# Graph Neural Stochastic Differential Equations

arXiv: https://arxiv.org/abs/2308.12316 · HTML: https://mlsanity.com/paper/2308.12316/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 40 references that are in the map.
- First posted on arXiv 23 Aug 2023.

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

- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Open Graph Benchmark: Datasets for Machine Learning on Graphs](https://mlsanity.com/paper/2005.00687/) (2020)
- [Spatio-Temporal Graph Convolutional Networks: A Deep Learning Framework for Traffic Forecasting](https://mlsanity.com/paper/1709.04875/) (2017)
- [Score-based Generative Modeling of Graphs via the System of Stochastic Differential Equations](https://mlsanity.com/paper/2202.02514/) (2022)
- [Scalable Gradients for Stochastic Differential Equations](https://mlsanity.com/paper/2001.01328/) (2020)
- [Graph Neural Ordinary Differential Equations](https://mlsanity.com/paper/1911.07532/) (2019)
- [Graph Neural Controlled Differential Equations for Traffic Forecasting](https://mlsanity.com/paper/2112.03558/) (2021)
- [Bayesian Graph Neural Networks with Adaptive Connection Sampling](https://mlsanity.com/paper/2006.04064/) (2020)
- [Multivariate Time Series Forecasting with Dynamic Graph Neural ODEs](https://mlsanity.com/paper/2202.08408/) (2022)
- [Efficient and Accurate Gradients for Neural SDEs](https://mlsanity.com/paper/2105.13493/) (2021)
- [Mat'ern Gaussian Processes on Graphs](https://mlsanity.com/paper/2010.15538/) (2020)
- [GraphGDP: Generative Diffusion Processes for Permutation Invariant Graph Generation](https://mlsanity.com/paper/2212.01842/) (2022)
- [NeuPDE: Neural Network Based Ordinary and Partial Differential Equations for Modeling Time-Dependent Data](https://mlsanity.com/paper/1908.03190/) (2019)
- [Infinitely Deep Bayesian Neural Networks with Stochastic Differential Equations](https://mlsanity.com/paper/2102.06559/) (2021)
- [Graph-based Multi-ODE Neural Networks for Spatio-Temporal Traffic Forecasting](https://mlsanity.com/paper/2305.18687/) (2023)
- [Gaussian Processes for Nonlinear Signal Processing](https://mlsanity.com/paper/1303.2823/) (2013)
- [Towards Complex Dynamic Physics System Simulation with Graph Neural ODEs](https://mlsanity.com/paper/2305.12334/) (2023)
- [Graph Neural Stochastic Differential Equations for Learning Brownian Dynamics](https://mlsanity.com/paper/2306.11435/) (2023)

## Built on by (most cited first, 2 of 2)

- [Partially Stochastic Infinitely Deep Bayesian Neural Networks](https://mlsanity.com/paper/2402.03495/) (2024)
- [Integrating Causality with Neurochaos Learning: Proposed Approach and Research Agenda](https://mlsanity.com/paper/2501.13763/) (2025)

## Abstract (arXiv)

We present a novel model Graph Neural Stochastic Differential Equations (Graph Neural SDEs). This technique enhances the Graph Neural Ordinary Differential Equations (Graph Neural ODEs) by embedding randomness into data representation using Brownian motion. This inclusion allows for the assessment of prediction uncertainty, a crucial aspect frequently missed in current models. In our framework, we spotlight the textitLatent Graph Neural SDE variant, demonstrating its effectiveness. Through empirical studies, we find that Latent Graph Neural SDEs surpass conventional models like Graph Convolutional Networks and Graph Neural ODEs, especially in confidence prediction, making them superior in handling out-of-distribution detection across both static and spatio-temporal contexts.