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

Ronak Tali, Ali Rabeh, Cheng-Hau Yang, Mehdi Shadkhah, Samundra Karki, Abhisek Upadhyaya, Suriya Dhakshinamoorthy, Marjan Saadati, Soumik Sarkar, Adarsh Krishnamurthy, Chinmay Hegde, Aditya Balu, Baskar Ganapathysubramanian

Abstract: 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 (*parametric vs. non-parametric*), spanning a range of flow conditions (*Reynolds number and Grashoff number*), capturing a diverse array of flow phenomena (*steady 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). 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 current (and future) neural PDE solvers. We benchmark the performance of several methods, including Fourier Neural Operators (FNO), Convolutional Neural Operators (CNO), DeepONets, and recent foundational models. This dataset ([here](https://huggingface.co/datasets/BGLab/FlowBench/tree/main)) will be a valuable resource for developing and evaluating AI-for-science approaches, specifically neural PDE solvers, that model complex fluid dynamics around 2D and 3D objects.

Keywords: SciML, Complex Geometries, Shifted Boundary Method, PDE

Assigned Action Editor: ~Sergio_Escalera1

Submission Number: 84