16.4.0 + [8f4d0f93] Conda v1.10.3 + [a93c6f00] DataFrames v1.8.2 + [0c46a032] DifferentialEquations v8.1.1 + [31c24e10] Distributions v0.25.131 + [86223c79] Graphs v1.14.0 + [faf0f6d7] JumpProblemLibrary v2.0.3 + [ccbc3e58] JumpProcesses v9.30.1 + [961ee093] ModelingToolkit v11.40.0 + [1dea7af3] OrdinaryDiffEq v7.8.1 + [86206cdf] PiecewiseDeterministicMarkovProcesses v0.0.12 + [91a5bcdd] Plots v1.41.7 [438e738f] PyCall v1.96.4 - [b4db0fb7] ReactionNetworkImporters v0.16.1 - [31c91b34] SciMLBenchmarks v0.1.3 - [860ef19b] StableRNGs v1.0.3 - [f3b207a7] StatsPlots v0.15.7 - [c3572dad] Sundials v4.28.0 + [b4db0fb7] ReactionNetworkImporters v1.5.0 +⌃ [31c91b34] SciMLBenchmarks v0.1.3 + [860ef19b] StableRNGs v1.0.4 + [f3b207a7] StatsPlots v0.15.8 + [c3572dad] Sundials v6.6.0 + [2efcf032] SymbolicIndexingInterface v0.3.55 [37e2e46d] LinearAlgebra [9a3f8284] Random [10745b16] Statistics v1.10.0 -Info Packages marked with ⌅ have new versions available but compatibility constraints restrict them from upgrading. 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Below, the value `N` will denote the +stochastic simulation algorithms (SSAs). Below, the value `N` will denote the number of subvolumes along one dimension of a cubic grid, representing the reaction volume. In [^1] this value ranges from 20 to 60. We first define some helper functions to convert concentration units into number units, as needed for spatial SSAs. + ```julia invmicromolar_to_cubicmicrometer(invconcen) = invconcen / (6.02214076e2) micromolar_to_invcubicmicrometer(concen) = (6.02214076e2) * concen @@ -32,29 +35,30 @@ micromolar_to_invcubicmicrometer (generic function with 1 method) Next we create a well-mixed model with the desired chemistry + ```julia rn = @reaction_network begin @parameters k₁ ka kd k₄ k₁, EA --> EA + A k₁, EB --> EB + B - (ka,kd), EA + B <--> EAB - (ka,kd), EAB + B <--> EAB₂ - (ka,kd), EB + A <--> EBA - (ka,kd), EBA + A <--> EBA₂ + (ka, kd), EA + B <--> EAB + (ka, kd), EAB + B <--> EAB₂ + (ka, kd), EB + A <--> EBA + (ka, kd), EBA + A <--> EBA₂ k₄, A --> ∅ k₄, B --> ∅ end ``` ``` -Model ##ReactionSystem#231: -Unknowns (8): see unknowns(##ReactionSystem#231) +Model ##ReactionSystem#234: +Unknowns (8): see unknowns(##ReactionSystem#234) EA(t) A(t) EB(t) B(t) ⋮ -Parameters (4): see parameters(##ReactionSystem#231) +Parameters (4): see parameters(##ReactionSystem#234) k₁ ka kd @@ -64,9 +68,11 @@ Parameters (4): see parameters(##ReactionSystem#231) + Let's next make a function to calculate the spatial transport rates, mesh/graph that will represent our domain, and initial condition. We use a cubic lattice of size `N` by `N` by `N` with reflecting boundary conditions + ```julia # domain_len is the physical length of each side of the cubic domain # units should be in μm (6.0 or 12.0 in Sanft) @@ -113,19 +119,23 @@ transport_model (generic function with 1 method) + Finally, let's make a function to setup the well-mixed model from the reaction model in a cube of side length `h`: + ```julia function wellmixed_model(rn, u0, end_time, h) kaval = invmicromolar_to_cubicmicrometer(46.2) / h^3 - setdefaults!(rn, [:k₁ => 150, :ka => kaval, :kd => 3.82, :k₄ => 6.0]) + parameters = [:k₁ => 150, :ka => kaval, :kd => 3.82, :k₄ => 6.0] # well-mixed initial condition corresponding to the spatial initial condition - u0wm = sum(u0, dims = 2) - dprobwm = DiscreteProblem(rn, u0wm, (0.0, end_time)) - jprobwm = JumpProblem(rn, dprobwm, Direct(), save_positions = (false,false)) + u0wm = species(rn) .=> vec(sum(u0, dims = 2)) + jprobwm = JumpProblem( + rn, u0wm, (0.0, end_time), parameters; + aggregator = Direct(), save_positions = (false, false) + ) majumps = jprobwm.massaction_jump - majumps, dprobwm, jprobwm, u0wm + return majumps, parameter_values(jprobwm), jprobwm, u0wm end ``` @@ -138,27 +148,29 @@ wellmixed_model (generic function with 1 method) # Model Solution + Let's look at one example to check our model seems reasonable. We'll plot the total number of molecules in the system to verify we get around 28,000 molecules, as reported in Sanft [^1], when using a domain length of 6 μm. + ```julia end_time = 3.0 grid, hopping_constants, h, u0 = transport_model(rn, 60) -majumps, dprobwm, jprobwm, u0wm = wellmixed_model(rn, u0, end_time, 6.0) +majumps, parameters_wm, jprobwm, u0wm = wellmixed_model(rn, u0, end_time, 6.0) sol = solve(jprobwm, SSAStepper(); saveat = end_time/200) Ntot = [sum(u) for u in sol.u] -plt = plot(sol.t, Ntot, label="Well-mixed", ylabel="Total Number of Molecules", - xlabel="time") +plt = plot(sol.t, Ntot, label = "Well-mixed", ylabel = "Total Number of Molecules", + xlabel = "time") # spatial model -majumps, dprobwm, jprobwm, u0wm = wellmixed_model(rn, u0, end_time, h) -dprob = DiscreteProblem(u0, (0.0, end_time), copy(dprobwm.p)) +majumps, parameters_wm, jprobwm, u0wm = wellmixed_model(rn, u0, end_time, h) +dprob = DiscreteProblem(u0, (0.0, end_time), copy(parameters_wm)) jprob = JumpProblem(dprob, DirectCRDirect(), majumps; hopping_constants, - spatial_system = grid, save_positions = (false, false)) + spatial_system = grid, save_positions = (false, false)) spatial_sol = solve(jprob, SSAStepper(); saveat = end_time/200) Ntot = [sum(vec(u)) for u in spatial_sol.u] -plot!(plt, spatial_sol.t, Ntot, label="Spatial", - title="Steady-state number of molecules is $(Ntot[end])") +plot!(plt, spatial_sol.t, Ntot, label = "Spatial", + title = "Steady-state number of molecules is $(Ntot[end])") ``` ![](figures/Spatial_Signaling_Sanft_6_1.png) @@ -166,11 +178,13 @@ plot!(plt, spatial_sol.t, Ntot, label="Spatial", # Benchmarking performance of the methods + We can now run the solvers and record the performance with `BenchmarkTools`. Let's first create a `DiscreteCallback` to terminate simulations once we reach `10^8` events: + ```julia -@Base.kwdef mutable struct EventCallback +Base.@kwdef mutable struct EventCallback n::Int = 0 end @@ -188,7 +202,9 @@ end + We next create a function to run and return our benchmarking results. + ```julia function benchmark_and_save!(bench_dict, end_times, Nv, algs, domain_len) @assert length(end_times) == length(Nv) @@ -198,15 +214,15 @@ function benchmark_and_save!(bench_dict, end_times, Nv, algs, domain_len) cb = DiscreteCallback(ecb, ecb) for (end_time, N) in zip(end_times, Nv) - names = ["$s"[1:end-2] for s in algs] + names = ["$s"[1:(end - 2)] for s in algs] grid, hopping_constants, h, u0 = transport_model(rn, N; domain_len) # we create a well-mixed model within a domain of the size of *one* voxel, h - majumps, dprobwm, jprobwm, u0wm = wellmixed_model(rn, u0, end_time, h) + majumps, parameters_wm, jprobwm, u0wm = wellmixed_model(rn, u0, end_time, h) # the spatial problem - dprob = DiscreteProblem(u0, (0.0, end_time), copy(dprobwm.p)) + dprob = DiscreteProblem(u0, (0.0, end_time), copy(parameters_wm)) @show N @@ -218,9 +234,9 @@ function benchmark_and_save!