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.
The seminar is in the interest of SURE-AI - Sustainable, Risk-Averse and Ethical AI.
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