An efficient reduced-order model based on dynamic mode decomposition for parameterized spatial high-dimensional PDEs
报告专家：孙祥（中国海洋大学）
报告时间：2024年7月24日（星期三）上午10：30-11：30
报告地点：数学学院西109报告厅
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.
专家简介：孙祥，中国海洋大学副教授，硕士生导师。主要研究领域为模型降阶、不确定性量化以及机器学习。在Journal of Computational Physics, Journal of Scientific Computing以及Communications in Computational Physics等计算数学高水平期刊上发表学术论文20余篇。现主持国家自然科学基金青年项目、山东省自然科学基金青年项目以及国家实验室科技创新项目等。
邀请人：陈刚
