# Differential evolution algorithm of solving an inverse problem for the spatial Solow mathematical model

## TL;DR

This paper applies a regularized, parallelized differential evolution algorithm to solve an inverse problem in the spatial Solow model, reconstructing the production function from GDP data with numerical validation.

## Contribution

It introduces a parallelized regularized differential evolution method for solving ill-posed inverse problems in spatial economic models.

## Key findings

- Effective reconstruction of production functions demonstrated.
- Parallelization improves computational efficiency.
- Robustness shown under data measurement errors.

## Abstract

The differential evolution algorithm is applied to solve the optimization problem to reconstruct the production function (inverse problem) for the spatial Solow mathematical model using additional measurements of the gross domestic product for the fixed points. Since the inverse problem is ill-posed the regularized differential evolution is applied. For getting the optimized solution of the inverse problem the differential evolution algorithm is paralleled to 32 kernels. Numerical results for different technological levels and errors in measured data are presented and discussed.