BrainDyn: A Sheaf Neural ODE for Generative Brain Dynamics

2026-05-19

AI Summary

Existing neural networks struggle to generate brain activity that simultaneously respects anatomical constraints and captures realistic dynamic properties. This work proposes BrainDyn, the first framework to integrate sheaf theory with neural differential equations for modeling continuous-time brain dynamics. Built upon a structured brain graph, BrainDyn employs LSTM units to encode regional historical activity, constructs edge-specific shared spaces via learnable restriction maps, and drives message passing and neural ODE evolution through a sheaf Laplacian. This approach enables explicit modeling of brain anatomy while supporting highly expressive continuous dynamics. Evaluated on fMRI, EEG, and NEST-simulated data, BrainDyn demonstrates strong multimodal predictive performance and facilitates downstream applications such as virtual perturbation experiments.

Abstract

Efficient neural network models that generate brain-like dynamic activity can be a valuable resource for generating synthetic data, analyzing differences in brain transients under conditions such as testing perturbation activity or inferring the underlying generative dynamics. However, large language models (LLMs) or standard recurrent neural networks (RNNs) ignore the anatomical organization and therefore do not produce components that align with brain regions. On the other hand, graph-based networks often have very simple message passing rules that are not sufficiently expressive for brain-like dynamics. To address this, we introduce BrainDyn, a sheaf neural ordinary differential equation (neural ODE) model for continuous-time dynamics on structured brain graphs. BrainDyn encodes the recent activity history of each brain region using a long short-term memory (LSTM) model over a sliding temporal window to produce hidden states, or stalks, that are projected through learnable restriction maps into edge-specific shared spaces. Discrepancies between neighboring nodes in these shared spaces are characterized by a sheaf Laplacian that can facilitate message passing between neuronal units. The output of these messages is then fed to a neural ODE that governs the continuous-time evolution of neuronal activity. We evaluated BrainDyn on resting-state fMRI (PNC dataset), scalp EEG with focal epilepsy (TUSZ dataset), and simulated activity from the NEST spiking network simulator. BrainDyn achieves strong forecasting ability across modalities, and the resulting representations support downstream tasks including in silico perturbation prediction.

Problem

• brain dynamics
• neural networks
• anatomical organization
• graph-based models
• generative modeling

Innovation

• Sheaf Neural ODE
• Brain Dynamics
• Structured Brain Graph
• Continuous-time Modeling
• In Silico Perturbation