Solving Heterogeneous Agent Models with Physics-Informed Neural Networks

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. We hope this will open new avenues for solving complex heterogeneous agent models in macroeconomics.

Marta Grześkiewicz

/ˈmɑːtə ɡrɛskɛvɪtʃ/
College Assistant Professor & Fellow in Economics

My interests lie at the intersection of economics and machine learning. My work aims to understand and model the underlying mechanisms of choice and decision-making behaviour, accounting for dynamic settings, across a range of environments.