(bench_dict, end_times, Nv, algs, domain_len) for (i, alg) in enumerate(algs) name = names[i] println("benchmarking $name") - jp = JumpProblem(dprob, alg, majumps, hopping_constants=hopping_constants, - spatial_system = grid, save_positions=(false,false)) - b = @benchmarkable solve($jp, SSAStepper(); saveat = $(dprob.tspan[2]), callback) setup = (callback = deepcopy($cb)) samples = 10 seconds = 3600 + jp = JumpProblem(dprob, alg, majumps, hopping_constants = hopping_constants, + spatial_system = grid, save_positions = (false, false)) + b = @benchmarkable solve($jp, SSAStepper(); saveat = $(dprob.tspan[2]), callback) setup=(callback=deepcopy($cb)) samples=3 seconds=300 bench_dict[name, N] = run(b) end end @@ -234,7 +250,9 @@ benchmark_and_save! (generic function with 1 method) + Finally, let's make a function to plot the benchmarking data. + ```julia function fetch_and_plot(bench_dict, domain_len) names = unique([key[1] for key in keys(bench_dict)]) @@ -244,7 +262,7 @@ function fetch_and_plot(bench_dict, domain_len) plt2 = plot() medtimes = [Float64[] for i in 1:length(names)] - for (i,name) in enumerate(names) + for (i, name) in enumerate(names) for N in Nv try push!(medtimes[i], median(bench_dict[name, N]).time/1e9) @@ -254,15 +272,15 @@ function fetch_and_plot(bench_dict, domain_len) end len = length(medtimes[i]) plot!(plt1, Nv[1:len], medtimes[i], marker = :hex, label = name, lw = 2) - plot!(plt2, (Nv.^3)[1:len], medtimes[i], marker = :hex, label = name, lw = 2) + plot!(plt2, (Nv .^ 3)[1:len], medtimes[i], marker = :hex, label = name, lw = 2) end plot!(plt1, xlabel = "number of sites per edge", ylabel = "median time in seconds", - xticks = Nv, legend = :bottomright) + xticks = Nv, legend = :bottomright) plot!(plt2, xlabel = "total number of sites", ylabel = "median time in seconds", - xticks = (Nv.^3, string.(Nv.^3)), legend = :bottomright) - plot(plt1, plt2; size = (1200,800), legendtitle = "SSAs", - plot_title="3D RDME, domain length = $domain_len", left_margin=5Plots.mm) + xticks = (Nv .^ 3, string.(Nv .^ 3)), legend = :bottomright) + plot(plt1, plt2; size = (1200, 800), legendtitle = "SSAs", + plot_title = "3D RDME, domain length = $domain_len", left_margin = 5Plots.mm) end ``` @@ -273,8 +291,10 @@ fetch_and_plot (generic function with 1 method) + We are now ready to run the benchmarks and plot the results. We start with a domain length of `12` μm, analogous to Fig. 6 in [^1]: + ```julia bench_dict = Dict{Tuple{String, Int}, BenchmarkTools.Trial}() algs = [NSM(), DirectCRDirect()] @@ -323,7 +343,9 @@ plt=fetch_and_plot(bench_dict, domain_len) ![](figures/Spatial_Signaling_Sanft_11_1.png) + We next consider a domain of length `6` μm, analogous to Fig. 7 in [^1]. + ```julia bench_dict = Dict{Tuple{String, Int}, BenchmarkTools.Trial}() domain_len = 6.0 @@ -371,8 +393,8 @@ plt=fetch_and_plot(bench_dict, domain_len) # References -[^1]: Sanft, Kevin R and Othmer, Hans G. *Constant-complexity stochastic simulation algorithm with optimal binning*. J. Chem. Phys., 143(7), 11 pp. (2015). +[^1]: Sanft, Kevin R and Othmer, Hans G. *Constant-complexity stochastic simulation algorithm with optimal binning*. J. Chem. Phys., 143(7), 11 pp. (2015). ## Appendix @@ -398,432 +420,373 @@ Platform Info: WORD_SIZE: 64 LIBM: libopenlibm LLVM: libLLVM-15.0.7 (ORCJIT, znver2) -Threads: 1 default, 0 interactive, 1 GC (on 128 virtual cores) +Threads: 128 default, 0 interactive, 64 GC (on 128 virtual cores) Environment: - JULIA_CPU_THREADS = 128 - JULIA_DEPOT_PATH = /cache/julia-buildkite-plugin/depots/5b300254-1738-4989-ae0a-f4d2d937f953 + JULIA_LOAD_PATH = @:/home/crackauc/sandbox/tmp_20260825_180339_53321/jumps-refresh:@stdlib + JULIA_PKG_PRECOMPILE_AUTO = 0 ``` Package Information: ``` -Status `/cache/build/exclusive-amdci1-0/julialang/scimlbenchmarks-dot-jl/benchmarks/Jumps/Project.toml` - [6e4b80f9] BenchmarkTools v1.6.0 - [479239e8] Catalyst v15.0.8 - [8f4d0f93] Conda v1.10.2 - [a93c6f00] DataFrames v1.7.0 - [0c46a032] DifferentialEquations v7.16.1 - [31c24e10] Distributions v0.25.120 - [86223c79] Graphs v1.12.1 - [faf0f6d7] JumpProblemLibrary v1.1.0 - [ccbc3e58] JumpProcesses v9.15.0 -⌅ [961ee093] ModelingToolkit v9.80.2 - [1dea7af3] OrdinaryDiffEq v6.98.0 - [86206cdf] PiecewiseDeterministicMarkovProcesses v0.0.10 - [91a5bcdd] Plots v1.40.13 +Status `~/sandbox/tmp_20260825_180339_53321/jumps-refresh/benchmarks/Jumps/Project.toml` + [6e4b80f9] BenchmarkTools v1.8.0 + [479239e8] Catalyst v16.4.0 + [8f4d0f93] Conda v1.10.3 + [a93c6f00] DataFrames v1.8.2 + [0c46a032] DifferentialEquations v8.1.1 + [31c24e10] Distributions v0.25.131 + [86223c79] Graphs v1.14.0 + [faf0f6d7] JumpProblemLibrary v2.0.3 +⌃ [ccbc3e58] JumpProcesses v9.30.1 + [961ee093] ModelingToolkit v11.40.0 + [1dea7af3] OrdinaryDiffEq v7.8.1 + [86206cdf] PiecewiseDeterministicMarkovProcesses v0.0.12 + [91a5bcdd] Plots v1.41.7 [438e738f] PyCall v1.96.4 - [b4db0fb7] ReactionNetworkImporters v0.16.1 - [31c91b34] SciMLBenchmarks v0.1.3 - [860ef19b] StableRNGs v1.0.3 - [f3b207a7] StatsPlots v0.15.7 - [c3572dad] Sundials v4.28.0 + [b4db0fb7] ReactionNetworkImporters v1.5.0 +⌃ [31c91b34] SciMLBenchmarks v0.1.3 + [860ef19b] StableRNGs v1.0.4 + [f3b207a7] StatsPlots v0.15.8 + [c3572dad] Sundials v6.6.0 + [2efcf032] SymbolicIndexingInterface v0.3.55 [37e2e46d] LinearAlgebra [9a3f8284] Random [10745b16] Statistics v1.10.0 -Info Packages marked with ⌅ have new versions available but compatibility constraints restrict them from upgrading. 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zCbR|kNMOB|mY0uO3xRh9rswaeIE;m-O^M_kJY9~Bz2+ys@coJZw{VaXxZ@ULkp16( b{tZZR^LDJhdtilvKlkJx$W_XiJpX?HEdqZF diff --git a/script/Jumps/Diffusion_CTRW.jl b/script/Jumps/Diffusion_CTRW.jl index a1b0be2fd..7fca7e4c6 100644 --- a/script/Jumps/Diffusion_CTRW.jl +++ b/script/Jumps/Diffusion_CTRW.jl @@ -1,29 +1,33 @@ - using Catalyst, JumpProcesses, JumpProblemLibrary, Plots, Statistics, DataFrames N = 256 h = 1 / N -u0 = 10 * ones(Int64, N) -tf = .01 -methods = (Direct(), FRM(), SortingDirect(), NRM(), DirectCR(), RSSA(), RSSACR(), Coevolve(), RDirect()) -shortlabels = [string(leg)[15:end-2] for leg in methods] +tf = 0.01 +methods = ( + Direct(), FRM(), SortingDirect(), NRM(), DirectCR(), + RSSA(), RSSACR(), Coevolve(), RDirect(), +) +shortlabels = [string(leg)[15:(end - 2)] for leg in methods] jprob = JumpProblemLibrary.prob_jump_diffnetwork rn = jprob.network(N) -prob = DiscreteProblem(rn, u0, (0.0, tf), [1 / (h*h)]) -ploth = plot(reuse=false) -for (i,method) in enumerate(methods) +u0 = jprob.u0(rn, N) +rates = [:K => 1 / (h * h)] +ploth = plot(reuse = false) +for (i, method) in enumerate(methods) println("Benchmarking method: ", method) - jump_prob = JumpProblem(rn, prob, method, save_positions=(false, false)) - sol = solve(jump_prob, SSAStepper(); saveat=tf/1000.) - plot!(ploth, sol.t, sol[Int(N//2),:], label=shortlabels[i]) + jump_prob = JumpProblem( + rn, u0, (0.0, tf), rates; aggregator = method, save_positions = (false, false) + ) + sol = solve(jump_prob, SSAStepper(); saveat = tf / 1000.0) + plot!(ploth, sol.t, sol[Int(N // 2), :], label = shortlabels[i]) end -plot!(ploth, title="Population at middle lattice site", xlabel="time") +plot!(ploth, title = "Population at middle lattice site", xlabel = "time") function run_benchmark!(t, jump_prob, stepper) sol = solve(jump_prob, stepper) - @inbounds for i in 1:length(t) + return @inbounds for i in 1:length(t) t[i] = @elapsed (sol = solve(jump_prob, stepper)) end end @@ -32,7 +36,9 @@ end nsims = 50 benchmarks = Vector{Vector{Float64}}() for method in methods - jump_prob = JumpProblem(rn, prob, method, save_positions=(false, false)) + jump_prob = JumpProblem( + rn, u0, (0.0, tf), rates; aggregator = method, save_positions = (false, false) + ) stepper = SSAStepper() t = Vector{Float64}(undef, nsims) run_benchmark!