ArticleProceedings of the National Academy of Sciences of the United States of America2020
A machine learning framework for solving high-dimensional mean field game and mean field control problems.
Article in Proceedings of the National Academy of Sciences of the United States of America, 2020. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 17 papers.
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17 citing papers in PubMed.
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- Integrating Dynamical Systems Modeling with Spatiotemporal scRNA-Seq Data Analysis.Entropy (Basel, Switzerland) · 2025Review
- A rapid-convergent particle swarm optimization approach for multiscale design of high-permeance seawater reverse osmosis systems.Communications engineering · 2024Article
- A physics-informed neural SDE network for learning cellular dynamics from time-series scRNA-seq data.Bioinformatics (Oxford, England) · 2024Article
- Modeling single cell trajectory using forward-backward stochastic differential equations.PLoS computational biology · 2024Article
- In-context operator learning with data prompts for differential equation problems.Proceedings of the National Academy of Sciences of the United States of America · 2023Article
- Explainable AI via learning to optimize.Scientific reports · 2023Article
- Decentralized Stochastic Control with Finite-Dimensional Memories: A Memory Limitation Approach.Entropy (Basel, Switzerland) · 2023Article
- Taming hyperparameter tuning in continuous normalizing flows using the JKO scheme.Scientific reports · 2023Article
- A physics-informed neural network based on mixed data sampling for solving modified diffusion equations.Scientific reports · 2023Article
- Forward-Backward Sweep Method for the System of HJB-FP Equations in Memory-Limited Partially Observable Stochastic Control.Entropy (Basel, Switzerland) · 2023Article
- Memory-Limited Partially Observable Stochastic Control and Its Mean-Field Control Approach.Entropy (Basel, Switzerland) · 2022Article
- A Mean-Field Game Control for Large-Scale Swarm Formation Flight in Dense Environments.Sensors (Basel, Switzerland) · 2022Article
- Mean field control problems for vaccine distribution.Research in the mathematical sciences · 2022Article
- Alternating the population and control neural networks to solve high-dimensional stochastic mean-field games.Proceedings of the National Academy of Sciences of the United States of America · 2021Article
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5 authors.
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Abstract
Mean field games (MFG) and mean field control (MFC) are critical classes of multiagent models for the efficient analysis of massive populations of interacting agents. Their areas of application span topics in economics, finance, game theory, industrial engineering, crowd motion, and more. In this paper, we provide a flexible machine learning framework for the numerical solution of potential MFG and MFC models. State-of-the-art numerical methods for solving such problems utilize spatial discretization that leads to a curse of dimensionality. We approximately solve high-dimensional problems by combining Lagrangian and Eulerian viewpoints and leveraging recent advances from machine learning. More precisely, we work with a Lagrangian formulation of the problem and enforce the underlying Hamilton-Jacobi-Bellman (HJB) equation that is derived from the Eulerian formulation. Finally, a tailored neural network parameterization of the MFG/MFC solution helps us avoid any spatial discretization. Our numerical results include the approximate solution of 100-dimensional instances of optimal transport and crowd motion problems on a standard work station and a validation using a Eulerian solver in two dimensions. These results open the door to much-anticipated applications of MFG and MFC models that are beyond reach with existing numerical methods.
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