Deep-MacroFin: Informed Equilibrium Neural Network for Continuous Time Economic Models

TL;DR

Deep-MacroFin introduces an innovative neural network framework that efficiently solves high-dimensional partial differential equations in continuous time economics, outperforming existing methods in computational efficiency and stability.

Contribution

It develops a novel equilibrium neural network architecture combining Kolmogorov-Arnold Networks with HJB-based optimization for high-dimensional economic models.

Findings

Achieves 5x less CUDA memory usage compared to existing methods.

Reduces FLOPs by 40x in 100D problems.

Successfully solves 50D economic models with improved stability.

Abstract

In this paper, we present Deep-MacroFin, a comprehensive framework designed to solve partial differential equations, with a particular focus on models in continuous time economics. This framework leverages deep learning methodologies, including Multi-Layer Perceptrons and the newly developed Kolmogorov-Arnold Networks. It is optimized using economic information encapsulated by Hamilton-Jacobi-Bellman (HJB) equations and coupled algebraic equations. The application of neural networks holds the promise of accurately resolving high-dimensional problems with fewer computational demands and limitations compared to other numerical methods. This framework can be readily adapted for systems of partial differential equations in high dimensions. Importantly, it offers a more efficient (5$\times$ less CUDA memory and 40$\times$ fewer FLOPs in 100D problems) and user-friendly implementation than existing libraries. We also incorporate a time-stepping scheme to enhance training stability for nonlinear HJB equations, enabling the solution of 50D economic models.