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.
Sharp error estimates on a stochastic structure-preserving scheme in computing effective diffusivity of 3D chaotic flows.Multiscale Modeling & Simulation, 19(3):1167–1189
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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.