mlsanityData to 14 Oct 2026

Mean-field neural networks: learning mappings on Wasserstein space

arXiv 2210.15179 ↗First posted 27 Oct 2022math.OC stat.MLcited by 16

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Abstract (arXiv)

We study the machine learning task for models with operators mapping between the Wasserstein space of probability measures and a space of functions, like e.g. in mean-field games/control problems. Two classes of neural networks, based on bin density and on cylindrical approximation, are proposed to learn these so-called mean-field functions, and are theoretically supported by universal approximation theorems. We perform several numerical experiments for training these two mean-field neural networks, and show their accuracy and efficiency in the generalization error with various test distributions. Finally, we present different algorithms relying on mean-field neural networks for solving time-dependent mean-field problems, and illustrate our results with numerical tests for the example of a semi-linear partial differential equation in the Wasserstein space of probability measures.

Key facts. Cited by 16 papers in the map (data through 14 Oct 2026). Builds on 12 of its 26 references that are in the map. First posted on arXiv 27 Oct 2022.

Builds on

12 of 26 references.

References · 12

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  5. 2019A Machine Learning Framework for Solving High-Dimensional Mean Field Game and Mean Field Control Problemscited by 97
  6. 2020An overview on deep learning-based approximation methods for partial differential equationscited by 65
  7. 2020Alternating the Population and Control Neural Networks to Solve High-Dimensional Stochastic Mean-Field Gamescited by 35
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  9. 2021Neural networks-based algorithms for stochastic control and PDEs in financecited by 26
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Cited by year (2026 to 14 Oct)

Citing papers per year: 2022: 1; 2023: 3; 2024: 3; 2025: 0; 2026: 9.

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  1. 2022Mean-field neural networks-based algorithms for McKean-Vlasov control problems *cited by 10
  2. 2023Actor critic learning algorithms for mean-field control with moment neural networkscited by 7
  3. 2024Universal Approximation of Mean-Field Models via Transformerscited by 7
  4. 2024An Overview on Machine Learning Methods for Partial Differential Equations: from Physics Informed Neural Networks to Deep Operator Learningcited by 6
  5. 2024Neural McKean-Vlasov Processes: Distributional Dependence in Diffusion Processescited by 4
  6. 2026Continuous-time q-learning for mean-field control with common noise, part-II: q-learning algorithmscited by 4
  7. 2026Policy Gradient for Continuous-Time Mean-Field Controlcited by 4
  8. 2026Learning operators on labelled conditional distributions with applications to mean field control of non exchangeable systemscited by 3
  9. 2026Deep Hilbert--Galerkin Methods for Infinite-Dimensional PDEs and Optimal Controlcited by 2
  10. 2023Algorithmically Designed Artificial Neural Networks (ADANNs): Higher order deep operator learning for parametric partial differential equationscited by 1
  11. 2023Quantile and moment neural networks for learning functionals of distributionscited by 1
  12. 2026MVNN: A Measure-Valued Neural Network for Learning McKean-Vlasov Dynamics from Particle Datacited by 1
4 more
  1. 2026Mean-Field PhiBE: Continuous-Time Mean-Field Reinforcement Learning from Discrete-Time Datacited by 1
  2. 2026Universal Approximation of Nonlinear Operators and Their Derivativescited by 0
  3. 2026A cylindrical neural approximation theorem for conditional laws of McKean-Vlasov equations with common noisecited by 0
  4. 2026From Distributions to Stochastic Processes: Neural Approximation of Measure-Valued Mapscited by 0