Speaker:    

Xiao Liu，University of Arkansas
Inviter:      
Title:
    Physics-Informed Statistical Learning for Spatio-Temporal Data
Time & Venue:
    2021.04.19 09:00-10:00 腾讯会议：ID 538 708 634
Abstract:
    

This talk focuses on the statistical modeling of spatio-temporal data arising from a class of advection-diffusion processes described by stochastic PDE. Such processes are widely found in scientific and engineering applications where fundamental physics imposes critical constraints on how data can be modeled and how statistical models should be interpreted. The idea of spectrum decomposition is employed to approximate the physical process by a linear combination of spatial basis functions and a multivariate stochastic process of spectral coefficients. We consider a complex but more realistic scenario with spatially-varying convection-diffusion and nonzero-mean source-sink. As a result, the temporal evolution of spectrum coefficients is closely coupled with each other, which corresponds to the non-linear redistribution of energy across multiple scales from the perspective of physics. Because of the spatially-varying convection-diffusion, the space-time covariance is naturally non-stationary. The theoretical results are integrated into the framework of hierarchical dynamical spatio-temporal models. Some practical considerations related to computational efficiency are discussed in order to make the proposed approach practical. The advantages of the proposed approach are demonstrated by numerical studies.
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