Deep-MacroFin: Informed Equilibrium Neural Network for Continuous Time Economic Models

2024-08-19

arXiv.org

AI Summary

To address the computational intractability of solving high-dimensional, continuous-time macroeconomic models governed by systems of Hamilton–Jacobi–Bellman (HJB) equations, this paper proposes Deep-MacroFin—a novel deep learning framework. Methodologically, it introduces the first integration of Kolmogorov–Arnold networks into an equilibrium neural architecture, jointly embedding HJB dynamics and algebraic economic constraints as structural priors. It further designs an economics-informed loss function, a stability-preserving temporal training scheme, and an adaptive time-stepping strategy. The key contributions are: (i) breaking the scalability barrier for nonlinear HJB solvers beyond 100 dimensions—achieving 5× reduction in CUDA memory and 40× fewer FLOPs versus state-of-the-art methods on a 100D benchmark; and (ii) enabling the first end-to-end, numerically stable solution of a 50D real-world macroeconomic model, supporting fully differentiable optimization.

Technology Category

• Machine Learning: Deep Neural Architectures and Foundation Models
• Game Theory and Economic Paradigms: Adversarial Learning
• Search and Optimization: Learning to Search

Application Category

• Economics, Online Markets and Human Computation: Economic ramifications for generative AI infrastructure and applications
• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Web Mining and Content Analysis: Large pretrained models with web data

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$ imes$ less CUDA memory and 40$ imes$ 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.

Problem

• Solves high-dimensional continuous time economic models efficiently
• Reduces computational demands using deep learning methodologies
• Enhances training stability for nonlinear HJB equations

Innovation

• Uses deep learning with MLP and Kolmogorov-Arnold Networks
• Optimized via HJB equations and algebraic constraints
• Efficient high-dimensional PDE solver with time-stepping