Bayesian spatiotemporal modeling for inverse problems

Inverse problems with spatiotemporal observations are ubiquitous in scientific studies and engineering applications. In these inverse problems, observed multivariate time series used to infer parameters of physical or biological interests. Traditional solutions for often ignore the spatial temporal correlations data (static model), simply model summarized over (time-averaged model). either case, information that contains interactions is not fully utilized parameter learning, which leads insufficient modeling problems. this paper, we apply Bayesian models based on Gaussian processess (STGP) show provides more effective estimation uncertainty quantification (UQ). We demonstrate merit compared traditional static time-averaged approaches using a time-dependent advection–diffusion partial different equation (PDE) three chaotic ordinary differential equations (ODE). also provide theoretic justification superiority fit trajectories even if it appears cumbersome (e.g. dynamics).