Deep operator learning for efficient sampling from invariant measures of stochastic differential equations
Read the original on arXiv Machine Learning →The paper presents an amortized neural sampler that merges operator learning with flow-based methods to efficiently sample from invariant measures of stochastic differential equations (SDEs). By mapping SDE coefficient functions to pushforwards from a reference measure, the approach shifts the sampling cost to an initial training phase, after which new SDE instances can be sampled with a single encoder pass and a few ODE solver steps, independent of mixing time. The framework incorporates Lagrangian trajectory sensors and cross attention to handle high-dimensional problems, and the authors provide theoretical guarantees of expressivity and resolution invariance, demonstrating competitive accuracy and significant speedups over MCMC in 1D, 2D, and 64D SDE families.
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