Automated identification of dominant physical processes

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-rigorou...

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