# Taming Epilepsy: Mean Field Control of Whole-Brain Dynamics

arXiv: https://arxiv.org/abs/2603.18035 · HTML: https://mlsanity.com/paper/2603.18035/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 19 of its 46 references that are in the map.
- First posted on arXiv 11 Mar 2026.

## Builds on (most cited first, 19 of 19)

- [A Mean-Field Optimal Control Formulation of Deep Learning](https://mlsanity.com/paper/1807.01083/) (2018)
- [Alternating the Population and Control Neural Networks to Solve High-Dimensional Stochastic Mean-Field Games](https://mlsanity.com/paper/2002.10113/) (2020)
- [Graph Neural Networks for Brain Graph Learning: A Survey](https://mlsanity.com/paper/2406.02594/) (2024)
- [A Measure Theoretical Approach to the Mean-field Maximum Principle for Training NeurODEs](https://mlsanity.com/paper/2107.08707/) (2021)
- [Dynamical systems and complex networks: A Koopman operator perspective](https://mlsanity.com/paper/2405.08940/) (2024)
- [Two methods to approximate the Koopman operator with a reservoir computer](https://mlsanity.com/paper/2008.10263/) (2020)
- [Controlling Chaotic Maps using Next-Generation Reservoir Computing](https://mlsanity.com/paper/2307.03813/) (2023)
- [Mean-field optimal control as Gamma-limit of finite agent controls](https://mlsanity.com/paper/1803.04689/) (2018)
- [Explore Brain-Inspired Machine Intelligence for Connecting Dots on Graphs Through Holographic Blueprint of Oscillatory Synchronization](https://mlsanity.com/paper/2602.00057/) (2026)
- [Mean-Field Sparse Optimal Control](https://mlsanity.com/paper/1402.5657/) (2014)
- [Mean-field optimal control and optimality conditions in the space of probability measures](https://mlsanity.com/paper/1902.05339/) (2019)
- [Critical Nodes Identification in Complex Networks: A Survey](https://mlsanity.com/paper/2507.06164/) (2025)
- [Graph Theoretical Analysis Reveals: Women's Brains are Better Connected than Men's](https://mlsanity.com/paper/1501.00727/) (2015)
- [On the Feedback Law in Stochastic Optimal Nonlinear Control](https://mlsanity.com/paper/2004.01041/) (2020)
- [Mean-field selective optimal control via transient leadership](https://mlsanity.com/paper/2106.07254/) (2021)
- [Semiconcavity and Sensitivity Analysis in Mean-Field Optimal Control and Applications](https://mlsanity.com/paper/2108.02609/) (2021)
- [Reverse engineering the brain input: Network control theory to identify cognitive task-related control nodes](https://mlsanity.com/paper/2404.16357/) (2024)
- [Suppressing seizure via optimal electrical stimulation to the hub of epileptic brain network](https://mlsanity.com/paper/2406.09989/) (2024)
- [Adaptive control for multi-scale stochastic dynamical systems with stochastic next generation reservoir computing](https://mlsanity.com/paper/2505.09327/) (2025)

## Abstract (arXiv)

Controlling the high-dimensional neural dynamics during epileptic seizures remains a significant challenge due to the nonlinear characteristics and complex connectivity of the brain. In this paper, we propose a novel framework, namely Graph-Regularized Koopman Mean-Field Game (GK-MFG), which integrates Reservoir Computing (RC) for Koopman operator approximation with Alternating Population and Agent Control Network (APAC-Net) for solving distributional control problems. By embedding Electroencephalogram (EEG) dynamics into a linear latent space and imposing graph Laplacian constraints derived from the Phase Locking Value (PLV), our method achieves robust seizure suppression while respecting the functional topological structure of the brain.