arXiv:2610.38273 · v1

NAGO: Noise-Aware Generative Operator via Flow Matching

首次提交 2026-10-28 12:42

版本更新 2026-10-28 12:42

雷达观测 2026-10-30 10:23

摘要

We introduce NAGO, a noise-aware generative operator for efficient sampling from invariant measures of stochastic partial differential equations (SPDEs) in function space. Our central idea is to treat the source measure as a design variable rather than a fixed Gaussian default. We establish admissibility conditions for well-defined infinite-dimensional flows and show that the finite-band source--target covariance ratio controls the spectral stiffness of the marginal velocity field. This analysis yields an admissibility-constrained spectral-matching rule: choose a source that is sufficiently rough for well-posedness, then minimize covariance mismatch over the resolved Fourier modes. On three representative stochastic-field benchmarks, this source design improves few-step spectral accuracy and several complementary distributional and physical statistics. In a controlled Matern-field ablation, it reduces the accurate RK4 budget from about 30 steps for Gaussian functional flow matching to 3--5 steps, a $6$--$10\times$ reduction in neural ODE evaluations. These gains are strongest for stationary multiscale fields and depend on the metric, resolution, and guidance protocol.

作者备注：Accepted at NeurIPS 2026. 49 pages including appendices and checklist. Code: https://github.com/cgymmy/NAGO