# Solving Heterogeneous Agent Models with Physics-informed Neural Networks

arXiv: https://arxiv.org/abs/2511.20283 · HTML: https://mlsanity.com/paper/2511.20283/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 3 of its 31 references that are in the map.
- First posted on arXiv 25 Nov 2025.

## Builds on (most cited first, 3 of 3)

- [Automatic differentiation in machine learning: a survey](https://mlsanity.com/paper/1502.05767/) (2015)
- [Uncovering Utility Functions from Observed Outcomes](https://mlsanity.com/paper/2503.13432/) (2025)
- [Differential evolution algorithm of solving an inverse problem for the spatial Solow mathematical model](https://mlsanity.com/paper/1904.10627/) (2019)

## Abstract (arXiv)

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.