Taming Epilepsy: Mean Field Control of Whole-Brain Dynamics

Ming Li; Ting Gao; Jingqiao Dua

cs.LGMar 11, 2026

Taming Epilepsy: Mean Field Control of Whole-Brain Dynamics

Authors: Ming Li, Ting Gao, Jingqiao Dua

Organizations: School of Mathematics and Information Science, Guangzhou University, Guangzhou 510000, China. · School of Sciences, Great Bay University, Dongguan 523000, China. · Guangdong Provincial Key Laboratory of Mathematical and Neural Dynamical Systems, Great Bay University, Dongguan 523000, China. · School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074, China. ·

Abstract

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.

Figures & tables

Figure 1: Brain Network Construction and Topological Structure Exploration : Figure 1(a) is the adjacency matrix A of the brain network connections constructed from PLV, with colors mapped to the weights of the edges. (b) is the Laplacian matrix of the brain network: $L=D-A$ , where D is the degree matrix. (c) is the 2-D visualization of the brain network constructed from PLV with an edge weight threshold of 0.4.

Figure 2: Solution of Control Matrix B : Figure 2 shows the top 5 key sub-nodes identified by the weighted combination of Degree Centrality, Betweenness Centrality, and Eigenvector Centrality. For the control matrix B, the diagonal elements corresponding to nodes with control inputs are all set to 1, and the remaining elements are all set to 0.

Figure 3: Linearization of Stochastic Nonlinear Dynamical Systems via RC Reservoir : Panels 3a-e show the prediction performance of the top 5 key sub-nodes (electrode channels) after approximating the Koopman operator with RC, where the solid black lines are the trajectories of the original data from 1300s to 1500s, and the dashed red lines are the predicted trajectories. Panels 3f-j show the corresponding Probability Density Functions (PDFs), where the gray represents the PDF of the original data from 1300s to 1500s, and the red represents the predicted PDF. Panel 3h is the global (23 channels) RMSE heatmap, where darker colors indicate larger errors. Panel 3i is the global (23 channels) PDF, where the gray represents the PDF of the original data from 1300s to 1500s across 23 channels, and the red represents the predicted PDF of the 23 channels from 1300s to 1500s.

Figure 4: Optimal Control $u^{*}$ Solution via MFG : Panels a-e show the trajectory control performance of the top 5 key sub-nodes (channels), where the red lines are the trajectories of the original uncontrolled data from 1300s to 1500s, and the blue lines are the corresponding controlled trajectories. Panels f-j are the corresponding control input signals. Panels k-o are the corresponding Probability Density Functions (PDFs), where the red represents the amplitude PDF of the original data from 1300s to 1500s, and the blue represents the amplitude PDF after corresponding control. Panel p is the global amplitude PDF, where the red represents the amplitude PDF of the original data (23 channels), the green represents the amplitude PDF of the original healthy state data from 0s to 500s, and the blue represents the amplitude PDF of the 23 channels after control. Panel q is the training loss curve of the $\phi$ function (purple) and the $G_{\theta}$ function (green) in the APAC-Net.

Figure 5: Controlled Probability Density Functions of 23 Channels : Panels a-w show the controlled PDFs of the 23 channels of original data, where the red represents the amplitude PDF of each channel from 1300s to 1500s, and the blue represents the corresponding PDF after control.

Appendix figures & tables2 assets

Supplementary material from the paper’s appendix.

Appendix

Figure 6: Model Predictive Control (MPC) Plots : Panels a-e show the model predictive trajectory control plots of the top 5 ranked channels, where the gray represents the original trajectories of the raw data from 1300s to 1500s, the green represents the corresponding controlled trajectories, and the orange lines below represent the corresponding control input signals. Panels f-j are the corresponding Probability Density Functions (PDFs), where the red represents the amplitude PDF of the original data from 1300s to 1500s, the green represents the corresponding amplitude PDF after control, and the blue represents the amplitude PDF of the original healthy state data (0s to 500s). Panel h represents the global (23 channels) amplitude PDF from 1300s to 1500s.

Figure 7: Model Predictive Control Results of 23 Channels : Panels a-w respectively represent the model predictive control effects of the 23 channels, where the red represents the amplitude PDF of the original data from 1300s to 1500s, the green represents the corresponding amplitude PDF after control, and the blue represents the amplitude PDF of the original healthy state data (0s to 500s).

Optimizing EEG Graph Structure for Seizure Detection: An Information Bottleneck and Self-Supervised Learning Approach
Apr 2, 2026Lincan Li, Rikuto Kotoge, Xihao Piao +2EEG Seizure Detection Graph Structure Learning
Department of Computer Science, Florida State University, Tallahassee, USA · SANKEN, The University of Osaka, Ibaraki, Japan
Spatiotemporal Hyperedges for EEG Seizure Detection and Prediction
Sep 29, 2026Hyunju Kim, Sheo Yon Jhin, Noseong Park +1EEG Seizure Detection Graph Neural Networks
School of Computational Science and Engineering Georgia Institute of Technology Atlanta, GA, USA · School of Computing Korea Advanced Institute of Science and Technology Daejeon, Republic of Korea
Graph-Based Approaches to Learning Epileptogenic Zone Localization Using Stereo-EEG Recordings
Aug 19, 2026Daniel Wendelken, Brian Ervin, Ravindra Arya +1Graph Structure Learning Brain Network Analysis
University of Cincinnati, Cincinnati, USA · Dept. of Computer Science University of Cincinnati Cincinnati, USA · Cincinnati Children's Hospital Medical Center, Cincinnati, USA +2

Apr 2, 2026J/K move · Enter open · S save

Optimizing EEG Graph Structure for Seizure Detection: An Information Bottleneck and Self-Supervised Learning Approach

Lincan Li, Rikuto Kotoge, Xihao Piao, Zheng Chen+1

Department of Computer Science, Florida State University, Tallahassee, USA · SANKEN, The University of Osaka, Ibaraki, Japan

EEG Seizure Detection Graph Structure Learning Dynamic Graph Learning Brain Network Analysis Graph SSL

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Seizure detection from EEG signals is highly challenging due to complex spatiotemporal dynamics and extreme inter-patient variability. To model them, recent methods construct dynamic graphs via statistical correlations, predefined similarity measures, or implicit learning, yet rarely account for EEG's noisy nature. Consequently, these graphs usually contain redundant or task-irrelevant connections, undermining model performance even with state-of-the-art architectures. In this paper, we present a new perspective for EEG seizure detection: jointly learning denoised dynamic graph structures and informative spatial-temporal representations guided by the Information Bottleneck (IB). Unlike prior approaches, our graph constructor explicitly accounts for the noisy characteristics of EEG data, producing compact and reliable connectivity patterns that better support downstream seizure detection. To further enhance representation learning, we employ a self-supervised Graph Masked AutoEncoder that reconstructs masked EEG signals based on dynamic graph context, promoting structure-aware and compact representations aligned with the IB principle. Bringing things together, we introduce Information Bottleneck-guided EEG SeizuRE DetectioN via SElf-Supervised Learning (IRENE), which explicitly learns dynamic graph structures and interpretable spatial-temporal EEG representations. IRENE addresses three core challenges: (i) Identifying the most informative nodes and edges; (ii) Explaining seizure propagation in the brain network; and (iii) Enhancing robustness against label scarcity and inter-patient variability. Extensive experiments on benchmark EEG datasets demonstrate that our method outperforms state-of-the-art baselines in seizure detection and provides clinically meaningful insights into seizure dynamics. The source code is available at https://github.com/LabRAI/IRENE.

Abstract

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