期刊
THEORETICAL AND COMPUTATIONAL FLUID DYNAMICS
卷 34, 期 4, 页码 385-400出版社
SPRINGER
DOI: 10.1007/s00162-020-00529-9
关键词
Reduced-order modeling; Traveling waves; Data decomposition; Transported quantities
资金
- Defense Threat Reduction Agency (DTRA) [HDTRA1-18-1-0038]
- Army Research Office [W911NF-19-1-0045]
We develop an unsupervised machine learning algorithm for the automated discovery and identification of traveling waves in spatiotemporal systems governed by partial differential equations (PDEs). Our method uses sparse regression and subspace clustering to robustly identify translational invariances that can be leveraged to build improved reduced-order models (ROMs). Invariances, whether translational or rotational, are well known to compromise the ability of ROMs to produce accurate and/or low-rank representations of the spatiotemporal dynamics. However, by discovering translations in a principled way, data can be shifted into a coordinate systems where quality, low-dimensional ROMs can be constructed. This approach can be used on either numerical or experimental data with or without knowledge of the governing equations. We demonstrate our method on a variety of PDEs of increasing difficulty, taken from the field of fluid dynamics, showing the efficacy and robustness of the proposed approach.
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