# LagrangeBench: A Lagrangian Fluid Mechanics Benchmarking Suite

arXiv: https://arxiv.org/abs/2309.16342 · HTML: https://mlsanity.com/paper/2309.16342/

## Key facts

- Cited by 27 papers in the map (data through 14 Oct 2026).
- Builds on 32 of its 91 references that are in the map.
- First posted on arXiv 28 Sep 2023.

## Builds on (most cited first, 30 of 32)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [PointNet++: Deep Hierarchical Feature Learning on Point Sets in a Metric Space](https://mlsanity.com/paper/1706.02413/) (2017)
- [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)
- [Datasheets for Datasets](https://mlsanity.com/paper/1803.09010/) (2018)
- [Relational inductive biases, deep learning, and graph networks](https://mlsanity.com/paper/1806.01261/) (2018)
- [E(n) Equivariant Graph Neural Networks](https://mlsanity.com/paper/2102.09844/) (2021)
- [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)
- [Tensor field networks: Rotation- and translation-equivariant neural networks for 3D point clouds](https://mlsanity.com/paper/1802.08219/) (2018)
- [Neural Operator: Graph Kernel Network for Partial Differential Equations](https://mlsanity.com/paper/2003.03485/) (2020)
- [E(3)-Equivariant Graph Neural Networks for Data-Efficient and Accurate Interatomic Potentials](https://mlsanity.com/paper/2101.03164/) (2021)
- [Graph Transformer Networks](https://mlsanity.com/paper/1911.06455/) (2019)
- [Interaction Networks for Learning about Objects, Relations and Physics](https://mlsanity.com/paper/1612.00222/) (2016)
- [Graph U-Nets](https://mlsanity.com/paper/1905.05178/) (2019)
- [Equivariant message passing for the prediction of tensorial properties and molecular spectra](https://mlsanity.com/paper/2102.03150/) (2021)
- [PDEBENCH: An Extensive Benchmark for Scientific Machine Learning](https://mlsanity.com/paper/2210.07182/) (2022)
- [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)
- [Learning Local Equivariant Representations for Large-Scale Atomistic Dynamics](https://mlsanity.com/paper/2204.05249/) (2022)
- [Graph networks as learnable physics engines for inference and control](https://mlsanity.com/paper/1806.01242/) (2018)
- [Geometric and Physical Quantities Improve E(3) Equivariant Message Passing](https://mlsanity.com/paper/2110.02905/) (2021)
- [Learning Particle Dynamics for Manipulating Rigid Bodies, Deformable Objects, and Fluids](https://mlsanity.com/paper/1810.01566/) (2018)
- [Towards Multi-spatiotemporal-scale Generalized PDE Modeling](https://mlsanity.com/paper/2209.15616/) (2022)
- [MultiScale MeshGraphNets](https://mlsanity.com/paper/2210.00612/) (2022)
- [Flexible Neural Representation for Physics Prediction](https://mlsanity.com/paper/1806.08047/) (2018)
- [JAX-FLUIDS: A fully-differentiable high-order computational fluid dynamics solver for compressible two-phase flows](https://mlsanity.com/paper/2203.13760/) (2022)
- [Scaling the leading accuracy of deep equivariant models to biomolecular simulations of realistic size](https://mlsanity.com/paper/2304.10061/) (2023)
- [Guaranteed Conservation of Momentum for Learning Particle-based Fluid Dynamics](https://mlsanity.com/paper/2210.06036/) (2022)
- [Learning Lagrangian Fluid Mechanics with E(3)-Equivariant Graph Neural Networks](https://mlsanity.com/paper/2305.15603/) (2023)

