Physics-Constrained Stochastic ROMs for Unsteady Airfoil Flows

Giacomo Baldan, Qiang Liu, Alberto Guardone, Nils Thuerey

Keywords: Flow Matching, Physics, PDE, Diffusion Models, Airfoil

TL;DR: Physics-Based Flow Matching (PBFM) is a generative modeling framework that incorporates physical constraints directly into the training process

Abstract:

We introduce Physics-Based Flow Matching (PBFM), a novel framework that integrates physical residuals into generative modeling to enforce physical consistency. PBFM leverages conflict-free gradient composition and trajectory unrolling to address the challenges of balancing generative fidelity and physical accuracy, eliminating the need for manual loss weighting. By mitigating Jensen's gap during nonlinear residual evaluation, PBFM achieves improved physical adherence without compromising sample quality. We validate our approach on a challenging unsteady compressible flow problem relevant to real-world engineering applications. PBFM demonstrates state-of-the-art performance, achieving high distributional fidelity and low residual errors at inference costs comparable to standard flow matching. Additionally, we provide a detailed analysis of the impact of noise-level selection and unrolling depth, offering practical insights for advancing physics-constrained generative modeling.

Code and datasets available at [https://github.com/tum-pbs/PBFM](https://github.com/tum-pbs/PBFM).

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Submission Number: 46