# Accelerating Particle and Fluid Simulations with Differentiable Graph Networks for Solving Forward and Inverse Problems

arXiv: https://arxiv.org/abs/2309.13348 · HTML: https://mlsanity.com/paper/2309.13348/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 19 references that are in the map.
- First posted on arXiv 23 Sep 2023.

## Builds on (most cited first, 10 of 10)

- [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)
- [DiffTaichi: Differentiable Programming for Physical Simulation](https://mlsanity.com/paper/1910.00935/) (2019)
- [Deep Graph Library: A Graph-Centric, Highly-Performant Package for Graph Neural Networks](https://mlsanity.com/paper/1909.01315/) (2019)
- [Boundary Graph Neural Networks for 3D Simulations](https://mlsanity.com/paper/2106.11299/) (2021)
- [Graph Neural Network-based surrogate model for granular flows](https://mlsanity.com/paper/2305.05218/) (2023)
- [GNS: A generalizable Graph Neural Network-based simulator for particulate and fluid modeling](https://mlsanity.com/paper/2211.10228/) (2022)
- [A cooperative game for automated learning of elasto-plasticity knowledge graphs and models with AI-guided experimentation](https://mlsanity.com/paper/1903.04307/) (2019)
- [Scalable and modular material point method for large-scale simulations](https://mlsanity.com/paper/1909.13380/) (2019)
- [Minority Report: A Graph Network Oracle for In Situ Visualization](https://mlsanity.com/paper/2206.12683/) (2022)

## Built on by (most cited first, 6 of 6)

- [DiffusionPDE: Generative PDE-Solving Under Partial Observation](https://mlsanity.com/paper/2406.17763/) (2024)
- [Hybrid Neural-MPM for Interactive Fluid Simulations in Real-Time](https://mlsanity.com/paper/2505.18926/) (2025)
- [Machine Learning Aided Modeling of Granular Materials: A Review](https://mlsanity.com/paper/2410.14767/) (2024)
- [Towards scientific machine learning for granular material simulations -- challenges and opportunities](https://mlsanity.com/paper/2504.08766/) (2025)
- [Convolution Operator Network for Forward and Inverse Problems (FI-Conv): Application to Plasma Turbulence Simulations](https://mlsanity.com/paper/2602.04287/) (2026)
- [TRACE: A spatiotemporal contact memory graph network simulator for granular dynamics](https://mlsanity.com/paper/2609.02991/) (2026)

## Abstract (arXiv)

We leverage physics-embedded differentiable graph network simulators (GNS) to accelerate particulate and fluid simulations to solve forward and inverse problems. GNS represents the domain as a graph with particles as nodes and learned interactions as edges. Compared to modeling global dynamics, GNS enables learning local interaction laws through edge messages, improving its generalization to new environments. GNS achieves over 165x speedup for granular flow prediction compared to parallel CPU numerical simulations. We propose a novel hybrid GNS/Material Point Method (MPM) to accelerate forward simulations by minimizing error on a pure surrogate model by interleaving MPM in GNS rollouts to satisfy conservation laws and minimize errors achieving 24x speedup compared to pure numerical simulations. The differentiable GNS enables solving inverse problems through automatic differentiation, identifying material parameters that result in target runout distances. We demonstrate the ability of GNS to solve inverse problems by iteratively updating the friction angle (a material property) by computing the gradient of a loss function based on the final and target runouts, thereby identifying the friction angle that best matches the observed runout. The physics-embedded and differentiable simulators open an exciting new paradigm for AI-accelerated design, control, and optimization.