Speaker: Sebastian Zeng (Linnæus University)

Title: Latent Variable Learning of SPDEs

Abstract: We study the problem of learning the law of linear stochastic partial differential equations (SPDEs) with additive Gaussian forcing from spatiotemporal observations. Most existing approaches either assume access to the driving noise or initial condition, rely on deterministic surrogates that fail to capture intrinsic stochasticity, or employ generative models (e.g., diffusion models) that capture local randomness but may accumulate distributional errors when used in an autoregressive rollout setting.

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 formulation reduces the infinite-dimensional SPDE to a finite system of parametrized ordinary differential equations governing latent dynamics.

The latent dynamics and stochastic forcing are jointly inferred through variational learning, enabling 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 on bounded and unbounded one-dimensional spatial domains.

Time and place: Oct. 8, 2026 11:15 AM–12:00 PM, NHA Room 723

Please see the full announcement for information about abstract, organisers, logistics and registration (the event is hybrid - please register for the mailing list to get the Zoom link).

This series of webinars addresses all interested people in probability, stochastic analysis, control, risk evaluation, statistics, with a view towards applications, in particular to finance, economy, energy markets and production, but also to physics and biology.

SURE-AI @ STAR seminar: Sebastian Zeng