ODEBrain: Continuous-Time EEG Graph for Modeling Dynamic Brain Networks

Haohui Jia; Zheng Chen; Lingwei Zhu; Rikuto Kotoge; Jathurshan Pradeepkumar; Yasuko Matsubara; Jimeng Sun; Yasushi Sakurai

cs.AIFeb 26, 2026

ODEBrain: Continuous-Time EEG Graph for Modeling Dynamic Brain Networks

Authors: Haohui Jia, Zheng Chen, Lingwei Zhu, Rikuto Kotoge, Jathurshan Pradeepkumar, Yasuko Matsubara, Jimeng Sun, Yasushi Sakurai,

Organizations: Information Science and Techinology, Hokkaido University, Japan · SANKEN, The University of Osaka, Japan · Great Bay University, China · Department of Computer Science, University of Illinois Urbana-Champaign, USA

Abstract

Modeling neural population dynamics is crucial for foundational neuroscientific research and various clinical applications. Conventional latent variable methods typically model continuous brain dynamics through discretizing time with recurrent architecture, which necessarily results in compounded cumulative prediction errors and failure of capturing instantaneous, nonlinear characteristics of EEGs. We propose ODEBRAIN, a Neural ODE latent dynamic forecasting framework to overcome these challenges by integrating spatio-temporal-frequency features into spectral graph nodes, followed by a Neural ODE modeling the continuous latent dynamics. Our design ensures that latent representations can capture stochastic variations of complex brain states at any given time point. Extensive experiments verify that ODEBRAIN can improve significantly over existing methods in forecasting EEG dynamics with enhanced robustness and generalization capabilities.

Figures & tables

Figure 1: (Left) Continuous EEG real-time neuronal activity recordings. (Mid) Recurrent-based methods employ discrete modeling. (Right) ODE provides a continuous representation for forecasting neuronal population dynamics.

Figure 2: Continuous neural dynamics modeling via ODEBRAIN with graph forecasting. In stage 1, multi-channel EEG signals are encoded into spectral graph snapshots and fused with raw features to construct noise-robust initial states for ODE integration, predicting future spectral graphs. In stage 2, ODEBRAIN propagates latent states through time, generating dynamic field $f$ that captures continuous trajectories. Finally, future graph node embeddings are obtained by $z_{T}$ and compared with the ground-truth graph nodes.

Figure 3: The full structure of the temporal-spatial ODE solving. (a)RK-4 step numerical solver. (b) Procedure of temporal-spatial

f_{\theta}

Model	Method	T(s)	AUROC	F1
Discrete & Continuous	BIOT	12	0.772 $\pm$ 0.006	0.294 $\pm$ 0.006
		60	0.642 $\pm$ 0.009	0.256 $\pm$ 0.003
	DCRNN	12	0.816 $\pm$ 0.002	0.416 $\pm$ 0.009
		60	0.802 $\pm$ 0.003	0.413 $\pm$ 0.005
	latent-ODE	12	0.791 $\pm$ 0.004	0.385 $\pm$ 0.005
		60	0.745 $\pm$ 0.036	0.331 $\pm$ 0.031

Table 1: Results (AUROC↑, F1↑) on TUSZ (12s and 60s seizure detection) against discrete and continuous baselines, with options on the gate and stochastic regularization. (-: w/o, +Random: gate with random coefficients for stochastic regularization.) Bold = best.

Method	TUSZ			TUAB
Method	Acc	F1	AUROC	Acc	F1	AUROC
CNN-LSTM	$0.735\pm 3$	$0.347\pm 12$	$0.757\pm 3$	$0.741\pm 2$	$0.736\pm 7$	$0.813\pm 3$
BIOT	$0.702\pm 3$	$0.294\pm 6$	$0.772\pm 6$	$0.717\pm 2$	$0.713\pm 4$	$0.788\pm 2$
EvolveGCN	$0.769\pm 2$	$0.385\pm 5$	$0.791\pm 4$	$0.708\pm 3$	$0.707\pm 2$	$0.777\pm 3$
DCRNN	$0.816\pm 2$	$0.416\pm 9$	$0.825\pm 2$	$0.768\pm 4$	$0.769\pm 2$	$0.848\pm 2$
latent-ODE	$0.827\pm 4$	$0.470\pm 5$	$0.849\pm 4$	$0.749\pm 3$	$0.745\pm 2$	$0.829\pm 4$

Table 2: Main results on TUSZ (12s seizure detection) and TUAB . Bold and underline indicate best and second-best results.

\star

: The performance depends on the discrete multi-steps forecasting.

{\dagger}

: The performance depends on the continuous multi-steps forecasting.

{\ddagger}

: The performance depends on the continuous single-step forecasting.

