# FlowBench: A Large Scale Benchmark for Flow Simulation over Complex Geometries

arXiv: https://arxiv.org/abs/2409.18032 · HTML: https://mlsanity.com/paper/2409.18032/

## Key facts

- Cited by 19 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 63 references that are in the map.
- First posted on arXiv 26 Sep 2024.

## Builds on (most cited first, 13 of 13)

- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators](https://mlsanity.com/paper/1910.03193/) (2019)
- [WeatherBench: A benchmark dataset for data-driven weather forecasting](https://mlsanity.com/paper/2002.00469/) (2020)
- [Convolutional Neural Operators for robust and accurate learning of PDEs](https://mlsanity.com/paper/2302.01178/) (2023)
- [AirfRANS: High Fidelity Computational Fluid Dynamics Dataset for Approximating Reynolds-Averaged Navier-Stokes Solutions](https://mlsanity.com/paper/2212.07564/) (2022)
- [Geom-DeepONet: A Point-cloud-based Deep Operator Network for Field Predictions on 3D Parameterized Geometries](https://mlsanity.com/paper/2403.14788/) (2024)
- [CFDBench: A Large-Scale Benchmark for Machine Learning Methods in Fluid Dynamics](https://mlsanity.com/paper/2310.05963/) (2023)
- [SkelNetOn 2019: Dataset and Challenge on Deep Learning for Geometric Shape Understanding](https://mlsanity.com/paper/1903.09233/) (2019)
- [An extensible Benchmarking Graph-Mesh dataset for studying Steady-State Incompressible Navier-Stokes Equations](https://mlsanity.com/paper/2206.14709/) (2022)
- [Industrial scale large eddy simulations (LES) with adaptive octree meshes using immersogeometric analysis](https://mlsanity.com/paper/2009.00706/) (2020)
- [Scalable adaptive PDE solvers in arbitrary domains](https://mlsanity.com/paper/2108.03757/) (2021)
- [The Second-Generation Shifted Boundary Method and Its Numerical Analysis](https://mlsanity.com/paper/2004.10584/) (2020)
- [Scalable adaptive algorithms for next-generation multiphase flow simulations](https://mlsanity.com/paper/2209.12130/) (2022)

## Built on by (most cited first, 19 of 19)

- [Walrus: A Cross-Domain Foundation Model for Continuum Dynamics](https://mlsanity.com/paper/2511.15684/) (2025)
- [Geometric Operator Learning with Optimal Transport](https://mlsanity.com/paper/2507.20065/) (2025)
- [RealPDEBench: A Benchmark for Complex Physical Systems with Real-World Data](https://mlsanity.com/paper/2601.01829/) (2026)
- [Geometry Matters: Benchmarking Scientific ML Approaches for Flow Prediction around Complex Geometries](https://mlsanity.com/paper/2501.01453/) (2024)
- [3D Neural Operator-Based Flow Surrogates around 3D geometries: Signed Distance Functions and Derivative Constraints](https://mlsanity.com/paper/2503.17289/) (2025)
- [A Spectral-Grassmann Wasserstein metric for operator representations of dynamical systems](https://mlsanity.com/paper/2509.24920/) (2025)
- [GenMed: A Pairwise Generative Reformulation of Medical Diagnostic Tasks](https://mlsanity.com/paper/2605.10645/) (2026)
- [Pre-Generating Multi-Difficulty PDE Data for Few-Shot Neural PDE Solvers](https://mlsanity.com/paper/2512.00564/) (2025)
- [FLUIDSPLAT: Reconstructing Physical Fields from Sparse Sensors via Gaussian Primitives](https://mlsanity.com/paper/2605.18866/) (2026)
- [Improving Large Vision-Language Models' Understanding for Flow Field Data](https://mlsanity.com/paper/2507.18311/) (2025)
- [GeoFunFlow: Geometric Function Flow Matching for Inverse Operator Learning over Complex Geometries](https://mlsanity.com/paper/2509.24117/) (2025)
- [Predicting Time-Dependent Flow Over Complex Geometries Using Operator Networks](https://mlsanity.com/paper/2512.04434/) (2025)
- [WeirNet: A Large-Scale 3D CFD Benchmark for Geometric Surrogate Modeling of Piano Key Weirs](https://mlsanity.com/paper/2602.20714/) (2026)
- [Do Neural Operators Forget Geometry? The Forgetting Hypothesis in Deep Operator Learning](https://mlsanity.com/paper/2605.05862/) (2026)
- [Breakeven complexity: A new perspective on neural partial differential equation solvers](https://mlsanity.com/paper/2605.15399/) (2026)
- [ThousandWorlds: A benchmark for climate emulation of potentially habitable exoplanets](https://mlsanity.com/paper/2606.18338/) (2026)
- [Dandelion: A Spherical Flower for Neural Simulation of Planetary Dynamics](https://mlsanity.com/paper/2608.27521/) (2026)
- [FSAN: Flow State Attention Network for Aerodynamic Prediction](https://mlsanity.com/paper/2609.06660/) (2026)
- [One-Way Coupling via Patchwise Adaptive Normalization in Transformer Surrogates](https://mlsanity.com/paper/2610.14687/) (2026)

## Abstract (arXiv)

Simulating fluid flow around arbitrary shapes is key to solving various engineering problems. However, simulating flow physics across complex geometries remains numerically challenging and computationally resource-intensive, particularly when using conventional PDE solvers. Machine learning methods offer attractive opportunities to create fast and adaptable PDE solvers. However, benchmark datasets to measure the performance of such methods are scarce, especially for flow physics across complex geometries. We introduce FlowBench, a dataset for neural simulators with over 10K samples, which is currently larger than any publicly available flow physics dataset. FlowBench contains flow simulation data across complex geometries (textitparametric vs. non-parametric), spanning a range of flow conditions (textitReynolds number and Grashoff number), capturing a diverse array of flow phenomena (textitsteady vs. transient; forced vs. free convection), and for both 2D and 3D. FlowBench contains over 10K data samples, with each sample the outcome of a fully resolved, direct numerical simulation using a well-validated simulator framework designed for modeling transport phenomena in complex geometries. For each sample, we include velocity, pressure, and temperature field data at 3 different resolutions and several summary statistics features of engineering relevance (such as coefficients of lift and drag, and Nusselt numbers). %Additionally, we include masks and signed distance fields for each shape. We envision that FlowBench will enable evaluating the interplay between complex geometry, coupled flow phenomena, and data sufficiency on the performance of current, and future, neural PDE solvers. We enumerate several evaluation metrics to help rank order the performance of neural PDE solvers. We benchmark the performance of several baseline methods including FNO, CNO, WNO, and DeepONet.