(t, jump_prob, stepper) @@ -40,26 +46,27 @@ for method in methods end -medtimes = Vector{Float64}(undef,length(methods)) -stdtimes = Vector{Float64}(undef,length(methods)) -avgtimes = Vector{Float64}(undef,length(methods)) +medtimes = Vector{Float64}(undef, length(methods)) +stdtimes = Vector{Float64}(undef, length(methods)) +avgtimes = Vector{Float64}(undef, length(methods)) for i in 1:length(methods) medtimes[i] = median(benchmarks[i]) avgtimes[i] = mean(benchmarks[i]) stdtimes[i] = std(benchmarks[i]) end -df = DataFrame(names=shortlabels, medtimes=medtimes, relmedtimes=(medtimes/medtimes[1]), - avgtimes=avgtimes, std=stdtimes, cv=stdtimes./avgtimes) +df = DataFrame( + names = shortlabels, medtimes = medtimes, relmedtimes = (medtimes / medtimes[1]), + avgtimes = avgtimes, std = stdtimes, cv = stdtimes ./ avgtimes +) -sa = [string(round(mt,digits=4),"s") for mt in df.medtimes] -bar(df.names, df.relmedtimes, legend=:false) -scatter!(df.names, .05 .+ df.relmedtimes, markeralpha=0, series_annotations=sa) +sa = [string(round(mt, digits = 4), "s") for mt in df.medtimes] +bar(df.names, df.relmedtimes, legend = :false) +scatter!(df.names, 0.05 .+ df.relmedtimes, markeralpha = 0, series_annotations = sa) ylabel!("median relative to Direct") title!("256 Site 1D Diffusion CTRW") using SciMLBenchmarks -SciMLBenchmarks.bench_footer(WEAVE_ARGS[:folder],WEAVE_ARGS[:file]) - +SciMLBenchmarks.bench_footer(WEAVE_ARGS[:folder], WEAVE_ARGS[:file]) diff --git a/script/Jumps/EGFR_Benchmark.jl b/script/Jumps/EGFR_Benchmark.jl index e23f7cec2..3ba314e18 100644 --- a/script/Jumps/EGFR_Benchmark.jl +++ b/script/Jumps/EGFR_Benchmark.jl @@ -1,45 +1,54 @@ +using JumpProcesses, Plots, StableRNGs, BenchmarkTools, ReactionNetworkImporters, + StatsPlots, Catalyst -using JumpProcesses, Plots, StableRNGs, BenchmarkTools, ReactionNetworkImporters, StatsPlots, Catalyst - -tf = 12. +tf = 12.0 rng = StableRNG(53124) algs = [NRM(), CCNRM(), DirectCR(), RSSACR()] -egfr_net = loadrxnetwork(BNGNetwork(), joinpath(@__DIR__, "Data/egfr_net.net")); -dprob = DiscreteProblem(complete(egfr_net.rn), egfr_net.u0, (0., tf), egfr_net.p) -dprob = remake(dprob,u0=Int64.(dprob.u0)) +egfr_net = complete(loadrxnetwork(BNGNetwork(), joinpath(@__DIR__, "Data/egfr_net.net"))) +egfr_u0 = Catalyst.get_u0_map(egfr_net) +egfr_parameters = Catalyst.get_parameter_map(egfr_net) -plt = plot(title="Dimer concentrations") +plt = plot(title = "Dimer concentrations") for alg in algs - jprob = JumpProblem(complete(egfr_net.rn), dprob, alg) - sol = solve(jprob, SSAStepper(), saveat = tf/200) - plot!(plt, sol, idxs = :Dimers, label="$alg") + jprob = JumpProblem( + egfr_net, egfr_u0, (0.0, tf), egfr_parameters; + aggregator = alg, u0_eltype = Int64 + ) + sol = solve(jprob, SSAStepper(), saveat = tf / 200) + plot!(plt, sol, idxs = :Dimers, label = "$alg") end plot!(plt) function benchmark_and_bar_plot(model, end_time, algs) times = Vector{Float64}() - alg_names = ["$s"[15:end-2] for s in algs] + alg_names = ["$s"[15:(end - 2)] for s in algs] + u0 = Catalyst.get_u0_map(model) + parameters = Catalyst.get_parameter_map(model) benchmarks = Vector{BenchmarkTools.Trial}(undef, length(algs)) for (i, alg) in enumerate(algs) alg_name = alg_names[i] println("Benchmarking $alg_name") - dprob = DiscreteProblem(complete(model.rn), model.u0, (0., end_time), model.p) - dprob = remake(dprob,u0 = Int64.(dprob.u0)) - jprob = JumpProblem(complete(model.rn), dprob, alg; rng, save_positions = (false, false)) + jprob = JumpProblem( + model, u0, (0.0, end_time), parameters; + aggregator = alg, rng, save_positions = (false, false), u0_eltype = Int64 + ) b = @benchmarkable solve($jprob; saveat = $end_time) samples = 5 seconds = 7200 bm = run(b) - push!(times, median(bm).time/1e9) + push!(times, median(bm).time / 1.0e9) end - bar(alg_names, times, xlabel = "Algorithm", ylabel = "Average Time (s)", title = "SSA Runtime for EGFR network", legend = false) + return bar( + alg_names, times, xlabel = "Algorithm", ylabel = "Average Time (s)", + title = "SSA Runtime for EGFR network", legend = false + ) end -tf = 12. +tf = 12.0 rng = StableRNG(53124) algs = [NRM(), CCNRM(), DirectCR(), RSSACR()] @@ -49,4 +58,3 @@ plt using SciMLBenchmarks SciMLBenchmarks.bench_footer(WEAVE_ARGS[:folder], WEAVE_ARGS[:file]) - diff --git a/script/Jumps/Mendes_multistate_example.jl b/script/Jumps/Mendes_multistate_example.jl index 5b4f83955..e6dc66fa7 100644 --- a/script/Jumps/Mendes_multistate_example.jl +++ b/script/Jumps/Mendes_multistate_example.jl @@ -1,52 +1,56 @@ - using Catalyst, JumpProcesses, JumpProblemLibrary, Plots, Statistics fmt = :png jprob = JumpProblemLibrary.prob_jump_multistate -rn = jprob.network +rn = jprob.network reactions(rn) -methods = (Direct(), FRM(), SortingDirect(), NRM(), DirectCR(), RSSA(), RSSACR(), Coevolve(), RDirect()) -shortlabels = [string(leg)[15:end-2] for leg in methods] -tf = 10.0 * jprob.tstop -prob = DiscreteProblem(rn, jprob.u0, (0.0, tf), jprob.rates) +methods = ( + Direct(), FRM(), SortingDirect(), NRM(), DirectCR(), + RSSA(), RSSACR(), Coevolve(), RDirect(), +) +shortlabels = [string(leg)[15:(end - 2)] for leg in methods] +tf = 10.0 * jprob.tstop varlegs = ["A_P" "A_bound_P" "A_unbound_P" "RLA_P"] @variables t S7(t) S8(t) S9(t) varsyms = [ - [S7,S8,S9], + [S7, S8, S9], [S9], - [S7,S8], - [S7] + [S7, S8], + [S7], ] varidxs = [] for vars in varsyms - push!(varidxs, [findfirst(isequal(sym),unknowns(rn)) for sym in vars]) + push!(varidxs, [findfirst(isequal(sym), unknowns(rn)) for sym in vars]) end p = [] -for (i,method) in enumerate(methods) - jump_prob = JumpProblem(rn, prob, method, save_positions=(false, false)) - sol = solve(jump_prob, SSAStepper(), saveat=tf/1000.) +for (i, method) in enumerate(methods) + jump_prob = JumpProblem( + rn, jprob.u0, (0.0, tf), jprob.rates; + aggregator = method, save_positions = (false, false) + ) + sol = solve(jump_prob, SSAStepper(), saveat = tf / 1000.0) solv = zeros(1001, 4) - for (i,varidx) in enumerate(varidxs) - solv[:,i] = sum(sol[varidx,:], dims=1) + for (i, varidx) in enumerate(varidxs) + solv[:, i] = sum(sol[varidx, :], dims = 1) end if i < length(methods) - push!(p, plot(sol.t, solv, title=shortlabels[i], legend=false, format=fmt)) + push!(p, plot(sol.t, solv, title = shortlabels[i], legend = false, format = fmt)) else - push!(p, plot(sol.t, solv, title=shortlabels[i], legend=false, format=fmt)) + push!(p, plot(sol.t, solv, title = shortlabels[i], legend = false, format = fmt)) end end -push!(p, plot((1:4)', framestyle = :none, legend=:inside, labels=varlegs)) -plot(p..., layout=(6,2), format=fmt) +push!(p, plot((1:4)', framestyle = :none, legend = :inside, labels = varlegs)) +plot(p..., layout = (6, 2), format = fmt) function run_benchmark!(t, jump_prob, stepper) sol = solve(jump_prob, stepper) - @inbounds for i in 1:length(t) + return @inbounds for i in 1:length(t) t[i] = @elapsed (sol = solve(jump_prob, stepper)) end end @@ -55,7 +59,10 @@ end nsims = 100 benchmarks = Vector{Vector{Float64}}() for method in methods - jump_prob = JumpProblem(rn, prob, method, save_positions=(false, false)) + jump_prob = JumpProblem( + rn, jprob.u0, (0.0, tf), jprob.rates; + aggregator = method, save_positions = (false, false) + ) stepper = SSAStepper() time = Vector{Float64}(undef, nsims) run_benchmark!