报告题目 (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
报告人 (Speaker)：孙祥（中国海洋大学）
报告时间 (Time)：2026年4月18日（周六）10:00
报告地点 (Place)：校本部A215
邀请人(Inviter)：潘晓敏
主办部门：理学院数学系
报告摘要：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.
