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Physics-Informed Proper Orthogonal Decomposition for Data Reconstruction

Zakaria, Kemas and Palar, Pramudita Satria and Zuhal, Lavi Rizki and Morlier, Joseph Physics-Informed Proper Orthogonal Decomposition for Data Reconstruction. (2023) In: AIAA SciTech 2023 Forum, 23 January 2023 - 27 January 2023 (National Harbor, United States).

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Official URL: https://doi.org/10.2514/6.2023-0538

Abstract

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.

Item Type:Conference or Workshop Item (Paper)
HAL Id:hal-04034316
Audience (conference):International conference proceedings
Uncontrolled Keywords:
Institution:French research institutions > Centre National de la Recherche Scientifique - CNRS (FRANCE)
Université de Toulouse > Ecole nationale supérieure des Mines d'Albi-Carmaux - IMT Mines Albi (FRANCE)
Université de Toulouse > Institut National des Sciences Appliquées de Toulouse - INSA (FRANCE)
Université de Toulouse > Institut Supérieur de l'Aéronautique et de l'Espace - ISAE-SUPAERO (FRANCE)
Other partners > Institut Teknologi Bandung - ITB (INDONESIA)
Université de Toulouse > Université Toulouse III - Paul Sabatier - UT3 (FRANCE)
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Deposited On:14 Mar 2023 10:24

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