# Splitting methods for a class of non-potential mean field games

arXiv: https://arxiv.org/abs/2007.00099 · HTML: https://mlsanity.com/paper/2007.00099/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Jun 2020.

## Built on by (most cited first, 6 of 6)

- [Coupled Multiwavelet Neural Operator Learning for Coupled Partial Differential Equations](https://mlsanity.com/paper/2303.02304/) (2023)
- [Efficient Natural Gradient Descent Methods for Large-Scale PDE-Based Optimization Problems](https://mlsanity.com/paper/2202.06236/) (2022)
- [MF-OML: Online Mean-Field Reinforcement Learning with Occupation Measures for Large Population Games](https://mlsanity.com/paper/2405.00282/) (2024)
- [Decoding Mean Field Games from Population and Environment Observations By Gaussian Processes](https://mlsanity.com/paper/2312.06625/) (2023)
- [Learning Surrogate Potential Mean Field Games via Gaussian Processes: A Data-Driven Approach to Ill-Posed Inverse Problems](https://mlsanity.com/paper/2502.11506/) (2025)
- [Gaussian process policy iteration with additive Schwarz acceleration for forward and inverse HJB and mean field game problems](https://mlsanity.com/paper/2505.00909/) (2025)

## Abstract (arXiv)

We extend the methods from Nurbekyan, Saude "Fourier approximation methods for first-order nonlocal mean-field games" [Port. Math. 75 (2018), no. 3-4] and Liu, Jacobs, Li, Nurbekyan, Osher "Computational methods for nonlocal mean field games with applications" [arXiv:2004.12210] to a class of non-potential mean-field game (MFG) systems with mixed couplings. Up to now, splitting methods have been applied to potential MFG systems that can be cast as convex-concave saddle-point problems. Here, we show that a class of non-potential MFG can be cast as primal-dual pairs of monotone inclusions and solved via extensions of convex optimization algorithms such as the primal-dual hybrid gradient (PDHG) algorithm. A critical feature of our approach is in considering dual variables of nonlocal couplings in Fourier or feature spaces.