(time, jump_prob, stepper) @@ -63,9 +70,9 @@ for method in methods end -medtimes = Vector{Float64}(undef,length(methods)) -stdtimes = Vector{Float64}(undef,length(methods)) -avgtimes = Vector{Float64}(undef,length(methods)) +medtimes = Vector{Float64}(undef, length(methods)) +stdtimes = Vector{Float64}(undef, length(methods)) +avgtimes = Vector{Float64}(undef, length(methods)) for i in 1:length(methods) medtimes[i] = median(benchmarks[i]) avgtimes[i] = mean(benchmarks[i]) @@ -73,16 +80,19 @@ for i in 1:length(methods) end using DataFrames -df = DataFrame(names=shortlabels, medtimes=medtimes, relmedtimes=(medtimes/medtimes[1]), - avgtimes=avgtimes, std=stdtimes, cv=stdtimes./avgtimes) +df = DataFrame( + names = shortlabels, medtimes = medtimes, relmedtimes = (medtimes / medtimes[1]), + avgtimes = avgtimes, std = stdtimes, cv = stdtimes ./ avgtimes +) -sa = [text(string(round(mt,digits=3),"s"),:center,12) for mt in df.medtimes] -bar(df.names,df.relmedtimes,legend=:false, fmt=fmt) -scatter!(df.names, .05 .+ df.relmedtimes, markeralpha=0, series_annotations=sa, fmt=fmt) +sa = [text(string(round(mt, digits = 3), "s"), :center, 12) for mt in df.medtimes] +bar(df.names, df.relmedtimes, legend = :false, fmt = fmt) +scatter!( + df.names, 0.05 .+ df.relmedtimes, markeralpha = 0, series_annotations = sa, fmt = fmt +) ylabel!("median relative to Direct") title!("Multistate Model") using SciMLBenchmarks -SciMLBenchmarks.bench_footer(WEAVE_ARGS[:folder],WEAVE_ARGS[:file]) - +SciMLBenchmarks.bench_footer(WEAVE_ARGS[:folder], WEAVE_ARGS[:file]) diff --git a/script/Jumps/MultivariateHawkes.jl b/script/Jumps/MultivariateHawkes.jl deleted file mode 100644 index d9a0728a8..000000000 --- a/script/Jumps/MultivariateHawkes.jl +++ /dev/null @@ -1,719 +0,0 @@ - -using JumpProcesses, Graphs, Statistics, BenchmarkTools, Plots -using OrdinaryDiffEq: Tsit5 -fmt = :png -width_px, height_px = default(:size); - - -function hawkes_rate(i::Int, g; use_recursion = false) - - @inline @inbounds function rate_recursion(u, p, t) - λ, α, β, h, urate, ϕ = p - urate[i] = λ + exp(-β*(t - h[i]))*ϕ[i] - return urate[i] - end - - @inline @inbounds function rate_brute(u, p, t) - λ, α, β, h, urate = p - x = zero(typeof(t)) - for j in g[i] - for _t in reverse(h[j]) - ϕij = α * exp(-β * (t - _t)) - if ϕij ≈ 0 - break - end - x += ϕij - end - end - urate[i] = λ + x - return urate[i] - end - - if use_recursion - return rate_recursion - else - return rate_brute - end - -end - - -function hawkes_jump(i::Int, g; use_recursion = false) - rate = hawkes_rate(i, g; use_recursion) - urate = rate - @inbounds rateinterval(u, p, t) = p[5][i] == p[1] ? typemax(t) : 2 / p[5][i] - @inbounds lrate(u, p, t) = p[1] - @inbounds function affect_recursion!(integrator) - λ, α, β, h, _, ϕ = integrator.p - for j in g[i] - ϕ[j] *= exp(-β*(integrator.t - h[j])) - ϕ[j] += α - h[j] = integrator.t - end - integrator.u[i] += 1 - end - @inbounds function affect_brute!(integrator) - push!(integrator.p[4][i], integrator.t) - integrator.u[i] += 1 - end - return VariableRateJump( - rate, - use_recursion ? affect_recursion! : affect_brute!; - lrate, - urate, - rateinterval, - ) -end - -function hawkes_jump(u, g; use_recursion = false) - return [hawkes_jump(i, g; use_recursion) for i = 1:length(u)] -end - - -function f!(du, u, p, t) - du .= 0 - nothing -end - -function hawkes_problem( - p, - agg; - u = [0.0], - tspan = (0.0, 50.0), - save_positions = (false, true), - g = [[1]], - use_recursion = false, -) - oprob = ODEProblem(f!, u, tspan, p) - jumps = hawkes_jump(u, g; use_recursion) - jprob = JumpProblem(oprob, agg, jumps...; save_positions = save_positions) - return jprob -end - - -function hawkes_problem( - p, - agg::Coevolve; - u = [0.0], - tspan = (0.0, 50.0), - save_positions = (false, true), - g = [[1]], - use_recursion = false, -) - dprob = DiscreteProblem(u, tspan, p) - jumps = hawkes_jump(u, g; use_recursion) - jprob = - JumpProblem(dprob, agg, jumps...; dep_graph = g, save_positions = save_positions) - return jprob -end - - -V = 10 -G = erdos_renyi(V, 0.2, seed = 9103) -g = [neighbors(G, i) for i = 1:nv(G)] - - -tspan = (0.0, 50.0) -u = [0.0 for i = 1:nv(G)] -p = (0.5, 0.1, 2.0) - - -algorithms = Tuple{Any, Any, Bool, String}[ - (Direct(), Tsit5(), false, "Direct (brute-force)"), - (Coevolve(), SSAStepper(), false, "Coevolve (brute-force)"), - (Direct(), Tsit5(), true, "Direct (recursive)"), - (Coevolve(), SSAStepper(), true, "Coevolve (recursive)"), -] - -let fig = [] - for (i, (algo, stepper, use_recursion, label)) in enumerate(algorithms) - @info label - if use_recursion - h = zeros(eltype(tspan), nv(G)) - urate = zeros(eltype(tspan), nv(G)) - ϕ = zeros(eltype(tspan), nv(G)) - _p = (p[1], p[2], p[3], h, ϕ, urate) - else - h = [eltype(tspan)[] for _ = 1:nv(G)] - urate = zeros(eltype(tspan), nv(G)) - _p = (p[1], p[2], p[3], h, urate) - end - jump_prob = hawkes_problem(_p, algo; u, tspan, g, use_recursion) - sol = solve(jump_prob, stepper) - push!(fig, plot(sol.t, sol[1:V, :]', title=label, legend=false, format=fmt)) - end - fig = plot(fig..., layout=(2,2), format=fmt, size=(width_px, 2*height_px/2)) -end - - -function hawkes_rate_simple_recursion(rate, xc, xd, p, t, issum::Bool) - λ, _, β, h, ϕ, g = p - for i in 1:length(g) - rate[i] = λ + exp(-β * (t - h[i])) * ϕ[i] - end - if issum - return sum(rate) - end - return 0.0 -end - -function hawkes_rate_simple_brute(rate, xc, xd, p, t, issum::Bool) - λ, α, β, h, g = p - for i in 1:length(g) - x = zero(typeof(t)) - for j in g[i] - for _t in reverse(h[j]) - ϕij = α * exp(-β * (t - _t)) - if ϕij ≈ 0 - break - end - x += ϕij - end - end - rate[i] = λ + x - end - if issum - return sum(rate) - end - return 0.0 -end - -function hawkes_affect_simple_recursion!(xc, xd, p, t, i::Int64) - _, α, β, h, ϕ, g = p - for j in g[i] - ϕ[j] *= exp(-β * (t - h[j])) - ϕ[j] += α - h[j] = t - end -end - -function hawkes_affect_simple_brute!(xc, xd, p, t, i::Int64) - push!(p[4][i], t) -end - - -function hawkes_drate_simple(dxc, xc, xd, p, t) - dxc .= 0 -end - - -import LinearAlgebra: I -using PiecewiseDeterministicMarkovProcesses -const PDMP = PiecewiseDeterministicMarkovProcesses - -struct PDMPCHVSimple end - -function hawkes_problem(p, - agg::PDMPCHVSimple; - u = [0.0], - tspan = (0.0, 50.0), - save_positions = (false, true), - g = [[1]], - use_recursion = true) - xd0 = Array{Int}(u) - xc0 = copy(u) - nu = one(eltype(xd0)) * I(length(xd0)) - if use_recursion - jprob = PDMPProblem(hawkes_drate_simple, hawkes_rate_simple_recursion, - hawkes_affect_simple_recursion!, nu, xc0, xd0, p, tspan) - else - jprob = PDMPProblem(hawkes_drate_simple, hawkes_rate_simple_brute, - hawkes_affect_simple_brute!, nu, xc0, xd0, p, tspan) - end - return jprob -end - -push!(algorithms, (PDMPCHVSimple(), CHV(Tsit5()), false, "PDMPCHVSimple (brute-force)")); -push!(algorithms, (PDMPCHVSimple(), CHV(Tsit5()), true, "PDMPCHVSimple (recursive)")); - - -function hawkes_drate_full(dxc, xc, xd, p, t) - λ, α, β, _, _, g = p - for i = 1:length(g) - dxc[i] = -β * (xc[i] - λ) - end -end - - -function hawkes_rate_full(rate, xc, xd, p, t, issum::Bool) - λ, α, β, _, _, g = p - if issum - return sum(@view(xc[1:length(g)])) - end - rate[1:length(g)] .= @view xc[1:length(g)] - return 0.0 -end - -function hawkes_affect_full!