Role of physics in physics-informed machine learning

Chandra, Abhishek; Bakarji, Joseph; Tartakovsky, Daniel

doi:10.1615/jmachlearnmodelcomput.2024053170

Role of physics in physics-informed machine learning

Journal Article · Mon Jan 01 00:00:00 EST 2024 · Journal of Machine Learning for Modeling and Computing

DOI:https://doi.org/10.1615/jmachlearnmodelcomput.2024053170· OSTI ID:2350949

Chandra, Abhishek ^[1]; Bakarji, Joseph ^[2]; Tartakovsky, Daniel ^[3]

Eindhoven University of Technology (The Netherlands); Stanford University; Stanford University
American University of Beirut (Lebanon)
Stanford University, CA (United States)

Physical systems are characterized by inherent symmetries, one of which is encapsulated in the units of their parameters and system states. These symmetries enable a lossless order-reduction, e.g., via dimensional analysis based on the Buckingham theorem. Despite the latter's benefits, machine learning (ML) strategies for the discovery of constitutive laws seldom subject experimental and/or numerical data to dimensional analysis. We demonstrate the potential of dimensional analysis to significantly enhance the interpretability and generalizability of ML-discovered secondary laws. Our numerical experiments with creeping fluid flow past solid ellipsoids show how dimensional analysis enable both deep neural networks and sparse regression reproduce old results, e.g., Stokes law for a sphere, and generate new ones, e.g., an expression for an ellipsoid misaligned with the flow direction. Furthermore, our results suggest the need to incorporate other physics-based symmetries and invariances into ML-based techniques for equation discovery.

View Accepted Manuscript (DOE)

Research Organization:: Stanford University, CA (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)

Grant/Contract Number:: SC0023163

OSTI ID:: 2350949

Journal Information:: Journal of Machine Learning for Modeling and Computing, Journal Name: Journal of Machine Learning for Modeling and Computing Journal Issue: 1 Vol. 5; ISSN 2689-3967

Publisher:: Begell HouseCopyright Statement

Country of Publication:: United States

Language:: English

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97 MATHEMATICS AND COMPUTING
dimensional analysis
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Role of physics in physics-informed machine learning

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