# Graph Neural Stochastic Differential Equations for Learning Brownian Dynamics

arXiv: https://arxiv.org/abs/2306.11435 · HTML: https://mlsanity.com/paper/2306.11435/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 37 references that are in the map.
- First posted on arXiv 20 Jun 2023.

## Builds on (most cited first, 17 of 17)

- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Learning to Simulate Complex Physics with Graph Networks](https://mlsanity.com/paper/2002.09405/) (2020)
- [Hamiltonian Neural Networks](https://mlsanity.com/paper/1906.01563/) (2019)
- [Discovering Symbolic Models from Deep Learning with Inductive Biases](https://mlsanity.com/paper/2006.11287/) (2020)
- [Symplectic ODE-Net: Learning Hamiltonian Dynamics with Control](https://mlsanity.com/paper/1909.12077/) (2019)
- [Hamiltonian Graph Networks with ODE Integrators](https://mlsanity.com/paper/1909.12790/) (2019)
- [Simplifying Hamiltonian and Lagrangian Neural Networks via Explicit Constraints](https://mlsanity.com/paper/2010.13581/) (2020)
- [Equivariant Graph Mechanics Networks with Constraints](https://mlsanity.com/paper/2203.06442/) (2022)
- [Benchmarking Energy-Conserving Neural Networks for Learning Dynamics from Data](https://mlsanity.com/paper/2012.02334/) (2020)
- [Deconstructing the Inductive Biases of Hamiltonian Neural Networks](https://mlsanity.com/paper/2202.04836/) (2022)
- [Learning Articulated Rigid Body Dynamics with Lagrangian Graph Neural Network](https://mlsanity.com/paper/2209.11588/) (2022)
- [Unravelling the Performance of Physics-informed Graph Neural Networks for Dynamical Systems](https://mlsanity.com/paper/2211.05520/) (2022)
- [NTFields: Neural Time Fields for Physics-Informed Robot Motion Planning](https://mlsanity.com/paper/2210.00120/) (2022)
- [Enhancing the Inductive Biases of Graph Neural ODE for Modeling Dynamical Systems](https://mlsanity.com/paper/2209.10740/) (2022)
- [Learning the Dynamics of Particle-based Systems with Lagrangian Graph Neural Networks](https://mlsanity.com/paper/2209.01476/) (2022)
- [Identifying Physical Law of Hamiltonian Systems via Meta-Learning](https://mlsanity.com/paper/2102.11544/) (2021)
- [Learning non-stationary Langevin dynamics from stochastic observations of latent trajectories](https://mlsanity.com/paper/2012.14944/) (2020)

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

- [Uncertainty Modeling in Graph Neural Networks via Stochastic Differential Equations](https://mlsanity.com/paper/2408.16115/) (2024)
- [Graph Neural Stochastic Differential Equations](https://mlsanity.com/paper/2308.12316/) (2023)

## Abstract (arXiv)

Neural networks (NNs) that exploit strong inductive biases based on physical laws and symmetries have shown remarkable success in learning the dynamics of physical systems directly from their trajectory. However, these works focus only on the systems that follow deterministic dynamics, for instance, Newtonian or Hamiltonian dynamics. Here, we propose a framework, namely Brownian graph neural networks (BROGNET), combining stochastic differential equations (SDEs) and GNNs to learn Brownian dynamics directly from the trajectory. We theoretically show that BROGNET conserves the linear momentum of the system, which in turn, provides superior performance on learning dynamics as revealed empirically. We demonstrate this approach on several systems, namely, linear spring, linear spring with binary particle types, and non-linear spring systems, all following Brownian dynamics at finite temperatures. We show that BROGNET significantly outperforms proposed baselines across all the benchmarked Brownian systems. In addition, we demonstrate zero-shot generalizability of BROGNET to simulate unseen system sizes that are two orders of magnitude larger and to different temperatures than those used during training. Altogether, our study contributes to advancing the understanding of the intricate dynamics of Brownian motion and demonstrates the effectiveness of graph neural networks in modeling such complex systems.