(xc, xd, p, t, i::Int64) - λ, α, β, _, _, g = p - for j in g[i] - xc[i] += α - end -end - - -struct PDMPCHVFull end - -function hawkes_problem( - p, - agg::PDMPCHVFull; - u = [0.0], - tspan = (0.0, 50.0), - save_positions = (false, true), - g = [[1]], - use_recursion = true, -) - xd0 = Array{Int}(u) - xc0 = [p[1] for i = 1:length(u)] - nu = one(eltype(xd0)) * I(length(xd0)) - jprob = PDMPProblem(hawkes_drate_full, hawkes_rate_full, hawkes_affect_full!, nu, xc0, xd0, p, tspan) - return jprob -end - -push!(algorithms, (PDMPCHVFull(), CHV(Tsit5()), true, "PDMPCHVFull")); - - -const BENCHMARK_PYTHON::Bool = tryparse(Bool, get(ENV, "SCIMLBENCHMARK_PYTHON", "true")) -const REBUILD_PYCALL::Bool = tryparse(Bool, get(ENV, "SCIMLBENCHMARK_REBUILD_PYCALL", "true")) - -struct PyTick end - -if BENCHMARK_PYTHON - if REBUILD_PYCALL - using Pkg, Conda - - # PyCall only works with Conda.ROOTENV - # tick requires python=3.8 - Conda.add("python=3.8", Conda.ROOTENV) - Conda.add("numpy", Conda.ROOTENV) - Conda.pip_interop(true, Conda.ROOTENV) - Conda.pip("install", "tick", Conda.ROOTENV) - - # rebuild PyCall to ensure it links to the python provided by Conda.jl - ENV["PYTHON"] = "" - Pkg.build("PyCall") - end - - ENV["PYTHON"] = "" - using PyCall - @info "PyCall" PyCall.libpython PyCall.pyversion PyCall.conda - - function hawkes_problem( - p, - agg::PyTick; - u = [0.0], - tspan = (0.0, 50.0), - save_positions = (false, true), - g = [[1]], - use_recursion = true, - ) - λ, α, β = p - SimuHawkesSumExpKernels = pyimport("tick.hawkes")[:SimuHawkesSumExpKernels] - jprob = SimuHawkesSumExpKernels( - baseline = fill(λ, length(u)), - adjacency = [i in j ? α / β : 0.0 for j in g, i = 1:length(u), u = 1:1], - decays = [β], - end_time = tspan[2], - verbose = false, - force_simulation = true, - ) - return jprob - end - - push!(algorithms, (PyTick(), nothing, true, "PyTick")); -end - - -let fig = [] - for (i, (algo, stepper, use_recursion, label)) in enumerate(algorithms[5:end]) - @info label - if algo isa PyTick - _p = (p[1], p[2], p[3]) - jump_prob = hawkes_problem(_p, algo; u, tspan, g, use_recursion) - jump_prob.reset() - jump_prob.simulate() - t = tspan[1]:0.1:tspan[2] - N = [[sum(jumps .< _t) for _t in t] for jumps in jump_prob.timestamps] - push!(fig, plot(t, N, title=label, legend=false, format=fmt)) - elseif algo isa PDMPCHVSimple - if use_recursion - h = zeros(eltype(tspan), nv(G)) - ϕ = zeros(eltype(tspan), nv(G)) - _p = (p[1], p[2], p[3], h, ϕ, g) - else - h = [eltype(tspan)[] for _ in 1:nv(G)] - _p = (p[1], p[2], p[3], h, g) - end - jump_prob = hawkes_problem(_p, algo; u, tspan, g, use_recursion) - sol = solve(jump_prob, stepper) - push!(fig, plot(sol.time, sol.xd[1:V, :]', title=label, legend=false, format=fmt)) - elseif algo isa PDMPCHVFull - _p = (p[1], p[2], p[3], nothing, nothing, g) - jump_prob = hawkes_problem(_p, algo; u, tspan, g, use_recursion) - sol = solve(jump_prob, stepper) - push!(fig, plot(sol.time, sol.xd[1:V, :]', title=label, legend=false, format=fmt)) - end - end - fig = plot(fig..., layout=(2,2), format=fmt, size=(width_px, 2*height_px/2)) -end - - -function hawkes_Λ(i::Int, g, p) - @inline @inbounds function Λ(t, h) - λ, α, β = p - x = λ * t - for j in g[i] - for _t in h[j] - if _t >= t - break - end - x += (α / β) * (1 - exp(-β * (t - _t))) - end - end - return x - end - return Λ -end - -function hawkes_Λ(g, p) - return [hawkes_Λ(i, g, p) for i = 1:length(g)] -end - -Λ = hawkes_Λ(g, p) - - -""" -Given an ODE solution `sol`, recover the timestamp in which events occurred. It -returns a vector with the history of each process in `sol`. - -It assumes that `JumpProblem` was initialized with `save_positions` equal to -`(true, false)`, `(false, true)` or `(true, true)` such the system's state is -saved before and/or after the jump occurs; and, that `sol.u` is a -non-decreasing series that counts the total number of events observed as a -function of time. -""" -function histories(u, t) - _u = permutedims(reduce(hcat, u)) - k = size(_u)[2] - # computes a mask that show when total counts change - mask = cat(fill(0.0, 1, k), _u[2:end, :] .- _u[1:end-1, :], dims = 1) .≈ 1 - h = Vector{typeof(t)}(undef, k) - @inbounds for i = 1:k - h[i] = t[mask[:, i]] - end - return h -end - -function histories(sol::S) where {S<:ODESolution} - # get u and permute the dimensions to get a matrix n x k with n obsevations and k processes. - if sol.u[1] isa ExtendedJumpArray - u = map((u) -> u.u, sol.u) - else - u = sol.u - end - return histories(u, sol.t) -end - -function histories(sol::S) where {S<:PDMP.PDMPResult} - return histories(sol.xd.u, sol.time) -end - -function histories(sols) - map(histories, sols) -end - - -import Distributions: Exponential - -""" -Computes the empirical and expected quantiles given a history of events `hs`, -the compensator `Λ` and the target quantiles `quant`. - -The history `hs` is a vector with the history of each process. Alternatively, -the function also takes a vector of histories containing the histories from -multiple runs. - -The compensator `Λ` can either be an homogeneous compensator function that -equally applies to all the processes in `hs`. Alternatively, it accepts a -vector of compensator that applies to each process. -""" -function qq(hs, Λ, quant = 0.01:0.01:0.99) - _hs = apply_Λ(hs, Λ) - T = typeof(hs[1][1][1]) - Δs = Vector{Vector{T}}(undef, length(hs[1])) - for k = 1:length(Δs) - _Δs = Vector{Vector{T}}(undef, length(hs)) - for i = 1:length(_Δs) - _Δs[i] = _hs[i][k][2:end] .- _hs[i][k][1:end-1] - end - Δs[k] = reduce(vcat, _Δs) - end - empirical_quant = map((_Δs) -> quantile(_Δs, quant), Δs) - expected_quant = quantile(Exponential(1.0), quant) - return empirical_quant, expected_quant -end - -""" -Compute the compensator `Λ` value for each timestamp recorded in history `hs`. - -The history `hs` is a vector with the history of each process. Alternatively, -the function also takes a vector of histories containing the histories from -multiple runs. - -The compensator `Λ` can either be an homogeneous compensator function that -equally applies to all the processes in `hs`. Alternatively, it accepts a -vector of compensator that applies to each process. -""" -function apply_Λ(hs::V, Λ) where {V<:Vector{<:Number}} - _hs = similar(hs) - @inbounds for n = 1:length(hs) - _hs[n] = Λ(hs[n], hs) - end - return _hs -end - -function apply_Λ(k::Int, hs::V, Λ::A) where {V<:Vector{<:Vector{<:Number}},A<:Array} - @inbounds hsk = hs[k] - @inbounds Λk = Λ[k] - _hs = similar(hsk) - @inbounds for n = 1:length(hsk) - _hs[n] = Λk(hsk[n], hs) - end - return _hs -end - -function apply_Λ(hs::V, Λ) where {V<:Vector{<:Vector{<:Number}}} - _hs = similar(hs) - @inbounds for k = 1:length(_hs) - _hs[k] = apply_Λ(hs[k], Λ) - end - return _hs -end - -function apply_Λ(hs::V, Λ::A) where {V<:Vector{<:Vector{<:Number}},A<:Array} - _hs = similar(hs) - @inbounds for k = 1:length(_hs) - _hs[k] = apply_Λ(k, hs, Λ) - end - return _hs -end - -function apply_Λ(hs::V, Λ) where {V<:Vector{<:Vector{<:Vector{<:Number}}}} - return map((_hs) -> apply_Λ(_hs, Λ), hs) -end - - -@userplot QQPlot -@recipe function f(x::QQPlot) - empirical_quant, expected_quant = x.args - max_empirical_quant = maximum(maximum, empirical_quant) - max_expected_quant = maximum(expected_quant) - upperlim = ceil(maximum([max_empirical_quant, max_expected_quant])) - @series begin - seriestype := :line - linecolor := :lightgray - label --> "" - (x) -> x - end - @series begin - seriestype := :scatter - aspect_ratio := :equal - xlims := (0.0, upperlim) - ylims := (0.0, upperlim) - xaxis --> "Expected" - yaxis --> "Empirical" - markerstrokewidth --> 0 - markerstrokealpha --> 0 - markersize --> 1.5 - size --> (400, 500) - label --> permutedims(["quantiles $i" for i = 1:length(empirical_quant)]) - expected_quant, empirical_quant - end -end - - -let fig = [] - for (i, (algo, stepper, use_recursion, label)) in enumerate(algorithms) - @info label - if algo isa PyTick - _p = (p[1], p[2], p[3]) - elseif algo isa PDMPCHVSimple - if use_recursion - h = zeros(eltype(tspan), nv(G)) - ϕ = zeros(eltype(tspan), nv(G)) - _p = (p[1], p[2], p[3], h, ϕ, g) - else - h = [eltype(tspan)[] for _ in 1:nv(G)] - _p = (p[1], p[2], p[3], h, g) - end - elseif algo isa PDMPCHVFull - _p = (p[1], p[2], p[3], nothing, nothing, g) - else - if use_recursion - h = zeros(eltype(tspan), nv(G)) - ϕ = zeros(eltype(tspan), nv(G)) - urate = zeros(eltype(tspan), nv(G)) - _p = (p[1], p[2], p[3], h, urate, ϕ) - else - h = [eltype(tspan)[] for _ = 1:nv(G)] - urate = zeros(eltype(tspan), nv(G)) - _p = (p[1], p[2], p[3], h, urate) - end - end - jump_prob = hawkes_problem(_p, algo; u, tspan, g, use_recursion) - runs = Vector{Vector{Vector{Number}}}(undef, 250) - for n = 1:length(runs) - if algo isa PyTick - jump_prob.reset() - jump_prob.simulate() - runs[n] = jump_prob.timestamps - else - if ~(algo isa PDMPCHVFull) - if use_recursion - h .= 0 - ϕ .= 0 - else - for _h in h empty!(_h) end - end - if ~(algo isa PDMPCHVSimple) - urate .= 0 - end - end - runs[n] = histories(solve(jump_prob, stepper)) - end - end - qqs = qq(runs, Λ) - push!(fig, qqplot(qqs..., legend = false, aspect_ratio = :equal, title=label, fmt=fmt)) - end - fig = plot(fig..., layout = (4, 2), fmt=fmt, size=(width_px, 4*height_px/2)) -end - - -tspan = (0.0, 25.0) -p = (0.5, 0.1, 5.0) -Vs = append!([1], 5:5:95) -Gs = [erdos_renyi(V, 0.2, seed = 6221) for V in Vs] - -bs = Vector{Vector{BenchmarkTools.Trial}}() - -for (algo, stepper, use_recursion, label) in algorithms - @info label - global _stepper = stepper - push!(bs, Vector{BenchmarkTools.Trial}()) - _bs = bs[end] - for (i, G) in enumerate(Gs) - local g = [neighbors(G, i) for i = 1:nv(G)] - local u = [0.0 for i = 1:nv(G)] - if algo isa PyTick - _p = (p[1], p[2], p[3]) - elseif algo isa PDMPCHVSimple - if use_recursion - global h = zeros(eltype(tspan), nv(G)) - global ϕ = zeros(eltype(tspan), nv(G)) - _p = (p[1], p[2], p[3], h, ϕ, g) - else - global h = [eltype(tspan)[] for _ in 1:nv(G)] - _p = (p[1], p[2], p[3], h, g) - end - elseif algo isa PDMPCHVFull - _p = (p[1], p[2], p[3], nothing, nothing, g) - else - if use_recursion - global h = zeros(eltype(tspan), nv(G)) - global urate = zeros(eltype(tspan), nv(G)) - global ϕ = zeros(eltype(tspan), nv(G)) - _p = (p[1], p[2], p[3], h, urate, ϕ) - else - global h = [eltype(tspan)[] for _ = 1:nv(G)] - global urate = zeros(eltype(tspan), nv(G)) - _p = (p[1], p[2], p[3], h, urate) - end - end - global jump_prob = hawkes_problem(_p, algo; u, tspan, g, use_recursion) - trial = try - if algo isa PyTick - @benchmark( - jump_prob.simulate(), - setup = (jump_prob.reset()), - samples = 50, - evals = 1, - seconds = 10, - ) - else - if algo isa PDMPCHVFull - @benchmark( - solve(jump_prob, _stepper), - setup = (), - samples = 50, - evals = 1, - seconds = 10, - ) - elseif algo isa PDMPCHVSimple - if use_recursion - @benchmark(solve(jump_prob, _stepper), - setup=(h .= 0; ϕ .= 0), - samples=50, - evals=1, - seconds=10,) - else - @benchmark(solve(jump_prob, _stepper), - setup=([empty!(_h) for _h in h]), - samples=50, - evals=1, - seconds=10,) - end - else - if use_recursion - @benchmark( - solve(jump_prob, _stepper), - setup = (h .= 0; urate .= 0; ϕ .= 0), - samples = 50, - evals = 1, - seconds = 10, - ) - else - @benchmark( - solve(jump_prob, _stepper), - setup = ([empty!(_h) for _h in h]; urate .= 0), - samples = 50, - evals = 1, - seconds = 10, - ) - end - end - end - catch e - BenchmarkTools.Trial( - BenchmarkTools.Parameters(samples = 50, evals = 1, seconds = 10), - ) - end - push!(_bs, trial) - if (nv(G) == 1 || nv(G) % 10 == 0) - median_time = - length(trial) > 0 ? "$(BenchmarkTools.prettytime(median(trial.times)))" : - "nan" - println("algo=$(label), V = $(nv(G)), length = $(length(trial.times)), median time = $median_time") - end - end -end - - -let fig = plot( - yscale = :log10, - xlabel = "V", - ylabel = "Time (ns)", - legend_position = :outertopright, -) - for (i, (algo, stepper, use_recursion, label)) in enumerate(algorithms) - _bs, _Vs = [], [] - for (j, b) in enumerate(bs[i]) - if length(b) == 50 - push!(_bs, median(b.times)) - push!(_Vs, Vs[j]) - end - end - plot!(_Vs, _bs, label=label) - end - title!("Simulations, 50 samples: nodes × time") -end - diff --git a/script/Jumps/NegFeedback_GeneExpr.jl b/script/Jumps/NegFeedback_GeneExpr.jl index ae6772407..34d7f8032 100644 --- a/script/Jumps/NegFeedback_GeneExpr.jl +++ b/script/Jumps/NegFeedback_GeneExpr.jl @@ -1,4 +1,3 @@ - using JumpProcesses, Catalyst, JumpProblemLibrary, Plots, Statistics import JumpProblemLibrary: prob_jump_dnarepressor fmt = :png @@ -8,22 +7,27 @@ rn = prob_jump_dnarepressor.network reactions(rn) -methods = (Direct(), FRM(), SortingDirect(), NRM(), DirectCR(), RSSA(), RSSACR(), Coevolve(), RDirect()) -shortlabels = [string(leg)[15:end-2] for leg in methods] -prob = prob_jump_dnarepressor.discrete_prob -tf = prob_jump_dnarepressor.tstop -ploth = plot(reuse=false) -for (i,method) in enumerate(methods) - jump_prob = JumpProblem(rn, prob, method, save_positions=(false, false)) - sol = solve(jump_prob, SSAStepper(), saveat=tf/1000.) - plot!(ploth,sol.t, sol[3,:], label=shortlabels[i], format=fmt) +methods = ( + Direct(), FRM(), SortingDirect(), NRM(), DirectCR(), + RSSA(), RSSACR(), Coevolve(), RDirect(), +) +shortlabels = [string(leg)[15:(end - 2)] for leg in methods] +tf = prob_jump_dnarepressor.tstop +ploth = plot(reuse = false) +for (i, method) in enumerate(methods) + jump_prob = JumpProblem( + rn, prob_jump_dnarepressor.u0, (0.0, tf), prob_jump_dnarepressor.rates; + aggregator = method, save_positions = (false, false) + ) + sol = solve(jump_prob, SSAStepper(), saveat = tf / 1000.0) + plot!(ploth, sol.t, sol[3, :], label = shortlabels[i], format = fmt) end -plot(ploth, title="Protein level", xlabel="time", format=fmt) +plot(ploth, title = "Protein level", xlabel = "time", format = fmt) function run_benchmark!(t, jump_prob, stepper) sol = solve(jump_prob, stepper) - @inbounds for i in 1:length(t) + return @inbounds for i in 1:length(t) t[i] = @elapsed (sol = solve(jump_prob, stepper)) end end @@ -32,9 +36,12 @@ end nsims = 2000 benchmarks = Vector{Vector{Float64}}() for method in methods - jump_prob = JumpProblem(rn, prob, method, save_positions=(false, false)) + jump_prob = JumpProblem( + rn, prob_jump_dnarepressor.u0, (0.0, tf), prob_jump_dnarepressor.rates; + aggregator = method, save_positions = (false, false) + ) stepper = SSAStepper() - t = Vector{Float64}(undef,nsims) + t = Vector{Float64}(undef, nsims) run_benchmark!(t, jump_prob, stepper) push!(benchmarks, t) end @@ -48,19 +55,22 @@ for i in 1:length(methods) avgtimes[i] = mean(benchmarks[i]) stdtimes[i] = std(benchmarks[i]) end -println(medtimes/medtimes[1]) +println(medtimes / medtimes[1]) using DataFrames -df = DataFrame(names=shortlabels, medtimes=medtimes, relmedtimes=(medtimes/medtimes[1]), - avgtimes=avgtimes, std=stdtimes, cv=stdtimes./avgtimes) -sa = [text(string(round(mt,sigdigits=2),"s"),:center,10) for mt in df.medtimes] -bar(df.names,df.relmedtimes,legend=:false, fmt=fmt) -scatter!