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

TL;DR

This work systematically benchmarks SciML approaches for predicting fluid flow around complex geometries using FlowBench's 2D lid-driven cavity data. By comparing neural operators and vision-transformer foundation models across Signed Distance Field (SDF) and binary mask geometry representations, it develops a unified scoring framework over global accuracy, boundary fidelity, and PDE consistency. The study shows that newer foundation models outperform neural operators in data-limited settings, while SDF representations offer advantages with sufficient data; however, out-of-distribution generalization remains a major challenge. The results highlight that model architecture and geometric representation jointly govern performance, with scOT and Poseidon typically delivering the strongest results across tasks, especially when data are scarce, and DeepONet excelling in PDE-consistency metrics. The work also delineates data-efficiency trends, boundary-layer accuracy, and residual behavior, offering actionable insights for deploying SciML solvers around complex geometries and motivating future physics-informed and multiphysics extensions.

Abstract

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.

Figures (12)

• Figure 1: A data-driven evaluation framework for accelerating PDE solvers of fluid flow around complex geometries using scientific machine learning models. This figure illustrates the scientific ML framework that assesses neural operators and foundation models for fluid flow solvers. Flow simulations are performed for steady-state lid-driven cavity flow across various complex geometries and Reynolds numbers. The top left subpanel shows model inputs, including a randomly selected geometry with two inputs: the Reynolds number and a representation of the geometry. It also shows model outputs---x-velocity ($u$), y-velocity ($v$), and the pressure field. The bottom subpanel presents 15 randomly chosen geometries and a Reynolds number distribution bar chart of the training dataset. The top right subpanel contrasts two representations of a sample geometry: the binary mask and the signed distance field (SDF).
• Figure 2: Comparison of geometry representations for different geometries: (a-c) Signed Distance Field (SDF) representations and (d-f) binary mask representations.
• Figure 3: Comparison of score values for different models using Signed Distance Field (SDF) and binary mask representations. The bar plot shows the score for each model, indicating the performance difference between SDF and mask representations.
• Figure 4: Comparison of score values vs. sample size for different scientific machine learning models using SDF and binary mask representations. The top row compares neural operators (CNO, FNO, Geo-DeepONet), while the bottom row compares foundation models (scOT-B, scOT-T, poseidon-T) across varying sample sizes (2400, 1200, 800, 400, and 240).
• Figure 5: Histogram of Reynolds numbers for Train and Test splits in random and extrapolatory cases.