Physics-Constrained Fine-Tuning of Flow-Matching Models for Generation and Inverse Problems

arXiv:2508.09156v3 Announce Type: replace Abstract: We present a framework for fine-tuning flow-matching generative models to enforce physical constraints and solve inverse problems in scientific systems. Starting from a model trained on low-fidelity or observational data, we apply a differentiable post-training procedure that minimizes weak-form residuals of governing partial differential equations (PDEs), promoting physical consistency and adherence to boundary conditions without distorting the underlying learned distribution. To infer unknown physical inputs, such as source terms, material

Source: arXiv cs.LG — read the full report at the original publisher.

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