报告题目 (Title)：An efficient reduced-order model based on dynamic mode decomposition for parameterized spatial high-dimensional PDEs（基于动态模态分解的参数化空间高维偏微分方程的高效降阶模型）

报告人 (Speaker)：孙祥（中国海洋大学）

报告时间 (Time)：2024年05月01日(周三) 15:00-17:00

报告地点 (Place)：校本部F309

邀请人(Inviter)：潘晓敏

主办部门：理学院数学系

报告摘要： Dynamic mode decomposition (DMD), as a data-driven method, has been frequently used to construct reduced-order models (ROMs) due to its good performance in time extrapolation. However, existing DMD-based ROMs suffer from high storage and computational costs for high-dimensional problems. To mitigate this problem, we develop a new DMD-based ROM, i.e., TDMD-GPR, by combining tensor train decomposition (TTD) and Gaussian process regression (GPR), where TTD is used to decompose the high-dimensional tensor into multiple factors, including parameter-dependent and time-dependent factors. Parameter-dependent factor is fed into GPR to build the map between parameter value and factor vector. For any parameter value, multiplying the corresponding parameter-dependent factor vector and the time-dependent factor matrix, the result describes the temporal behavior of the spatial basis for this parameter value and is then used to train the DMD model. In addition, incremental singular value decomposition is adopted to acquire a collection of important instants, which can further reduce the computational and storage costs of TDMD-GPR. The comparison TDMD and standard DMD in terms of computational and storage complexities shows that TDMD is more advantageous. The performance of the TDMD and TDMD-GPR is assessed through several cases, and the numerical results confirm the effectiveness of them.