@Article{CiCP-37-575,
author = {Lin , YifanSun , XiangNie , JieChen , Yuanhong and Gao , Zhen},
title = {An Efficient Reduced-Order Model Based on Dynamic Mode Decomposition for Parameterized Spatial High-Dimensional PDEs},
journal = {Communications in Computational Physics},
year = {2025},
volume = {37},
number = {2},
pages = {575--602},
abstract = {<p style="text-align: justify;">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.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.OA-2023-0135},
url = {http://global-sci.org/intro/article_detail/cicp/23874.html}
}