汇报标题 (Title)：基于高斯过程动力学模型的时变参数化偏微分方程降阶模型
汇报人 (Speaker)：孙祥（中国海洋大学）
汇报功夫 (Time)：2026年4月18日（周六）10:00
汇报地址 (Place)：校本部A215
约请人(Inviter)：潘晓敏
主办部门：理学院数学系
汇报提要：A reduced-order modeling framework is developed to address the high-dimensional challenges of parameterized partial differential equations by integrating tensor-train decomposition (TTD), Gaussian process regression (GPR), and Gaussian process dynamical models (GPDMs).TTD furnishes a low-rank approximation of the solution snapshots, while GPR learns the nonlinear mapping from the input parameter space to the tensor-train format. GPDM then models the temporal dynamics, enabling accurate time evolution prediction and uncertainty quantification. The method is validated on several benchmark problems, including Burgers’equations and the incompressible Navie–Stokes equations. Comparative experiments against traditional methods such as proper orthogonal decomposition–Gaussian process regression and dynamic mode decomposition based on tensor-train decomposition–Gaussian process regression demonstrate that the proposed approach achieves superior accuracy in modeling nonlinear temporal dynamics, conducting time-domain interpolation, and quantifying prediction uncertainty.
