Projection-based model reduction: Formulations for physics-based machine learning

•New approach for physics-based machine learning using POD expansions.•Machine learning methods learn map between inputs and POD coefficients.•Particular solutions in the POD expansion embed physical constraints in ML models.•Particular solutions enforce boundary conditions and other physical soluti...

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Vydáno v:Computers & fluids Ročník 179; s. 704 - 717
Hlavní autoři: Swischuk, Renee, Mainini, Laura, Peherstorfer, Benjamin, Willcox, Karen
Médium: Journal Article
Jazyk:angličtina
Vydáno: Amsterdam Elsevier Ltd 30.01.2019
Elsevier BV
Témata:
Artificial intelligence
Boundary conditions
Constraint modelling
Data-driven reduced models
Decision trees
Forecasting
Formulations
Machine learning
Model reduction
Neural networks
Parameterization
Physics-based machine learning
Polynomials
Proper Orthogonal Decomposition
Surrogate models
Thermal expansion
Physics-based machine learning
Proper orthogonal decomposition
Model reduction
Surrogate models
Data-driven reduced models
ISSN:0045-7930, 1879-0747
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Shrnutí:•New approach for physics-based machine learning using POD expansions.•Machine learning methods learn map between inputs and POD coefficients.•Particular solutions in the POD expansion embed physical constraints in ML models.•Particular solutions enforce boundary conditions and other physical solution features.•Incorporating physics in ML models is critical when we have limited training data. This paper considers the creation of parametric surrogate models for applications in science and engineering where the goal is to predict high-dimensional output quantities of interest, such as pressure, temperature and strain fields. The proposed methodology develops a low-dimensional parametrization of these quantities of interest using the proper orthogonal decomposition (POD), and combines this parametrization with machine learning methods to learn the map between the input parameters and the POD expansion coefficients. The use of particular solutions in the POD expansion provides a way to embed physical constraints, such as boundary conditions and other features of the solution that must be preserved. The relative costs and effectiveness of four different machine learning techniques—neural networks, multivariate polynomial regression, k-nearest-neighbors and decision trees—are explored through two engineering examples. The first example considers prediction of the pressure field around an airfoil, while the second considers prediction of the strain field over a damaged composite panel. The case studies demonstrate the importance of embedding physical constraints within learned models, and also highlight the important point that the amount of model training data available in an engineering setting is often much less than it is in other machine learning applications, making it essential to incorporate knowledge from physical models.
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ISSN:0045-7930
1879-0747
DOI:10.1016/j.compfluid.2018.07.021