# Numerical resolution of McKean-Vlasov FBSDEs using neural networks

arXiv: https://arxiv.org/abs/1909.12678 · HTML: https://mlsanity.com/paper/1909.12678/

## Key facts

- Cited by 19 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Sep 2019.

## Built on by (most cited first, 19 of 19)

- [Scalable Deep Reinforcement Learning Algorithms for Mean Field Games](https://mlsanity.com/paper/2203.11973/) (2022)
- [Scaling up Mean Field Games with Online Mirror Descent](https://mlsanity.com/paper/2103.00623/) (2021)
- [Actor-Critic learning for mean-field control in continuous time](https://mlsanity.com/paper/2303.06993/) (2023)
- [Deep Learning for Mean Field Games and Mean Field Control with Applications to Finance](https://mlsanity.com/paper/2107.04568/) (2021)
- [Reinforcement Learning for Mean Field Games, with Applications to Economics](https://mlsanity.com/paper/2106.13755/) (2021)
- [Learning High-Dimensional McKean-Vlasov Forward-Backward Stochastic Differential Equations with General Distribution Dependence](https://mlsanity.com/paper/2204.11924/) (2022)
- [Mean-field neural networks-based algorithms for McKean-Vlasov control problems *](https://mlsanity.com/paper/2212.11518/) (2022)
- [Actor critic learning algorithms for mean-field control with moment neural networks](https://mlsanity.com/paper/2309.04317/) (2023)
- [Deep Backward and Galerkin Methods for the Finite State Master Equation](https://mlsanity.com/paper/2403.04975/) (2024)
- [Simultaneously Solving Infinitely Many LQ Mean Field Games In Hilbert Spaces: The Power of Neural Operators](https://mlsanity.com/paper/2510.20017/) (2025)
- [Finite-Sample Convergence Bounds for Trust Region Policy Optimization in Mean-Field Games](https://mlsanity.com/paper/2505.22781/) (2025)
- [Deep Learning for Mean Field Optimal Transport](https://mlsanity.com/paper/2302.14739/) (2023)
- [Learning to Stop: Deep Learning for Mean Field Optimal Stopping](https://mlsanity.com/paper/2410.08850/) (2024)
- [Networked Communication for Decentralised Agents in Mean-Field Games](https://mlsanity.com/paper/2306.02766/) (2023)
- [A Deep Learning Method for Optimal Investment Under Relative Performance Criteria Among Heterogeneous Agents](https://mlsanity.com/paper/2402.07365/) (2024)
- [Mean-field Chaos Diffusion Models](https://mlsanity.com/paper/2406.05396/) (2024)
- [Deep Learning and Elicitability for McKean-Vlasov FBSDEs With Common Noise](https://mlsanity.com/paper/2512.14967/) (2025)
- [Learning Generative Dynamics with Soft Law Constraints: A McKean-Vlasov FBSDE Approach](https://mlsanity.com/paper/2605.08928/) (2026)
- [A Posteriori Error Analysis for Decoupled Neural Approximations of Fully Coupled FBSDEs with Control Mismatch](https://mlsanity.com/paper/2606.29474/) (2026)

## Abstract (arXiv)

We propose several algorithms to solve McKean-Vlasov Forward Backward Stochastic Differential Equations. Our schemes rely on the approximating power of neural networks to estimate the solution or its gradient through minimization problems. As a consequence, we obtain methods able to tackle both mean field games and mean field control problems in moderate dimension. We analyze the numerical behavior of our algorithms on several examples including non linear quadratic models.