# BrainODE: Dynamic Brain Signal Analysis via Graph-Aided Neural Ordinary Differential Equations

arXiv: https://arxiv.org/abs/2405.00077 · HTML: https://mlsanity.com/paper/2405.00077/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- Builds on 26 of its 43 references that are in the map.
- First posted on arXiv 30 Apr 2024.

## Builds on (most cited first, 26 of 26)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Self-Attention with Relative Position Representations](https://mlsanity.com/paper/1803.02155/) (2018)
- [Graph Transformer Networks](https://mlsanity.com/paper/1911.06455/) (2019)
- [A Transformer-based Framework for Multivariate Time Series Representation Learning](https://mlsanity.com/paper/2010.02803/) (2020)
- [Fundamentals of Recurrent Neural Network (RNN) and Long Short-Term Memory (LSTM) Network](https://mlsanity.com/paper/1808.03314/) (2018)
- [Graph Neural Networks with Learnable Structural and Positional Representations](https://mlsanity.com/paper/2110.07875/) (2021)
- [Transformer Quality in Linear Time](https://mlsanity.com/paper/2202.10447/) (2022)
- [BrainGB: A Benchmark for Brain Network Analysis with Graph Neural Networks](https://mlsanity.com/paper/2204.07054/) (2022)
- [FBNETGEN: Task-aware GNN-based fMRI Analysis via Functional Brain Network Generation](https://mlsanity.com/paper/2205.12465/) (2022)
- [Learning Continuous System Dynamics from Irregularly-Sampled Partial Observations](https://mlsanity.com/paper/2011.03880/) (2020)
- [Interpretable Graph Neural Networks for Connectome-Based Brain Disorder Analysis](https://mlsanity.com/paper/2207.00813/) (2022)
- [A probabilistic model for the numerical solution of initial value problems](https://mlsanity.com/paper/1610.05261/) (2016)
- [Generalizing Graph ODE for Learning Complex System Dynamics across Environments](https://mlsanity.com/paper/2307.04287/) (2023)
- [Polynomial Matrix Completion for Missing Data Imputation and Transductive Learning](https://mlsanity.com/paper/1912.06989/) (2019)
- [Learning Task-Aware Effective Brain Connectivity for fMRI Analysis with Graph Neural Networks](https://mlsanity.com/paper/2211.00261/) (2022)
- [Edges in Brain Networks: Contributions to Models of Structure and Function](https://mlsanity.com/paper/2105.07069/) (2021)
- [Analyzing complex functional brain networks: fusing statistics and network science to understand the brain](https://mlsanity.com/paper/1302.5721/) (2013)
- [Bayesian Joint Modeling of Multiple Brain Functional Networks](https://mlsanity.com/paper/1708.02123/) (2017)
- [Contrastive Graph Pooling for Explainable Classification of Brain Networks](https://mlsanity.com/paper/2307.11133/) (2023)
- [A symmetry-based method to infer structural brain networks from tractography data](https://mlsanity.com/paper/1508.03788/) (2015)
- [Consistency of Regions of Interest as nodes of functional brain networks measured by fMRI](https://mlsanity.com/paper/1704.07635/) (2017)
- [Whole Brain Network Dynamics of Epileptic Seizures at Single Cell Resolution](https://mlsanity.com/paper/2212.05874/) (2022)

## Built on by (most cited first, 12 of 12)

- [Graph ODEs and Beyond: A Comprehensive Survey on Integrating Differential Equations with Graph Neural Networks](https://mlsanity.com/paper/2503.23167/) (2025)
- [Simulator and Experience Enhanced Diffusion Model for Comprehensive ECG Generation](https://mlsanity.com/paper/2511.09895/) (2025)
- [FD-Bench: A Modular and Fair Benchmark for Data-driven Fluid Simulation](https://mlsanity.com/paper/2505.20349/) (2025)
- [ODEBrain: Continuous-Time EEG Graph for Modeling Dynamic Brain Networks](https://mlsanity.com/paper/2602.23285/) (2026)
- [NeuroTree: Hierarchical Functional Brain Pathway Decoding for Mental Health Disorders](https://mlsanity.com/paper/2502.18786/) (2025)
- [Spatio-Temporal Graph Deep Learning with Stochastic Differential Equations for Uncovering Alzheimer's Disease Progression](https://mlsanity.com/paper/2509.21735/) (2025)
- [GeoDynamics: A Geometric State-Space Neural Network for Understanding Brain Dynamics on Riemannian Manifolds](https://mlsanity.com/paper/2601.13570/) (2026)
- [SDE-Driven Spatio-Temporal Hypergraph Neural Networks for Irregular Longitudinal fMRI Connectome Modeling in Alzheimer's Disease](https://mlsanity.com/paper/2603.20452/) (2026)
- [Integrating Mechanistic and Data-Driven Models for Neurological Disorders through Differentiable Programming](https://mlsanity.com/paper/2606.06094/) (2026)
- [DevelopmentODE: Structured Neural ODEs for Early Brain Development Dynamics Across a Decade](https://mlsanity.com/paper/2609.33048/) (2026)
- [FAST-Brain: A Flow-Aligned Spatio-Temporal Surrogate Brain Model](https://mlsanity.com/paper/2609.34354/) (2026)
- [GRFBrain: Graph-Structured Rectified Flows for EEG Dynamic Modeling](https://mlsanity.com/paper/2609.37934/) (2026)

## Abstract (arXiv)

Brain network analysis is vital for understanding the neural interactions regarding brain structures and functions, and identifying potential biomarkers for clinical phenotypes. However, widely used brain signals such as Blood Oxygen Level Dependent (BOLD) time series generated from functional Magnetic Resonance Imaging (fMRI) often manifest three challenges: (1) missing values, (2) irregular samples, and (3) sampling misalignment, due to instrumental limitations, impacting downstream brain network analysis and clinical outcome predictions. In this work, we propose a novel model called BrainODE to achieve continuous modeling of dynamic brain signals using Ordinary Differential Equations (ODE). By learning latent initial values and neural ODE functions from irregular time series, BrainODE effectively reconstructs brain signals at any time point, mitigating the aforementioned three data challenges of brain signals altogether. Comprehensive experimental results on real-world neuroimaging datasets demonstrate the superior performance of BrainODE and its capability of addressing the three data challenges.