Curvature-adaptive grid refinement on all axes

[jc-macdonald]

Generalise the curvature-adaptive trait grid from structured-observables into a reusable, axis-agnostic grid refinement engine.

Origin

The structured-observables computational companion notebook implements generate_adaptive_theta_from_curvature() — a function that:

1. Evaluates curvature κ = |η''w + 2η'w' + ηw''| on a dense reference grid
2. Builds a cumulative weight function from κ
3. Distributes N points uniformly in weight-space → non-uniform in θ-space

This concentrates resolution where the solution has structure and saves points where it's smooth. Currently hardcoded for a single trait axis (θ) with specific functions (η, w).

Generalisation

The same idea applies to every axis in an operator-partitioned system:

• Trait axes (phytoplankton size θ, zooplankton size ϑ, detritus size ξ in TRIDENT)
• Spatial axes (depth z in TRIDENT, with curvature from thermocline/nutricline)
• Age/stage axes (in epidemiological or demographic models)

Tasks

• Define an AdaptiveGrid type parameterised by axis and curvature estimator
• Implement curvature estimation from: (a) known analytic curvature, (b) numerical second derivatives of a reference solution, (c) user-supplied weight function
• Build grid from curvature weights (the inverse-CDF / quantile approach)
• Support multi-axis grids: independent adaptive refinement per axis, with tensor-product assembly
• Integrate with the finite-volume discretisation in OpEngine.jl Core operator-splitting solver: ODE + IMEX #1 — non-uniform cell widths
• Allow runtime re-gridding (solution-adaptive: re-estimate curvature from current state and rebuild grid)

Cross-references

• structured-observables: computational companion notebook (generate_adaptive_theta_from_curvature)
• trident Core operator-splitting solver: ODE + IMEX #1: TRIDENT has trait + spatial axes that will consume this
• representation-matters: ρ = ε/h — adaptive h means ρ varies across the domain, concentrating resolution where biology demands it

Boundary

This is a solver feature — grid refinement lives in OpEngine. The declaration of which axes exist and their bounds lives in OpSystem.jl.