# Geometry Matters: Benchmarking Scientific ML Approaches for Flow Prediction around Complex Geometries

arXiv: https://arxiv.org/abs/2501.01453 · HTML: https://mlsanity.com/paper/2501.01453/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 48 references that are in the map.
- First posted on arXiv 31 Dec 2024.

## Builds on (most cited first, 18 of 18)

- [Swin Transformer: Hierarchical Vision Transformer using Shifted Windows](https://mlsanity.com/paper/2103.14030/) (2021)
- [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)
- [Normalizing Flows for Probabilistic Modeling and Inference](https://mlsanity.com/paper/1912.02762/) (2019)
- [Convolutional Neural Operators for robust and accurate learning of PDEs](https://mlsanity.com/paper/2302.01178/) (2023)
- [Uncertainty Quantification in Scientific Machine Learning: Methods, Metrics, and Comparisons](https://mlsanity.com/paper/2201.07766/) (2022)
- [Towards Foundation Models for Scientific Machine Learning: Characterizing Scaling and Transfer Behavior](https://mlsanity.com/paper/2306.00258/) (2023)
- [AirfRANS: High Fidelity Computational Fluid Dynamics Dataset for Approximating Reynolds-Averaged Navier-Stokes Solutions](https://mlsanity.com/paper/2212.07564/) (2022)
- [A trans-disciplinary review of deep learning research for water resources scientists](https://mlsanity.com/paper/1712.02162/) (2017)
- [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)
- [Deep Learning for Reduced Order Modelling and Efficient Temporal Evolution of Fluid Simulations](https://mlsanity.com/paper/2107.04556/) (2021)
- [Learning stiff chemical kinetics using extended deep neural operators](https://mlsanity.com/paper/2302.12645/) (2023)
- [FlowBench: A Large Scale Benchmark for Flow Simulation over Complex Geometries](https://mlsanity.com/paper/2409.18032/) (2024)
- [Interpretable models for extrapolation in scientific machine learning](https://mlsanity.com/paper/2212.10283/) (2022)
- [SkelNetOn 2019: Dataset and Challenge on Deep Learning for Geometric Shape Understanding](https://mlsanity.com/paper/1903.09233/) (2019)
- [NeuFENet: Neural Finite Element Solutions with Theoretical Bounds for Parametric PDEs](https://mlsanity.com/paper/2110.01601/) (2021)
- [Neural PDE Solvers for Irregular Domains](https://mlsanity.com/paper/2211.03241/) (2022)

## Built on by (most cited first, 3 of 3)

- [Defining Foundation Models for Computational Science: A Call for Clarity and Rigor](https://mlsanity.com/paper/2505.22904/) (2025)
- [3D Neural Operator-Based Flow Surrogates around 3D geometries: Signed Distance Functions and Derivative Constraints](https://mlsanity.com/paper/2503.17289/) (2025)
- [Shaping the Wind: Nested Potentials for Kinematically Admissible Urban Wind Prediction](https://mlsanity.com/paper/2610.07033/) (2026)

## Abstract (arXiv)

Rapid and accurate simulations of fluid dynamics around complicated geometric bodies are critical in a variety of engineering and scientific applications, including aerodynamics and biomedical flows. However, while scientific machine learning (SciML) has shown considerable promise, most studies in this field are limited to simple geometries, and complex, real-world scenarios are underexplored. This paper addresses this gap by benchmarking diverse SciML models, including neural operators and vision transformer-based foundation models, for fluid flow prediction over intricate geometries. Using a high-fidelity dataset of steady-state flows across various geometries, we evaluate the impact of geometric representations -- Signed Distance Fields (SDF) and binary masks -- on model accuracy, scalability, and generalization. Central to this effort is the introduction of a novel, unified scoring framework that integrates metrics for global accuracy, boundary layer fidelity, and physical consistency to enable a robust, comparative evaluation of model performance. Our findings demonstrate that newer foundation models significantly outperform neural operators, particularly in data-limited scenarios, and that SDF representations yield superior results with sufficient training data. Despite these promises, all models struggle with out-of-distribution generalization, highlighting a critical challenge for future SciML applications. By advancing both evaluation models and modeling capabilities, our work paves the way for robust and scalable ML solutions for fluid dynamics across complex geometries.