# Global Solutions to Master Equations for Continuous Time Heterogeneous Agent Macroeconomic Models

arXiv: https://arxiv.org/abs/2406.13726 · HTML: https://mlsanity.com/paper/2406.13726/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 66 references that are in the map.
- First posted on arXiv 19 Jun 2024.

## Builds on (most cited first, 6 of 6)

- [Physics Informed Deep Learning (Part I): Data-driven Solutions of Nonlinear Partial Differential Equations](https://mlsanity.com/paper/1711.10561/) (2017)
- [Signatured Deep Fictitious Play for Mean Field Games with Common Noise](https://mlsanity.com/paper/2106.03272/) (2021)
- [DeepHAM: A Global Solution Method for Heterogeneous Agent Models with Aggregate Shocks](https://mlsanity.com/paper/2112.14377/) (2021)
- [Deep Backward and Galerkin Methods for the Finite State Master Equation](https://mlsanity.com/paper/2403.04975/) (2024)
- [Mean field games master equations: from discrete to continuous state space](https://mlsanity.com/paper/2207.03191/) (2022)
- [A Deep Learning Analysis of Climate Change, Innovation, and Uncertainty](https://mlsanity.com/paper/2310.13200/) (2023)

## Built on by (most cited first, 2 of 2)

- [Structural Reinforcement Learning for Heterogeneous Agent Macroeconomics](https://mlsanity.com/paper/2512.18892/) (2025)
- [Population-Aware Imitation Learning in Mean-field Games with Common Noise](https://mlsanity.com/paper/2605.03357/) (2026)

## Abstract (arXiv)

We propose and compare new global solution algorithms for continuous time heterogeneous agent economies with aggregate shocks. First, we approximate the agent distribution so that equilibrium in the economy can be characterized by a high, but finite, dimensional non-linear partial differential equation. We consider different approximations: discretizing the number of agents, discretizing the agent state variables, and projecting the distribution onto a finite set of basis functions. Second, we represent the value function using a neural network and train it to solve the differential equation using deep learning tools. We refer to the solution as an Economic Model Informed Neural Network (EMINN). The main advantage of this technique is that it allows us to find global solutions to high dimensional, non-linear problems. We demonstrate our algorithm by solving important models in the macroeconomics and spatial literatures (e.g. Krusell and Smith (1998), Khan and Thomas (2007), Bilal (2023)).