Solving Heterogeneous Agent Models with Physics-informed Neural Networks

TL;DR

This paper introduces a novel neural network-based solver for heterogeneous agent models that embeds key equations into the training process, offering improved scalability and accuracy over traditional grid-based methods.

Contribution

It presents the ABH-PINN solver, a physics-informed neural network approach that efficiently solves continuous-time heterogeneous agent models by embedding PDEs directly into the training.

Findings

Achieves results comparable to finite-difference solvers.

Offers improved scalability and smoother solutions.

Reduces computational costs and numerical inaccuracies.

Abstract

Understanding household behaviour is essential for modelling macroeconomic dynamics and designing effective policy. While heterogeneous agent models offer a more realistic alternative to representative agent frameworks, their implementation poses significant computational challenges, particularly in continuous time. The Aiyagari-Bewley-Huggett (ABH) framework, recast as a system of partial differential equations, typically relies on grid-based solvers that suffer from the curse of dimensionality, high computational cost, and numerical inaccuracies. This paper introduces the ABH-PINN solver, an approach based on Physics-Informed Neural Networks (PINNs), which embeds the Hamilton-Jacobi-Bellman and Kolmogorov Forward equations directly into the neural network training objective. By replacing grid-based approximation with mesh-free, differentiable function learning, the ABH-PINN solver benefits from the advantages of PINNs of improved scalability, smoother solutions, and computational efficiency. Preliminary results show that the PINN-based approach is able to obtain economically valid results matching the established finite-difference solvers.