# Fast Simulation of Particulate Suspensions Enabled by Graph Neural Network

arXiv: https://arxiv.org/abs/2206.13905 · HTML: https://mlsanity.com/paper/2206.13905/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 53 references that are in the map.
- First posted on arXiv 17 Jun 2022.

## Builds on (most cited first, 9 of 9)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [Dynamic Graph CNN for Learning on Point Clouds](https://mlsanity.com/paper/1801.07829/) (2018)
- [Relational inductive biases, deep learning, and graph networks](https://mlsanity.com/paper/1806.01261/) (2018)
- [Learning to Simulate Complex Physics with Graph Networks](https://mlsanity.com/paper/2002.09405/) (2020)
- [Automatic differentiation in machine learning: a survey](https://mlsanity.com/paper/1502.05767/) (2015)
- [Interaction Networks for Learning about Objects, Relations and Physics](https://mlsanity.com/paper/1612.00222/) (2016)
- [Propagation Networks for Model-Based Control Under Partial Observation](https://mlsanity.com/paper/1809.11169/) (2018)
- [A scalable computational platform for particulate Stokes suspensions](https://mlsanity.com/paper/1909.06623/) (2019)

## Built on by (most cited first, 5 of 5)

- [A Finite Element-Inspired Hypergraph Neural Network: Application to Fluid Dynamics Simulations](https://mlsanity.com/paper/2212.14545/) (2022)
- [Physics-aware Machine Learning Revolutionizes Scientific Paradigm for Machine Learning and Process-based Hydrology](https://mlsanity.com/paper/2310.05227/) (2023)
- [Beyond Grid Data: Exploring Graph Neural Networks for Earth Observation](https://mlsanity.com/paper/2411.03223/) (2024)
- [A Mesh-Adaptive Hypergraph Neural Network for Unsteady Flow Around Oscillating and Rotating Structures](https://mlsanity.com/paper/2503.22252/) (2025)
- [Data-driven low-dimensional model of a sedimenting flexible fiber](https://mlsanity.com/paper/2405.10442/) (2024)

## Abstract (arXiv)

Predicting the dynamic behaviors of particles in suspension subject to hydrodynamic interaction (HI) and external drive can be critical for many applications. By harvesting advanced deep learning techniques, the present work introduces a new framework, hydrodynamic interaction graph neural network (HIGNN), for inferring and predicting the particles' dynamics in Stokes suspensions. It overcomes the limitations of traditional approaches in computational efficiency, accuracy, and/or transferability. In particular, by uniting the data structure represented by a graph and the neural networks with learnable parameters, the HIGNN constructs surrogate modeling for the mobility tensor of particles which is the key to predicting the dynamics of particles subject to HI and external forces. To account for the many-body nature of HI, we generalize the state-of-the-art GNN by introducing higher-order connectivity into the graph and the corresponding convolutional operation. For training the HIGNN, we only need the data for a small number of particles in the domain of interest, and hence the training cost can be maintained low. Once constructed, the HIGNN permits fast predictions of the particles' velocities and is transferable to suspensions of different numbers/concentrations of particles in the same domain and to any external forcing. It has the ability to accurately capture both the long-range HI and short-range lubrication effects. We demonstrate the accuracy, efficiency, and transferability of the proposed HIGNN framework in a variety of systems. The requirement on computing resource is minimum: most simulations only require a desktop with one GPU; the simulations for a large suspension of 100,000 particles call for up to 6 GPUs.