# FD-Bench: A Modular and Fair Benchmark for Data-driven Fluid Simulation

arXiv: https://arxiv.org/abs/2505.20349 · HTML: https://mlsanity.com/paper/2505.20349/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 88 of its 150 references that are in the map.
- First posted on arXiv 25 May 2025.

## Builds on (most cited first, 30 of 88)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [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)
- [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)
- [Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets](https://mlsanity.com/paper/2103.10974/) (2021)
- [Physics-Informed Neural Operator for Learning Partial Differential Equations](https://mlsanity.com/paper/2111.03794/) (2021)
- [Fourier Neural Operator with Learned Deformations for PDEs on General Geometries](https://mlsanity.com/paper/2207.05209/) (2022)
- [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)
- [Multipole Graph Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2006.09535/) (2020)
- [Choose a Transformer: Fourier or Galerkin](https://mlsanity.com/paper/2105.14995/) (2021)
- [GNOT: A General Neural Operator Transformer for Operator Learning](https://mlsanity.com/paper/2302.14376/) (2023)
- [Transolver: A Fast Transformer Solver for PDEs on General Geometries](https://mlsanity.com/paper/2402.02366/) (2024)
- [Geometry-Informed Neural Operator for Large-Scale 3D PDEs](https://mlsanity.com/paper/2309.00583/) (2023)
- [U-FNO -- An enhanced Fourier neural operator-based deep-learning model for multiphase flow](https://mlsanity.com/paper/2109.03697/) (2021)
- [Factorized Fourier Neural Operators](https://mlsanity.com/paper/2111.13802/) (2021)
- [Multiwavelet-based Operator Learning for Differential Equations](https://mlsanity.com/paper/2109.13459/) (2021)
- [U-NO: U-shaped Neural Operators](https://mlsanity.com/paper/2204.11127/) (2022)
- [Towards Physics-informed Deep Learning for Turbulent Flow Prediction](https://mlsanity.com/paper/1911.08655/) (2019)
- [Poseidon: Efficient Foundation Models for PDEs](https://mlsanity.com/paper/2405.19101/) (2024)
- [MIONet: Learning multiple-input operators via tensor product](https://mlsanity.com/paper/2202.06137/) (2022)
- [Physics-informed learning of governing equations from scarce data](https://mlsanity.com/paper/2005.03448/) (2020)
- [DPOT: Auto-Regressive Denoising Operator Transformer for Large-Scale PDE Pre-Training](https://mlsanity.com/paper/2403.03542/) (2024)
- [The Well: a Large-Scale Collection of Diverse Physics Simulations for Machine Learning](https://mlsanity.com/paper/2412.00568/) (2024)
- [Scalable Transformer for PDE Surrogate Modeling](https://mlsanity.com/paper/2305.17560/) (2023)

## Built on by (most cited first, 5 of 5)

- [Generalized Neural Operator for Parametric and Boundary-Value Problems](https://mlsanity.com/paper/2607.21932/) (2026)
- [Derived Fields Preserve Fine-Scale Detail in Budgeted Neural Simulators](https://mlsanity.com/paper/2603.29224/) (2026)
- [Open datasets and machine learning for two-phase heat transfer: a review following a spatial-temporal taxonomy](https://mlsanity.com/paper/2605.23037/) (2026)
- [Hybrid Lagrangian-Eulerian Model for Lagrangian Fluid Simulation](https://mlsanity.com/paper/2608.01164/) (2026)
- [AutoPDEBench: Benchmarking LLM Auto-Research for Neural PDE Solver Design](https://mlsanity.com/paper/2609.32245/) (2026)

## Abstract (arXiv)

Data-driven modeling of fluid dynamics has advanced rapidly with neural PDE solvers, yet a fair and strong benchmark remains fragmented due to the absence of unified PDE datasets and standardized evaluation protocols. Although architectural innovations are abundant, fair assessment is further impeded by the lack of clear disentanglement between spatial, temporal and loss modules. In this paper, we introduce FD-Bench, the first fair, modular, comprehensive and reproducible benchmark for data-driven fluid simulation. FD-Bench systematically evaluates 85 baseline models across 10 representative flow scenarios under a unified experimental setup. It provides four key contributions: (1) a modular design enabling fair comparisons across spatial, temporal, and loss function modules; (2) the first systematic framework for direct comparison with traditional numerical solvers; (3) fine-grained generalization analysis across resolutions, initial conditions, and temporal windows; and (4) a user-friendly, extensible codebase to support future research. Through rigorous empirical studies, FD-Bench establishes the most comprehensive leaderboard to date, resolving long-standing issues in reproducibility and comparability, and laying a foundation for robust evaluation of future data-driven fluid models. The code is open-sourced at https://github.com/WillDreamer/FD-Bench.