DISA

When? April 24, 14.00-15.00
Where? Onsite: D2272 and via zoom
Registration: Please sign up for the seminar via this link https://forms.gle/9RnPVPc51CkQMgRc7 by April 22. This is especially important if you plan to attend onsite so we can make sure there is fika for everyone.

Agenda
14.00-14.10 Welcome and practical information
14.10-14.55 Latent-Variable Learning of SPDEs via Wiener Chaos – Sebastian Zeng  
14.55 – 15.00 Sum up and plan for our upcoming seminars

Abstract

Latent-Variable Learning of SPDEs via Wiener Chaos – Sebastian Zeng  
We study the problem of learning the law of linear stochastic partial differential equations (SPDEs) with additive Gaussian forcing from spatiotemporal observations. Most existing deep learning approaches either assume access to the driving noise or initial condition, or rely on deterministic surrogate models that fail to capture intrinsic stochasticity. We propose a structured latent-variable formulation that requires only observations of solution realizations and learns the underlying randomly forced dynamics.

Our approach combines a spectral Galerkin projection with a truncated Wiener chaos expansion, yielding a principled separation between deterministic evolution and stochastic forcing. This reduces the infinite-dimensional SPDE to a finite system of parametrized ordinary differential equations governing latent temporal dynamics. The latent dynamics and stochastic forcing are jointly inferred through variational learning, allowing recovery of stochastic structure without explicit observation or simulation of noise during training. Empirical evaluation on synthetic data demonstrates state-of-the-art performance under comparable modeling assumptions across bounded and unbounded one-dimensional spatial domains.