(df.names, .05 .+ df.relmedtimes, markeralpha=0, series_annotations=sa, fmt=fmt) +df = DataFrame( + names = shortlabels, medtimes = medtimes, relmedtimes = (medtimes / medtimes[1]), + avgtimes = avgtimes, std = stdtimes, cv = stdtimes ./ avgtimes +) +sa = [text(string(round(mt, sigdigits = 2), "s"), :center, 10) for mt in df.medtimes] +bar(df.names, df.relmedtimes, legend = :false, fmt = fmt) +scatter!( + df.names, 0.05 .+ df.relmedtimes, markeralpha = 0, series_annotations = sa, fmt = fmt +) ylabel!("median relative to Direct") title!("Negative Feedback Gene Expression Model") using SciMLBenchmarks -SciMLBenchmarks.bench_footer(WEAVE_ARGS[:folder],WEAVE_ARGS[:file]) - +SciMLBenchmarks.bench_footer(WEAVE_ARGS[:folder], WEAVE_ARGS[:file]) diff --git a/script/Jumps/NegFeedback_GeneExpr_Marchetti.jl b/script/Jumps/NegFeedback_GeneExpr_Marchetti.jl index 05ffb0953..452e04a1d 100644 --- a/script/Jumps/NegFeedback_GeneExpr_Marchetti.jl +++ b/script/Jumps/NegFeedback_GeneExpr_Marchetti.jl @@ -1,4 +1,3 @@ - using OrdinaryDiffEq, Catalyst, JumpProcesses, JumpProblemLibrary, Plots, Statistics fmt = :png @@ -11,25 +10,30 @@ rn = jprob.network reactions(rn) -u0f = [1000., 0., 0., 0., 0.] -odeprob = ODEProblem(rn, u0f, (0.,tf), rnpar) +u0f = [variable => Float64(value) for (variable, value) in u0] +odeprob = ODEProblem(rn, u0f, (0.0, tf), rnpar) solution = solve(odeprob, Tsit5()) -plot(solution, format=fmt) +plot(solution, format = fmt) -tf = 4000. -methods = (Direct(), FRM(), SortingDirect(), NRM(), DirectCR(), RSSA(), RSSACR(), Coevolve(), RDirect()) -shortlabels = [string(leg)[15:end-2] for leg in methods] -prob = prob = DiscreteProblem(rn, u0, (0.0, tf), rnpar) -ploth = plot(reuse=false) +tf = 4000.0 +methods = ( + Direct(), FRM(), SortingDirect(), NRM(), DirectCR(), + RSSA(), RSSACR(), Coevolve(), RDirect(), +) +shortlabels = [string(leg)[15:(end - 2)] for leg in methods] +ploth = plot(reuse = false) p = [] -for (i,method) in enumerate(methods) - jump_prob = JumpProblem(rn, prob, method, save_positions=(false, false)) - sol = solve(jump_prob, SSAStepper(), saveat=tf/1000.) - plot!(ploth, sol.t, sol[3,:], label=shortlabels[i], format=fmt) - push!(p, plot(sol, title=shortlabels[i], format=fmt)) +for (i, method) in enumerate(methods) + jump_prob = JumpProblem( + rn, u0, (0.0, tf), rnpar; + aggregator = method, save_positions = (false, false) + ) + sol = solve(jump_prob, SSAStepper(), saveat = tf / 1000.0) + plot!(ploth, sol.t, sol[3, :], label = shortlabels[i], format = fmt) + push!(p, plot(sol, title = shortlabels[i], format = fmt)) end -plot(ploth, title="Protein level", xlabel="time", format=fmt) +plot(ploth, title = "Protein level", xlabel = "time", format = fmt) plot(p[end]) @@ -37,7 +41,7 @@ plot(p[end]) function run_benchmark!(t, jump_prob, stepper) sol = solve(jump_prob, stepper) - @inbounds for i in 1:length(t) + return @inbounds for i in 1:length(t) t[i] = @elapsed (sol = solve(jump_prob, stepper)) end end @@ -46,7 +50,10 @@ end nsims = 200 benchmarks = Vector{Vector{Float64}}() for method in methods - jump_prob = JumpProblem(rn, prob, method, save_positions=(false, false)) + jump_prob = JumpProblem( + rn, u0, (0.0, tf), rnpar; + aggregator = method, save_positions = (false, false) + ) stepper = SSAStepper() t = Vector{Float64}(undef, nsims) run_benchmark!(t, jump_prob, stepper) @@ -64,15 +71,18 @@ for i in 1:length(methods) end using DataFrames -df = DataFrame(names=shortlabels, medtimes=medtimes, relmedtimes=(medtimes/medtimes[1]), - avgtimes=avgtimes, std=stdtimes, cv=stdtimes./avgtimes) -sa = [text(string(round(mt,digits=3),"s"),:center,12) for mt in df.medtimes] -bar(df.names,df.relmedtimes,legend=:false, fmt=fmt) -scatter!(df.names, .05 .+ df.relmedtimes, markeralpha=0, series_annotations=sa, fmt=fmt) +df = DataFrame( + names = shortlabels, medtimes = medtimes, relmedtimes = (medtimes / medtimes[1]), + avgtimes = avgtimes, std = stdtimes, cv = stdtimes ./ avgtimes +) +sa = [text(string(round(mt, digits = 3), "s"), :center, 12) for mt in df.medtimes] +bar(df.names, df.relmedtimes, legend = :false, fmt = fmt) +scatter!( + df.names, 0.05 .+ df.relmedtimes, markeralpha = 0, series_annotations = sa, fmt = fmt +) ylabel!("median relative to Direct") title!("Marchetti Gene Expression Model") using SciMLBenchmarks -SciMLBenchmarks.bench_footer(WEAVE_ARGS[:folder],WEAVE_ARGS[:file]) - +SciMLBenchmarks.bench_footer(WEAVE_ARGS[:folder], WEAVE_ARGS[:file]) diff --git a/script/Jumps/Spatial_Signaling_Sanft.jl b/script/Jumps/Spatial_Signaling_Sanft.jl index 8e511a95b..3e49a9c6c 100644 --- a/script/Jumps/Spatial_Signaling_Sanft.jl +++ b/script/Jumps/Spatial_Signaling_Sanft.jl @@ -1,5 +1,5 @@ - using Catalyst, JumpProcesses, BenchmarkTools, Plots, Random +using SymbolicIndexingInterface: parameter_values invmicromolar_to_cubicmicrometer(invconcen) = invconcen / (6.02214076e2) @@ -10,10 +10,10 @@ rn = @reaction_network begin @parameters k₁ ka kd k₄ k₁, EA --> EA + A k₁, EB --> EB + B - (ka,kd), EA + B <--> EAB - (ka,kd), EAB + B <--> EAB₂ - (ka,kd), EB + A <--> EBA - (ka,kd), EBA + A <--> EBA₂ + (ka, kd), EA + B <--> EAB + (ka, kd), EAB + B <--> EAB₂ + (ka, kd), EB + A <--> EBA + (ka, kd), EBA + A <--> EBA₂ k₄, A --> ∅ k₄, B --> ∅ end @@ -44,7 +44,7 @@ function transport_model(rn, N; domain_len = 6.0, D = 1.0, rng = Random.default_ # spatial initial condition # initial concentration of 12.3 nM = 12.3 * 1e-3 μM - num_molecules = trunc(Int, micromolar_to_invcubicmicrometer(12.3*1e-3) * (domain_len^3)) + num_molecules = trunc(Int, micromolar_to_invcubicmicrometer(12.3 * 1.0e-3) * (domain_len^3)) u0 = zeros(Int, 8, num_nodes) rand_EA = rand(rng, 1:num_nodes, num_molecules) rand_EB = rand(rng, 1:num_nodes, num_molecules) @@ -53,55 +53,63 @@ function transport_model(rn, N; domain_len = 6.0, D = 1.0, rng = Random.default_ u0[EBidx, rand_EB[i]] += 1 end - grid, hopping_constants, h, u0 + return grid, hopping_constants, h, u0 end function wellmixed_model(rn, u0, end_time, h) kaval = invmicromolar_to_cubicmicrometer(46.2) / h^3 - setdefaults!(rn, [:k₁ => 150, :ka => kaval, :kd => 3.82, :k₄ => 6.0]) + parameters = [:k₁ => 150, :ka => kaval, :kd => 3.82, :k₄ => 6.0] # well-mixed initial condition corresponding to the spatial initial condition - u0wm = sum(u0, dims = 2) - dprobwm = DiscreteProblem(rn, u0wm, (0.0, end_time)) - jprobwm = JumpProblem(rn, dprobwm, Direct(), save_positions = (false,false)) + u0wm = species(rn) .=> vec(sum(u0, dims = 2)) + jprobwm = JumpProblem( + rn, u0wm, (0.0, end_time), parameters; + aggregator = Direct(), save_positions = (false, false) + ) majumps = jprobwm.massaction_jump - majumps, dprobwm, jprobwm, u0wm + return majumps, parameter_values(jprobwm), jprobwm, u0wm end end_time = 3.0 grid, hopping_constants, h, u0 = transport_model(rn, 60) -majumps, dprobwm, jprobwm, u0wm = wellmixed_model(rn, u0, end_time, 6.0) -sol = solve(jprobwm, SSAStepper(); saveat = end_time/200) +majumps, parameters_wm, jprobwm, u0wm = wellmixed_model(rn, u0, end_time, 6.0) +sol = solve(jprobwm, SSAStepper(); saveat = end_time / 200) Ntot = [sum(u) for u in sol.u] -plt = plot(sol.t, Ntot, label="Well-mixed", ylabel="Total Number of Molecules", - xlabel="time") +plt = plot( + sol.t, Ntot, label = "Well-mixed", ylabel = "Total Number of Molecules", + xlabel = "time" +) # spatial model -majumps, dprobwm, jprobwm, u0wm = wellmixed_model(rn, u0, end_time, h) -dprob = DiscreteProblem(u0, (0.0, end_time), copy(dprobwm.p)) -jprob = JumpProblem(dprob, DirectCRDirect(), majumps; hopping_constants, - spatial_system = grid, save_positions = (false, false)) -spatial_sol = solve(jprob, SSAStepper(); saveat = end_time/200) +majumps, parameters_wm, jprobwm, u0wm = wellmixed_model(rn, u0, end_time, h) +dprob = DiscreteProblem(u0, (0.0, end_time), copy(parameters_wm)) +jprob = JumpProblem( + dprob, DirectCRDirect(), majumps; hopping_constants, + spatial_system = grid, save_positions = (false, false) +) +spatial_sol = solve(jprob, SSAStepper(); saveat = end_time / 200) Ntot = [sum(vec(u)) for u in spatial_sol.u] -plot!