Deep-MacroFin: Informed Equilibrium Neural Network for Continuous Time Economic Models (2408.10368v4)

Abstract: In this paper, we present Deep-MacroFin, a comprehensive framework designed to solve partial differential equations, with a particular focus on models in continuous time economics. This framework leverages deep learning methodologies, including Multi-Layer Perceptrons and the newly developed Kolmogorov-Arnold Networks. It is optimized using economic information encapsulated by Hamilton-Jacobi-Bellman (HJB) equations and coupled algebraic equations. The application of neural networks holds the promise of accurately resolving high-dimensional problems with fewer computational demands and limitations compared to other numerical methods. This framework can be readily adapted for systems of partial differential equations in high dimensions. Importantly, it offers a more efficient (5$\times$ less CUDA memory and 40$\times$ fewer FLOPs in 100D problems) and user-friendly implementation than existing libraries. We also incorporate a time-stepping scheme to enhance training stability for nonlinear HJB equations, enabling the solution of 50D economic models.