The paper proves Hölder continuity of optimal transport maps for PDE-induced measures via doubling conditions and derives excess-risk bounds for one-step generative models like DeepParticle.
A mesh-free method for interface problems using the deep learning approach.Journal of Computational Physics, 400:108963
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On the Regularity and Generalization of One-Step Wasserstein-guided Generative Models for PDE-Induced Measures
The paper proves Hölder continuity of optimal transport maps for PDE-induced measures via doubling conditions and derives excess-risk bounds for one-step generative models like DeepParticle.