Figure 4: Visualization results between the multichannel EEG signal (upper and lower) and its latent dynamic field $f_{\theta}$ (middle) obtained by ODEBRAIN . Local minima appearing in (a) and (c) indicate rapid changes, corresponding to seizure states.

Figure 5: Visualizing learned dynamic fields between our spatial-temporal(ST)-ODE solver and the frequency (F)-ODE solver.

Figure 6: Results on (a) graph similarity and (b) functional connections.

Figure 7: Summary of ablation study. (a) State initialization. We compare spatial-only, mixed, and temporal–spatial initialization and summarized results in F1, Recall and AUROC. Temporal–Spatial achieves the best F1 $(0.502)$ with a competitive recall. (b) Loss function. Replacing our structural forecasting loss with reconstruction-only or raw-signal forecasting degrades performance on AUROC. (c) Forecast horizon. AUROC decreases as the horizon grows ( $1$ s $\rightarrow 3$ s $\rightarrow$ $11$ s), and Temporal–Spatial remains the best across all horizons over others.

Table 10

Appendix figures & tables6 assets

Supplementary material from the paper’s appendix.

Appendix

Figure 8: Visualization results between the multichannel EEG signal (upper) and its latent dynamic field $f_{\theta}$ (lower) in our temporal-spatial neural ODE.

Panel of Figure 9 — Figure 9: Comparison of the predicted graph output between our continuous predictor and discrete predictor.

Method	TUSZ			TUAB
Method	Acc	F1	AUROC	Acc	F1	AUROC
Max pooling	$\mathbf{0.877\pm 0.004}$	$\mathbf{0.496\pm 0.017}$	$\mathbf{0.881\pm 0.006}$	$\mathbf{0.778\pm 0.003}$	$\mathbf{0.774\pm 0.005}$	$\mathbf{0.857\pm 0.005}$
Mean pooling	$0.842\pm 2$	$0.385\pm 5$	$0.827\pm 3$	$0.748\pm 2$	$0.635\pm 2$	$0.827\pm 4$
Sum pooling	$0.851\pm 2$	$0.466\pm 5$	$0.867\pm 4$	$0.753\pm 3$	$0.755\pm 2$	$0.831\pm 4$

Appendix

Table 5: Ablation of pooling options over ODE-trajectory on TUSZ (12s seizure detection) and TUAB . Bold indicates best result.

ODE	Method	T(Sec.)	AUROC	F1
Temporal-spatial	EvolveGCN	12	0.791 $\pm$ 0.003	0.401 $\pm$ 0.002
		60	0.729 $\pm$ 0.002	0.378 $\pm$ 0.003
	DCRNN	12	0.823 $\pm$ 0.005	0.433 $\pm$ 0.005
		60	0.818 $\pm$ 0.004	0.417 $\pm$ 0.007
	GRU-GCN	12	0.881 $\pm$ 0.006	0.496 $\pm$ 0.017
		60	0.828 $\pm$ 0.003	0.430 $\pm$ 0.021

Appendix

Table 6: Ablation of GNN options on TUSZ (12s and 60s seizure detection) (AUROC↑, F1↑) Bold = best.

MV	Method	Sim.	AUROC	F1
0%	latent-ODE	0.53	0.791 $\pm$ 0.003	0.401 $\pm$ 0.002
0%	ODEBRAIN	0.63	0.881 $\pm$ 0.006	0.496 $\pm$ 0.017
30%	latent-ODE	0.41	0.721 $\pm$ 0.004	0.377 $\pm$ 0.003
30%	ODEBRAIN	0.55	0.845 $\pm$ 0.002	0.464 $\pm$ 0.007

Appendix

Table 7: Ablation of missing value (MV) on TUSZ (12s seizure detection) with AUROC↑, F1↑, and predicted missing graph structural similarity (Sim.)↑ (Bold = best).

Top- $\tau$	AUROC	Recall	F1
2	0.867 $\pm$ 0.003	0.575 $\pm$ 0.003	0.484 $\pm$ 0.009
3	0.881 $\pm$ 0.006	0.605 $\pm$ 0.003	0.496 $\pm$ 0.017
7	0.870 $\pm$ 0.004	0.602 $\pm$ 0.004	0.488 $\pm$ 0.013
9	0.868 $\pm$ 0.004	0.589 $\pm$ 0.004	0.487 $\pm$ 0.011
11	0.866 $\pm$ 0.004	0.571 $\pm$ 0.002	0.491 $\pm$ 0.003
13	0.865 $\pm$ 0.003	0.562 $\pm$ 0.004	0.474 $\pm$ 0.003

Appendix

Table 8: Ablation on TUSZ dataset for 12s seizure detection with different top-

\tau

options. Bold and underline indicate best and second-best results.

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