Physics-informed dynamic mode decomposition

被引:88
作者
Baddoo, Peter J. J. [1 ]
Herrmann, Benjamin [2 ]
McKeon, BeverleyJ. J. [3 ]
Kutz, J. Nathan [4 ]
Brunton, Steven L. L. [5 ]
机构
[1] MIT, Dept Math, Cambridge, MA 02139 USA
[2] Univ Chile, Dept Mech Engn, Beauchef 851, Santiago, Chile
[3] CALTECH, Grad Aerosp Labs, Pasadena, CA 91125 USA
[4] Univ Washington, Dept Appl Math, Seattle, WA 98195 USA
[5] Univ Washington, Dept Mech Engn, Seattle, WA 98195 USA
来源
PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES | 2023年 / 479卷 / 2271期
基金
美国国家科学基金会;
关键词
machine learning; dynamic mode decomposition; data-driven dynamical systems; SPECTRAL-ANALYSIS; ROTATION; APPROXIMATION; OPERATORS; EQUATIONS; FRAMEWORK; NETWORKS; PATTERNS; DISEASE; SYSTEMS;
D O I
10.1098/rspa.2022.0576
中图分类号
O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];
学科分类号
07 ; 0710 ; 09 ;
摘要
In this work, we demonstrate how physical principles-such as symmetries, invariances and conservation laws-can be integrated into the dynamic mode decomposition (DMD). DMD is a widely used data analysis technique that extracts low-rank modal structures and dynamics from high-dimensional measurements. However, DMD can produce models that are sensitive to noise, fail to generalize outside the training data and violate basic physical laws. Our physics-informed DMD (piDMD) optimization, which may be formulated as a Procrustes problem, restricts the family of admissible models to a matrix manifold that respects the physical structure of the system. We focus on five fundamental physical principles-conservation, self-adjointness, localization, causality and shift-equivariance-and derive several closed-form solutions and efficient algorithms for the corresponding piDMD optimizations. With fewer degrees of freedom, piDMD models are less prone to overfitting, require less training data, and are often less computationally expensive to build than standard DMD models. We demonstrate piDMD on a range of problems, including energy-preserving fluid flow, the Schrodinger equation, solute advection-diffusion and three-dimensional transitional channel flow. In each case, piDMD outperforms standard DMD algorithms in metrics such as spectral identification, state prediction and estimation of optimal forcings and responses.
引用
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页数:23
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