(plt, spatial_sol.t, Ntot, label="Spatial", - title="Steady-state number of molecules is $(Ntot[end])") +plot!( + plt, spatial_sol.t, Ntot, label = "Spatial", + title = "Steady-state number of molecules is $(Ntot[end])" +) -@Base.kwdef mutable struct EventCallback +Base.@kwdef mutable struct EventCallback n::Int = 0 end function (ecb::EventCallback)(u, t, integ) ecb.n += 1 - ecb.n == 10^8 + return ecb.n == 10^8 end function (ecb::EventCallback)(integ) # save the final state terminate!(integ) - nothing + return nothing end @@ -113,15 +121,15 @@ function benchmark_and_save!(bench_dict, end_times, Nv, algs, domain_len) cb = DiscreteCallback(ecb, ecb) for (end_time, N) in zip(end_times, Nv) - names = ["$s"[1:end-2] for s in algs] + names = ["$s"[1:(end - 2)] for s in algs] grid, hopping_constants, h, u0 = transport_model(rn, N; domain_len) # we create a well-mixed model within a domain of the size of *one* voxel, h - majumps, dprobwm, jprobwm, u0wm = wellmixed_model(rn, u0, end_time, h) + majumps, parameters_wm, jprobwm, u0wm = wellmixed_model(rn, u0, end_time, h) # the spatial problem - dprob = DiscreteProblem(u0, (0.0, end_time), copy(dprobwm.p)) + dprob = DiscreteProblem(u0, (0.0, end_time), copy(parameters_wm)) @show N @@ -133,12 +141,15 @@ function benchmark_and_save!(bench_dict, end_times, Nv, algs, domain_len) for (i, alg) in enumerate(algs) name = names[i] println("benchmarking $name") - jp = JumpProblem(dprob, alg, majumps, hopping_constants=hopping_constants, - spatial_system = grid, save_positions=(false,false)) - b = @benchmarkable solve($jp, SSAStepper(); saveat = $(dprob.tspan[2]), callback) setup = (callback = deepcopy($cb)) samples = 10 seconds = 3600 + jp = JumpProblem( + dprob, alg, majumps, hopping_constants = hopping_constants, + spatial_system = grid, save_positions = (false, false) + ) + b = @benchmarkable solve($jp, SSAStepper(); saveat = $(dprob.tspan[2]), callback) setup = (callback = deepcopy($cb)) samples = 3 seconds = 300 bench_dict[name, N] = run(b) end end + return end @@ -150,25 +161,31 @@ function fetch_and_plot(bench_dict, domain_len) plt2 = plot() medtimes = [Float64[] for i in 1:length(names)] - for (i,name) in enumerate(names) + for (i, name) in enumerate(names) for N in Nv try - push!(medtimes[i], median(bench_dict[name, N]).time/1e9) + push!(medtimes[i], median(bench_dict[name, N]).time / 1.0e9) catch break end end len = length(medtimes[i]) plot!(plt1, Nv[1:len], medtimes[i], marker = :hex, label = name, lw = 2) - plot!(plt2, (Nv.^3)[1:len], medtimes[i], marker = :hex, label = name, lw = 2) + plot!(plt2, (Nv .^ 3)[1:len], medtimes[i], marker = :hex, label = name, lw = 2) end - plot!(plt1, xlabel = "number of sites per edge", ylabel = "median time in seconds", - xticks = Nv, legend = :bottomright) - plot!(plt2, xlabel = "total number of sites", ylabel = "median time in seconds", - xticks = (Nv.^3, string.(Nv.^3)), legend = :bottomright) - plot(plt1, plt2; size = (1200,800), legendtitle = "SSAs", - plot_title="3D RDME, domain length = $domain_len", left_margin=5Plots.mm) + plot!( + plt1, xlabel = "number of sites per edge", ylabel = "median time in seconds", + xticks = Nv, legend = :bottomright + ) + plot!( + plt2, xlabel = "total number of sites", ylabel = "median time in seconds", + xticks = (Nv .^ 3, string.(Nv .^ 3)), legend = :bottomright + ) + return plot( + plt1, plt2; size = (1200, 800), legendtitle = "SSAs", + plot_title = "3D RDME, domain length = $domain_len", left_margin = 5Plots.mm + ) end @@ -180,7 +197,7 @@ domain_len = 12.0 benchmark_and_save!(bench_dict, end_times, Nv, algs, domain_len) -plt=fetch_and_plot(bench_dict, domain_len) +plt = fetch_and_plot(bench_dict, domain_len) bench_dict = Dict{Tuple{String, Int}, BenchmarkTools.Trial}() @@ -188,9 +205,8 @@ domain_len = 6.0 benchmark_and_save!(bench_dict, end_times, Nv, algs, domain_len) -plt=fetch_and_plot(bench_dict, domain_len) +plt = fetch_and_plot(bench_dict, domain_len) using SciMLBenchmarks SciMLBenchmarks.bench_footer(WEAVE_ARGS[:folder], WEAVE_ARGS[:file]) - diff --git a/script/Jumps/Synapse.jl b/script/Jumps/Synapse.jl deleted file mode 100644 index 8ed110369..000000000 --- a/script/Jumps/Synapse.jl +++ /dev/null @@ -1,120 +0,0 @@ - -using Synapse -using PiecewiseDeterministicMarkovProcesses, JumpProcesses, OrdinaryDiffEq, Plots -using BenchmarkTools -fmt = :png - - -p_synapse = SynapseParams(t_end = 1000.0); -glu = 0.0; -events_sorted_times = [500.0]; -is_pre_or_post_event = [true]; -events_bap = events_sorted_times[is_pre_or_post_event.==false]; -bap_by_epsp = Float64[]; -nu = buildTransitionMatrix(); - - -xc0 = initial_conditions_continuous_temp(p_synapse); -xd0 = initial_conditions_discrete(p_synapse); - - -solver = AutoTsit5(Rosenbrock23()); -algorithms = [ - ( - label = "PDMP", - agg = nothing, - solver = (CHV(solver), CHV(solver)), - saveat = [], - ), - ( - label = "Coevolve", - agg = Coevolve(), - solver = (solver, solver), - saveat = 1 / p_synapse.sampling_rate, - ), -]; - - -results = [] - -for algo in algorithms - push!( - results, - evolveSynapse( - xc0, - xd0, - p_synapse, - events_sorted_times, - is_pre_or_post_event, - bap_by_epsp, - [true], - nu, - algo.solver, - algo.agg; - save_positions = (false, true), - saveat = algo.saveat, - save_everystep = false, - ), - ) -end - - -fig = plot(xlabel = "Voltage", ylabel = "Time"); -for (i, algo) in enumerate(algorithms) - res = results[i] - plot!(res.t, res.Vsp, label = algo.label) -end -title!("Vsp") - - -fig = plot(xlabel = "N", ylabel = "Time"); -for (i, algo) in enumerate(algorithms) - res = results[i] - plot!(res.t, res.XD[1, :], label = algo.label) -end -title!("2line-Go, AMPA") - - -bs = Vector{BenchmarkTools.Trial}() - -for algo in algorithms - push!( - bs, - @benchmark( - evolveSynapse( - xc0, - xd0, - p_synapse, - events_sorted_times, - is_pre_or_post_event, - bap_by_epsp, - [true], - nu, - $(algo).solver, - $(algo).agg; - save_positions = (false, true), - saveat = $(algo).saveat, - save_everystep = false, - ), - samples = 50, - evals = 1, - seconds = 500, - ) - ) -end - - -labels = [a.label for a in algorithms] -medtimes = [text(string(round(median(b).time/1e9, digits=3),"s"), :center, 12) for b in bs] -relmedtimes = [median(b).time for b in bs] -relmedtimes ./= relmedtimes[1] -bar(labels, relmedtimes, markeralpha=0, series_annotation=medtimes, fmt=fmt) -title!("evolveSynapse (Median time)") - - -medmem = [text(string(round(median(b).memory/1e6, digits=3),"Mb"), :center, 12) for b in bs] -relmedmem = Float64[median(b).memory for b in bs] -relmedmem ./= relmedmem[1] -bar(labels, relmedmem, markeralpha=0, series_annotation=medmem, fmt=fmt) -title!("evolveSynapse (Median memory)") -