Bayesian hierarchical modeling of a multivariate spatiotemporal system based on interdependent physics–informed dynamic processes
提出一种贝叶斯分层建模方法，将B样条与偏微分方程结合，处理多元时空系统中变量间的相互依赖关系，并通过数值实验和粮仓储粮温湿度案例验证有效性。
Multivariate spatiotemporal systems have become invaluable tools for facilitating informed decision making and effective management in real-world applications. Modeling such systems faces the challenge of revealing the latent physical mechanisms in multiple response variables. While partial differential equation (PDE)–informed methods provide reliable physical insights, they fall short of adequately addressing the critical aspect of interactions among response variables. To address this challenge, our article proposes a Bayesian hierarchical modeling method for a multivariate spatiotemporal system driven by interdependent physics–informed dynamic processes with time-varying parameters. Specifically, we integrate B-spline basis functions with PDEs to model dynamic processes of multiple response variables and time-varying parameters, along with a parameter correlation model to more effectively manage the complexities of variable interactions. We enhance parameter estimation via a Bayesian hierarchical analysis tailored for interdependent physics–informed dynamic processes, which achieves theoretical superiority in the fitting of both B-spline and PDE models by providing deeper insights into the dynamics of physical processes and their intervariable coupling. The practicality of the proposed method is validated through numerical experiments and a real-world case study focused on modeling temperature and humidity fields in grain storage.