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2. Physics-Informed Proper Orthogonal Decomposition for Data Reconstruction

Author

Zakaria, Kemas, Palar, Pramudita Satria, Zuhal, Lavi Rizki, Morlier, Joseph, Centre National de la Recherche Scientifique - CNRS (FRANCE), Ecole nationale supérieure des Mines d'Albi-Carmaux - IMT Mines Albi (FRANCE), Institut National des Sciences Appliquées de Toulouse - INSA (FRANCE), Institut Supérieur de l'Aéronautique et de l'Espace - ISAE-SUPAERO (FRANCE), Institut Teknologi Bandung - ITB (INDONESIA), Université Toulouse III - Paul Sabatier - UT3 (FRANCE), Institut Clément Ader - ICA (Toulouse, France), Institut Teknologi Bandung (ITB), Institut Clément Ader (ICA), Institut Supérieur de l'Aéronautique et de l'Espace (ISAE-SUPAERO)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS)-IMT École nationale supérieure des Mines d'Albi-Carmaux (IMT Mines Albi), and Institut Mines-Télécom [Paris] (IMT)-Institut Mines-Télécom [Paris] (IMT)

Subjects
Mécanique des structures, Physics-Informed, Poisson Equatioon, [SPI.MECA.STRU]Engineering Sciences [physics]/Mechanics [physics.med-ph]/Structural mechanics [physics.class-ph], [SPI.MECA.MEMA]Engineering Sciences [physics]/Mechanics [physics.med-ph]/Mechanics of materials [physics.class-ph], Proper Orthogonal Decomposition, Mécanique des matériaux
Abstract

International audience; Many engineering problems are governed by complex governing equations that are difficult and typically require high computational costs to solve. Machine learning and surrogate modelling aid such an endeavour by providing a cheap-to-evaluate prediction model that acts as a replacement of the original model. While most research focuses on predicting scalar values (e.g., lift and drag), predicting the solution field is also of interest in many practical engineering and scientific applications. This paper proposes a Physics-Informed Proper Orthogonal Decomposition (POD) technique that improves the solution field prediction by enforcing governing equations as a loss penalty. The proposed idea utilizes a reduced-order modeling technique based on POD to decompose solution snapshots into singular vectors and values. A Gaussian Process Regression is then utilized to predict the singular values from variable parameters. The predicted singular values from the data of the problem are then adjusted via optimization to minimize the physics-informed loss and achieve better prediction. In this paper, we illustrate the efficacy of the proposed method on simple two-dimensional partial differential equations. The result clearly shows that the proposed physics-informed POD outperforms the conventional POD in terms of approximation error.

Published
2023

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