<ul><li>Deep generative models have been used for physical systems governed by PDEs to enable scalable simulation and uncertainty-aware inference.</li><li>Enforcing physical constraints like conservation laws and physical consistencies in generative models is challenging, often relying on soft penalties or architectural biases that do not guarantee hard constraints.</li><li>Physics-Constrained Flow Matching (PCFM) is introduced as a zero-shot inference framework that enforces arbitrary nonlinear constraints in pretrained flow-based generative models by guiding the sampling process through physics-based corrections.</li><li>Empirical results show that PCFM outperforms unconstrained and constrained baselines on various PDEs, including cases with shocks and sharp features, while ensuring exact constraint satisfaction at the final solution, providing a general framework for enforcing hard constraints in generative models.</li></ul>

Physics-Constrained Flow Matching: Sampling Generative Models with Hard Constraints

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