Automated identification of dominant physical processes

• Published in: Engineering applications of artificial intelligence Vol. 116; p. 105496
• Main Authors: Kaiser, Bryan E., Saenz, Juan A., Sonnewald, Maike, Livescu, Daniel
• Format: Journal Article
• Language: English
• Published: United States Elsevier Ltd 01-11-2022; Elsevier
• Subjects: Clustering; Dominant balance; Dynamical process; ENGINEERING; Nonlinear partial differential equations; scale analysis; Unsupervised machine learning; Unsupervised machine learning; Nonlinear partial differential equations; Clustering; Dominant balance; Dynamical process
• ISSN: 0952-1976; 1873-6769
• DOI: 10.1016/j.engappai.2022.105496

The identification of processes that locally and approximately dominate dynamical system behavior has enabled significant advances in understanding and modeling nonlinear differential dynamical systems. Conventional methods of dominant process identification involve piecemeal and ad hoc (non-rigorous, informal) scaling analyses to identify dominant balances of governing equation terms and to delineate the spatiotemporal boundaries (boundaries in space and/or time) of each dominant balance. For the first time, we present an objective global measure of the fit of dominant balances to observations, which is desirable for automation, and was previously undefined. Furthermore, we propose a formal definition of the dominant balance identification problem in the form of an optimization problem. We show that the optimization can be performed by various machine learning algorithms, enabling the automatic identification of dominant balances. Our method is algorithm agnostic and it eliminates reliance upon expert knowledge to identify dominant balances which are not known beforehand.
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•Discovery of dominant balances of two or more equation terms yields insights.•Dominant balances often arise in nonlinear dynamical systems.•Automated dominant balance discovery requires hyperparameter tuning.•We present a robust objective criterion for dominant balance identification.•Objective hyper-parameter tuning enables automated dominant balance discovery.