AI RESEARCH
Wiener Chaos Expansion based Neural Operator for Singular Stochastic Partial Differential Equations
arXiv CS.LG
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ArXi:2603.08219v1 Announce Type: new In this paper, we explore how our recently developed Wiener Chaos Expansion (WCE)-based neural operator (NO) can be applied to singular stochastic partial differential equations, e.g., the dynamic $\boldsymbol{\Phi}^4_2$ model simulated in the recent works. Unlike the previous WCE-NO which solves SPDEs by simply inserting Wick-Hermite features into the backbone NO model, we leverage feature-wise linear modulation (FiLM) to appropriately capture the dependency between the solution of singular SPDE and its smooth remainder.