[Seminar] Learning Singular Stochastic PDEs via Regularity Features and Spectral–Temporal Loss

Thời gian: 14:45 đến 16:00 ngày 14/01/2026.
Địa điểm: Phòng 1404, Nhà A1, ĐHKTQD.
Người trình bày: TS. Vương Văn Yên, Lê Duy Anh – ĐHKTQD
Nội dung: Learning Singular Stochastic PDEs via Regularity Features and Spectral–Temporal Loss

Abstract: Learning stochastic partial differential equations (SPDEs) driven by space–time white noise remains challenging due to the low regularity of solutions and the long-range temporal dependencies induced by stochastic convolution. In this talk, we present a hybrid framework that combines regularity-aware feature construction with a neural SPDE solver to approximate mild solutions of singular SPDEs. Our approach employs a Deep Latent Regularity (DLR) encoder to construct features derived from stochastic convolutions and state–noise interactions appearing in the mild formulation. These features condition the drift and diffusion terms of a latent SPDE model discretized via a spectral Galerkin scheme. To mitigate the over-smoothing effects of standard L^2-based objectives, we introduce a composite loss that combines a log-spectral discrepancy in Fourier space with a differentiable temporal autocorrelation loss.