NeSTR: Neural S-Transform Reconstruction for Gaussian SPDEs

This paper introduces Neural S-Transform Reconstruction (NeSTR) for Gaussian stochastic partial differential equations (SPDEs). Rather than learning the random solution directly, NeSTR learns its S-Transform on a finite dimensional subspace of the white noise test space. For Wick type SPDEs, the method yields a deterministic parametric PDE for the restricted S-Transform, enabling recovery of the stochastic solution from the Taylor coefficients of this transform.