## Built on by (most cited first, 27 of 27)

- [The Well: a Large-Scale Collection of Diverse Physics Simulations for Machine Learning](https://mlsanity.com/paper/2412.00568/) (2024)
- [DrivAerNet++: A Large-Scale Multimodal Car Dataset with Computational Fluid Dynamics Simulations and Deep Learning Benchmarks](https://mlsanity.com/paper/2406.09624/) (2024)
- [Universal Physics Transformers: A Framework For Efficiently Scaling Neural Operators](https://mlsanity.com/paper/2402.12365/) (2024)
- [Active Learning for Neural PDE Solvers](https://mlsanity.com/paper/2408.01536/) (2024)
- [Curly Flow Matching for Learning Non-gradient Field Dynamics](https://mlsanity.com/paper/2510.26645/) (2025)
- [RealPDEBench: A Benchmark for Complex Physical Systems with Real-World Data](https://mlsanity.com/paper/2601.01829/) (2026)
- [Neural SPH: Improved Neural Modeling of Lagrangian Fluid Dynamics](https://mlsanity.com/paper/2402.06275/) (2024)
- [SIMSHIFT: A Benchmark for Adapting Neural Surrogates to Distribution Shifts](https://mlsanity.com/paper/2506.12007/) (2025)
- [DrivAerStar: An Industrial-Grade CFD Dataset for Vehicle Aerodynamic Optimization](https://mlsanity.com/paper/2510.16857/) (2025)
- [EngiBench: A Framework for Data-Driven Engineering Design Research](https://mlsanity.com/paper/2508.00831/) (2025)
- [A Neural Material Point Method for Particle-based Emulation](https://mlsanity.com/paper/2408.15753/) (2024)
- [A Cosmic-Scale Benchmark for Symmetry-Preserving Data Processing](https://mlsanity.com/paper/2410.20516/) (2024)
- [JAX-SPH: A Differentiable Smoothed Particle Hydrodynamics Framework](https://mlsanity.com/paper/2403.04750/) (2024)
- [Emergent Transfer of a Physics Foundation Model from Simulation to Laboratory Turbulence](https://mlsanity.com/paper/2606.01470/) (2026)
- [AneumoBench: A Source-Linked Benchmark for Synthetic-Geometry Transfer in Aneurysm CFD](https://mlsanity.com/paper/2505.14717/) (2025)
- [PDEInvBench: A Comprehensive Dataset and Design Space Exploration of Neural Networks for PDE Inverse Problems](https://mlsanity.com/paper/2605.25353/) (2026)
- [ConDiff: A Challenging Dataset for Neural Solvers of Partial Differential Equations](https://mlsanity.com/paper/2406.04709/) (2024)
- [CORGI: GNNs with Convolutional Residual Global Interactions for Lagrangian Simulation](https://mlsanity.com/paper/2511.22938/) (2025)
- [BubbleSH: A Dataset of Rising Bubbles with Deformable Interfaces](https://mlsanity.com/paper/2607.07275/) (2026)
- [Generalized Neural Operator for Parametric and Boundary-Value Problems](https://mlsanity.com/paper/2607.21932/) (2026)
- [Response Renormalization for Critical Deep Equilibrium Models](https://mlsanity.com/paper/2608.23725/) (2026)
- [PLAID: A Unified Data Model for Machine Learning on Heterogeneous Physics Simulations](https://mlsanity.com/paper/2505.02974/) (2025)
- [Stabilizing Test-Time Adaptation of High-Dimensional Simulation Surrogates via D-Optimal Statistics](https://mlsanity.com/paper/2602.15820/) (2026)
- [CarCrashNet: A Large-Scale Dataset and Hierarchical Neural Solver for Data-Driven Structural Crash Simulation](https://mlsanity.com/paper/2605.07098/) (2026)
- [Hybrid Lagrangian-Eulerian Model for Lagrangian Fluid Simulation](https://mlsanity.com/paper/2608.01164/) (2026)
- [From Fixed Grids to Moving Particles:A Transferable Latent Operator for Fluid Dynamics](https://mlsanity.com/paper/2608.14120/) (2026)
- [World Embedding Benchmark](https://mlsanity.com/paper/2610.03632/) (2026)

## Abstract (arXiv)

Machine learning has been successfully applied to grid-based PDE modeling in various scientific applications. However, learned PDE solvers based on Lagrangian particle discretizations, which are the preferred approach to problems with free surfaces or complex physics, remain largely unexplored. We present LagrangeBench, the first benchmarking suite for Lagrangian particle problems, focusing on temporal coarse-graining. In particular, our contribution is: (a) seven new fluid mechanics datasets (four in 2D and three in 3D) generated with the Smoothed Particle Hydrodynamics (SPH) method including the Taylor-Green vortex, lid-driven cavity, reverse Poiseuille flow, and dam break, each of which includes different physics like solid wall interactions or free surface, (b) efficient JAX-based API with various recent training strategies and three neighbor search routines, and (c) JAX implementation of established Graph Neural Networks (GNNs) like GNS and SEGNN with baseline results. Finally, to measure the performance of learned surrogates we go beyond established position errors and introduce physical metrics like kinetic energy MSE and Sinkhorn distance for the particle distribution. Our codebase is available at https://github.com/tumaer/lagrangebench .