Physics-constrained DeepONet for Surrogate CFD models: a curved backward-facing step case

2025/03/14 by Anas Jnini, Jnini, Anas, Harshinee Goordoyal +9 · 2 citations
Physics and Astronomy · Computer Science · Materials Science · #Model Reduction and Neural Networks #Generative Adversarial Networks and Image Synthesis #Machine Learning in Materials Science

paper · pdf · doi:10.48550/arxiv.2503.11196

Abstract

The Physics-Constrained DeepONet (PC-DeepONet), an architecture that incorporates fundamental physics knowledge into the data-driven DeepONet model, is presented in this study. This methodology is exemplified through surrogate modeling of fluid dynamics over a curved backward-facing step, a benchmark problem in computational fluid dynamics. The model was trained on computational fluid dynamics data generated for a range of parameterized geometries. The PC-DeepONet was able to learn the mapping from the parameters describing the geometry to the velocity and pressure fields. While the DeepONet is solely data-driven, the PC-DeepONet imposes the divergence constraint from the continuity equation onto the network. The PC-DeepONet demonstrates higher accuracy than the data-driven baseline, especially when trained on sparse data. Both models attain convergence with a small dataset of 50 samples and require only 50 iterations for convergence, highlighting the efficiency of neural operators in learning the dynamics governed by partial differential equations.

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• Hybrid twinning using PBDW and DeepONet for the effective state estimation and prediction on partially known systems
• Analysis of the Rarefied Flow at Micro-Step using a DeepONet Surrogate Model with a Physics-Guided Zonal Loss Function

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