An Efficient Reduced-Order Model Based on Dynamic Mode Decomposition for Parameterized Spatial High-Dimensional PDEs: An efficient reduced-order model based on dynamic mode decomposition for parameterized spatial high-dimensional PDEs
Uložené v:
| Názov: | An Efficient Reduced-Order Model Based on Dynamic Mode Decomposition for Parameterized Spatial High-Dimensional PDEs: An efficient reduced-order model based on dynamic mode decomposition for parameterized spatial high-dimensional PDEs |
|---|---|
| Autori: | Lin, Yifan, Sun, Xiang, Nie, Jie, Chen, Yuanhong, Gao, Zhen |
| Zdroj: | Communications in Computational Physics. 37:575-602 |
| Informácie o vydavateľovi: | Global Science Press, 2025. |
| Rok vydania: | 2025 |
| Predmety: | tensor train decomposition, parameterized time-dependent PDEs, incremental singular value decomposition, Nonlinear parabolic equations, dynamic mode decomposition, Theoretical approximation in context of PDEs |
| Popis: | Summary: 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. |
| Druh dokumentu: | Article |
| Popis súboru: | application/xml |
| ISSN: | 1991-7120 1815-2406 |
| DOI: | 10.4208/cicp.oa-2023-0135 |
| Prístupové číslo: | edsair.doi.dedup.....f94e48a2cd301c8367002573ad5719d4 |
| Databáza: | OpenAIRE |
Nájsť tento článok vo Web of Science | Abstrakt: | Summary: 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. |
|---|---|
| ISSN: | 19917120 18152406 |
| DOI: | 10.4208/cicp.oa-2023-0135 |