Physics-informed genetic programming for discovery of partial differential equations from scarce and noisy data.

Autor: Cohen BG; Department of Chemical and Biomolecular Engineering, University of Connecticut, Storrs, 06269, CT, USA., Beykal B; Department of Chemical and Biomolecular Engineering, University of Connecticut, Storrs, 06269, CT, USA.; Center for Clean Energy Engineering, University of Connecticut, Storrs, 06269, CT, USA., Bollas G; Department of Chemical and Biomolecular Engineering, University of Connecticut, Storrs, 06269, CT, USA.
Jazyk: angličtina
Zdroj: Journal of computational physics [J Comput Phys] 2024 Oct 01; Vol. 514. Date of Electronic Publication: 2024 Jul 08.
DOI: 10.1016/j.jcp.2024.113261
Abstrakt: A novel framework is proposed that utilizes symbolic regression via genetic programming to identify free-form partial differential equations from scarce and noisy data. The framework successfully identified ground truth models for four synthetic systems (an isothermal plug flow reactor, a continuously stirred tank reactor, a nonisothermal reactor, and viscous flow governed by Burgers' equation) from time-variant data collected at one location. A comparative analysis against the so-called weak Sparse Identification of Nonlinear Dynamics (SINDy) demonstrated the proposed framework's superior ability to identify meaningful partial differential equation (PDE) models when data was scarce. The framework was further tested for robustness to noise and scarcity, showing successful model recovery from as few as eight time series data points collected at a single point in space with 50% noise. These results emphasize the potential of the proposed framework for the discovery of PDE models when data collection is expensive or otherwise difficult.
Competing Interests: Declaration of Generative AI and AI-assisted technologies in the writing process During the preparation of this work the authors used OpenAI’s ChatGPT in order to receive recommended feedback and edits. After using this tool, the authors reviewed and edited the content as needed and take full responsibility for the content of this publication.
Databáze: MEDLINE
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