Revolutionizing Economic Growth Forecasting: Integrating Neural Ordinary Differential Equations and Universal Differential Equations with the Solow-Swan Model

Overview

This repository contains an implementation of the Solow-Swan model using Universal Differential Equations (UDEs). The Solow-Swan model is a mathematical model used in economics to describe the long-run growth of an economy. UDEs are a type of machine learning model that can be used to learn the dynamics of complex systems.

Code Structure

The code is written in Julia and is organized into several sections:

• Importing Libraries: The code begins by importing the necessary libraries, including OrdinaryDiffEq, ModelingToolkit, DataDrivenDiffEq, SciMLSensitivity, LinearAlgebra, Statistics, DataDrivenSparse, Optimization, OptimizationOptimisers, OptimizationOptimJL, ComponentArrays, Lux, Zygote, Plots, and StableRNGs.
• Defining the Solow-Swan Model: The Solow-Swan model is defined using the capital_ode function, which describes the dynamics of the capital stock over time.
• Defining the UDE Model: The UDE model is defined using the ude_dynamics function, which learns the dynamics of the Solow-Swan model.
• Training the UDE Model: The UDE model is trained using the train_ude function, which takes the training data and returns the trained model parameters.
• Forecasting with the UDE Model: The trained UDE model is used to make forecasts using the ude_forecast function.
• Plotting the Results: The results are plotted using the plot_case_1, plot_case_2, plot_case_3, plot_case_4, and plot_case_5 functions.

Running the Code

To run the code, simply execute the main function. This will train the UDE model and generate plots for each of the five cases.

Case Studies

The code includes five case studies, each with a different training period:

• Case 1: Train till t = 9.0
• Case 2: Train till t = 7.0
• Case 3: Train till t = 5.0
• Case 4: Train till t = 3.0
• Case 5: Train till t = 1.0

Requirements

• Julia 1.7 or higher
• OrdinaryDiffEq, ModelingToolkit, DataDrivenDiffEq, SciMLSensitivity, LinearAlgebra, Statistics, DataDrivenSparse, Optimization, OptimizationOptimisers, OptimizationOptimJL, ComponentArrays, Lux, Zygote, Plots, and StableRNGs libraries

Acknowledgments

This code is based on the work of Dr. Raj Abhijit Dandekar, Dr. Rajat Dandekar , Dr. Sreedath Panat and Satwik Sinha.