mlsanityData to 14 Oct 2026

Decoding Mean Field Games from Population and Environment Observations By Gaussian Processes

arXiv 2312.06625 ↗First posted 8 Dec 2023cs.GT cs.LG cs.NAcited by 2

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Abstract (arXiv)

This paper presents a Gaussian Process (GP) framework, a non-parametric technique widely acknowledged for regression and classification tasks, to address inverse problems in mean field games (MFGs). By leveraging GPs, we aim to recover agents' strategic actions and the environment's configurations from partial and noisy observations of the population of agents and the setup of the environment. Our method is a probabilistic tool to infer the behaviors of agents in MFGs from data in scenarios where the comprehensive dataset is either inaccessible or contaminated by noises.

Key facts. Cited by 2 papers in the map (data through 14 Oct 2026). Builds on 21 of its 53 references that are in the map. First posted on arXiv 8 Dec 2023.

Builds on

21 of 53 references.

References · 21

  1. 2017Machine Learning of Linear Differential Equations using Gaussian Processescited by 140
  2. 2021Solving and Learning Nonlinear PDEs with Gaussian Processescited by 129
  3. 2023In-Context Operator Learning with Data Prompts for Differential Equation Problemscited by 101
  4. 2019A Machine Learning Framework for Solving High-Dimensional Mean Field Game and Mean Field Control Problemscited by 97
  5. 2017Numerical Gaussian Processes for Time-dependent and Non-linear Partial Differential Equationscited by 72
  6. 2020Alternating the Population and Control Neural Networks to Solve High-Dimensional Stochastic Mean-Field Gamescited by 35
  7. 2019Convergence Analysis of Machine Learning Algorithms for the Numerical Solution of Mean Field Control and Games: II -- The Finite Horizon Casecited by 34
  8. 2023Sparse Cholesky Factorization for Solving Nonlinear PDEs via Gaussian Processescited by 31
  9. 2020Mean Field Games and Applications: Numerical Aspectscited by 22
  10. 2021Numerical Methods for Mean Field Games and Mean Field Type Controlcited by 22
  11. 2023Learning Dynamical Systems from Data: A Simple Cross-Validation Perspective, Part V: Sparse Kernel Flows for 132 Chaotic Dynamical Systemscited by 15
  12. 2021Learning dynamical systems from data: A simple cross-validation perspective, part III: Irregularly-Sampled Time Seriescited by 14
9 more
  1. 2016Proximal methods for stationary Mean Field Games with local couplingscited by 11
  2. 2018On the implementation of a primal-dual algorithm for second order time-dependent mean field games with local couplingscited by 9
  3. 2020A mean field game inverse problemcited by 8
  4. 2021Numerical methods for Mean field Games based on Gaussian Processes and Fourier Featurescited by 7
  5. 2020Splitting methods for a class of non-potential mean field gamescited by 6
  6. 2021Mean field control problems for vaccine distributioncited by 4
  7. 2022Inverse problems for mean field gamescited by 4
  8. 2018Long Time Behavior of First Order Mean Field Games on Euclidean Spacecited by 2
  9. 2023Simultaneously recovering running cost and Hamiltonian in Mean Field Games systemcited by 2

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Citing papers per year: 2025: 2.

2 papers.

  1. 2025Learning Surrogate Potential Mean Field Games via Gaussian Processes: A Data-Driven Approach to Ill-Posed Inverse Problemscited by 2
  2. 2025Gaussian process policy iteration with additive Schwarz acceleration for forward and inverse HJB and mean field game problemscited by 0