# Neural SPH: Improved Neural Modeling of Lagrangian Fluid Dynamics

arXiv: https://arxiv.org/abs/2402.06275 · HTML: https://mlsanity.com/paper/2402.06275/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Builds on 38 of its 83 references that are in the map.
- First posted on arXiv 9 Feb 2024.

## Builds on (most cited first, 30 of 38)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [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)
- [Learning Mesh-Based Simulation with Graph Networks](https://mlsanity.com/paper/2010.03409/) (2020)
- [FourCastNet: A Global Data-driven High-resolution Weather Model using Adaptive Fourier Neural Operators](https://mlsanity.com/paper/2202.11214/) (2022)
- [E(3)-Equivariant Graph Neural Networks for Data-Efficient and Accurate Interatomic Potentials](https://mlsanity.com/paper/2101.03164/) (2021)
- [Interaction Networks for Learning about Objects, Relations and Physics](https://mlsanity.com/paper/1612.00222/) (2016)
- [MACE: Higher Order Equivariant Message Passing Neural Networks for Fast and Accurate Force Fields](https://mlsanity.com/paper/2206.07697/) (2022)
- [Machine learning accelerated computational fluid dynamics](https://mlsanity.com/paper/2102.01010/) (2021)
- [Message Passing Neural PDE Solvers](https://mlsanity.com/paper/2202.03376/) (2022)
- [3D Steerable CNNs: Learning Rotationally Equivariant Features in Volumetric Data](https://mlsanity.com/paper/1807.02547/) (2018)
- [GemNet: Universal Directional Graph Neural Networks for Molecules](https://mlsanity.com/paper/2106.08903/) (2021)
- [ClimaX: A foundation model for weather and climate](https://mlsanity.com/paper/2301.10343/) (2023)
- [GraphCast: Learning skillful medium-range global weather forecasting](https://mlsanity.com/paper/2212.12794/) (2022)
- [A Note on Over-Smoothing for Graph Neural Networks](https://mlsanity.com/paper/2006.13318/) (2020)
- [The Open Catalyst 2020 (OC20) Dataset and Community Challenges](https://mlsanity.com/paper/2010.09990/) (2020)
- [Geometric and Physical Quantities Improve E(3) Equivariant Message Passing](https://mlsanity.com/paper/2110.02905/) (2021)
- [PDE-Refiner: Achieving Accurate Long Rollouts with Neural PDE Solvers](https://mlsanity.com/paper/2308.05732/) (2023)
- [Solver-in-the-Loop: Learning from Differentiable Physics to Interact with Iterative PDE-Solvers](https://mlsanity.com/paper/2007.00016/) (2020)
- [Towards Multi-spatiotemporal-scale Generalized PDE Modeling](https://mlsanity.com/paper/2209.15616/) (2022)
- [Forecasting Global Weather with Graph Neural Networks](https://mlsanity.com/paper/2202.07575/) (2022)
- [MetNet: A Neural Weather Model for Precipitation Forecasting](https://mlsanity.com/paper/2003.12140/) (2020)
- [MatterGen: a generative model for inorganic materials design](https://mlsanity.com/paper/2312.03687/) (2023)
- [Improving data-driven global weather prediction using deep convolutional neural networks on a cubed sphere](https://mlsanity.com/paper/2003.11927/) (2020)
- [Forces are not Enough: Benchmark and Critical Evaluation for Machine Learning Force Fields with Molecular Simulations](https://mlsanity.com/paper/2210.07237/) (2022)
- [Physics-based Deep Learning](https://mlsanity.com/paper/2109.05237/) (2021)
- [Understanding convolution on graphs via energies](https://mlsanity.com/paper/2206.10991/) (2022)
- [Learning the Dynamics of Physical Systems from Sparse Observations with Finite Element Networks](https://mlsanity.com/paper/2203.08852/) (2022)

## Built on by (most cited first, 11 of 11)

- [Universal Physics Transformers: A Framework For Efficiently Scaling Neural Operators](https://mlsanity.com/paper/2402.12365/) (2024)
- [NeuralDEM -- Real-time Simulation of Industrial Particulate Flows](https://mlsanity.com/paper/2411.09678/) (2024)
- [JAX-SPH: A Differentiable Smoothed Particle Hydrodynamics Framework](https://mlsanity.com/paper/2403.04750/) (2024)
- [Hybrid Neural-MPM for Interactive Fluid Simulations in Real-Time](https://mlsanity.com/paper/2505.18926/) (2025)
- [Bridging Data and Physics: A Graph Neural Network-Based Hybrid Twin Framework](https://mlsanity.com/paper/2512.15767/) (2025)
- [Reversible GNS for Dissipative Fluids with Consistent Bidirectional Dynamics](https://mlsanity.com/paper/2509.22207/) (2025)
- [CORGI: GNNs with Convolutional Residual Global Interactions for Lagrangian Simulation](https://mlsanity.com/paper/2511.22938/) (2025)
- [Breaking Scale Anchoring: Frequency Representation Learning for Accurate High-Resolution Inference from Low-Resolution Training](https://mlsanity.com/paper/2512.05132/) (2025)
- [A meshfree exterior calculus for generalizable and data-efficient learning of physics from point clouds](https://mlsanity.com/paper/2605.08436/) (2026)
- [Adaptive Interaction Graphs for Particle Simulation](https://mlsanity.com/paper/2609.30822/) (2026)
- [AutoPDEBench: Benchmarking LLM Auto-Research for Neural PDE Solver Design](https://mlsanity.com/paper/2609.32245/) (2026)

## Abstract (arXiv)

Smoothed particle hydrodynamics (SPH) is omnipresent in modern engineering and scientific disciplines. SPH is a class of Lagrangian schemes that discretize fluid dynamics via finite material points that are tracked through the evolving velocity field. Due to the particle-like nature of the simulation, graph neural networks (GNNs) have emerged as appealing and successful surrogates. However, the practical utility of such GNN-based simulators relies on their ability to faithfully model physics, providing accurate and stable predictions over long time horizons - which is a notoriously hard problem. In this work, we identify particle clustering originating from tensile instabilities as one of the primary pitfalls. Based on these insights, we enhance both training and rollout inference of state-of-the-art GNN-based simulators with varying components from standard SPH solvers, including pressure, viscous, and external force components. All Neural SPH-enhanced simulators achieve better performance than the baseline GNNs, often by orders of magnitude in terms of rollout error, allowing for significantly longer rollouts and significantly better physics modeling. Code available at https://github.com/tumaer/neuralsph.