<ul><li>A new generative framework called Physics-Based Flow Matching (PBFM) has been introduced to embed physical constraints into flow matching objectives.</li><li>PBFM jointly minimizes flow matching loss and physics-based residual loss without requiring hyperparameter tuning of their relative weights.</li><li>Temporal unrolling during training time is utilized to improve the accuracy of noise-free sample prediction.</li><li>Extensive benchmarks on three PDE problems show that PBFM yields up to an 8 times more accurate physical residuals compared to existing algorithms, making it efficient for surrogate modeling and accelerated simulation in physics and engineering applications.</li></ul>

Flow Matching Meets PDEs: A Unified Framework for Physics-Constrained Generation

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