用神经网络求解异质主体模型，提升计算效率与精度
Solving Heterogeneous Agent Models with Physics-informed Neural Networks
- 将哈密顿-雅可比-贝尔曼方程嵌入神经网络训练目标
- 相比传统网格方法，计算速度更快且结果更平滑
- 适合需要高效求解宏观经济学动态模型的研究者
理解家庭行为对建模宏观经济动态和制定有效政策至关重要。尽管异质主体模型比代表性主体框架更具现实性，但其在连续时间下的实现面临重大计算挑战。经典的Aiyagari-Bewley-Huggett（ABH）框架被重构成偏微分方程组，通常依赖网格求解器，存在维数灾难、高计算成本和数值误差问题。本文提出ABH-PINN求解器，基于物理信息神经网络（PINNs），将哈密顿-雅可比-贝尔曼方程与科尔莫戈罗夫前向方程直接嵌入神经网络训练目标。通过以无网格、可微函数学习替代网格近似，该方法充分利用了PINNs在可扩展性、解的平滑性及计算效率方面的优势。初步结果显示，基于PINN的方法能获得与传统有限差分求解器一致的经济有效结果。
原文摘要 · Abstract (English)
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.
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