# SURF: A Generalization Benchmark for GNNs Predicting Fluid Dynamics

arXiv: https://arxiv.org/abs/2310.20049 · HTML: https://mlsanity.com/paper/2310.20049/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 35 references that are in the map.
- First posted on arXiv 30 Oct 2023.

## Builds on (most cited first, 14 of 14)

- [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)
- [Fourier Neural Operator with Learned Deformations for PDEs on General Geometries](https://mlsanity.com/paper/2207.05209/) (2022)
- [GNOT: A General Neural Operator Transformer for Operator Learning](https://mlsanity.com/paper/2302.14376/) (2023)
- [Prediction of Aerodynamic Flow Fields Using Convolutional Neural Networks](https://mlsanity.com/paper/1905.13166/) (2019)
- [Combining Differentiable PDE Solvers and Graph Neural Networks for Fluid Flow Prediction](https://mlsanity.com/paper/2007.04439/) (2020)
- [Latent-space Physics: Towards Learning the Temporal Evolution of Fluid Flow](https://mlsanity.com/paper/1802.10123/) (2018)
- [Learned Coarse Models for Efficient Turbulence Simulation](https://mlsanity.com/paper/2112.15275/) (2021)
- [Predicting Physics in Mesh-reduced Space with Temporal Attention](https://mlsanity.com/paper/2201.09113/) (2022)
- [Eagle: Large-Scale Learning of Turbulent Fluid Dynamics with Mesh Transformers](https://mlsanity.com/paper/2302.10803/) (2023)
- [Graph Element Networks: adaptive, structured computation and memory](https://mlsanity.com/paper/1904.09019/) (2019)
- [Application of Convolutional Neural Network to Predict Airfoil Lift Coefficient](https://mlsanity.com/paper/1712.10082/) (2017)

## Abstract (arXiv)

Simulating fluid dynamics is crucial for the design and development process, ranging from simple valves to complex turbomachinery. Accurately solving the underlying physical equations is computationally expensive. Therefore, learning-based solvers that model interactions on meshes have gained interest due to their promising speed-ups. However, it is unknown to what extent these models truly understand the underlying physical principles and can generalize rather than interpolate. Generalization is a key requirement for a general-purpose fluid simulator, which should adapt to different topologies, resolutions, or thermodynamic ranges. We propose SURF, a benchmark designed to test the textitgeneralization of learned graph-based fluid simulators. SURF comprises individual datasets and provides specific performance and generalization metrics for evaluating and comparing different models. We empirically demonstrate the applicability of SURF by thoroughly investigating the two state-of-the-art graph-based models, yielding new insights into their generalization.