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Machine-learning-based pressure reconstruction with moving boundaries

Published online by Cambridge University Press:  02 April 2025

Hongping Wang Open the ORCID record for Hongping Wang [Opens in a new window] ,
Fan Wu ,
Yi Liu ,
Xinyi He ,
Shuyi Feng  and
Shizhao Wang Open the ORCID record for Shizhao Wang [Opens in a new window]
Hongping Wang
Affiliation:
State Key Laboratory of Nonlinear Mechanics, Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, PR China School of Engineering Science, University of Chinese Academy of Sciences, Beijing 100049, PR China
Fan Wu
Affiliation:
State Key Laboratory of Nonlinear Mechanics, Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, PR China School of Engineering Science, University of Chinese Academy of Sciences, Beijing 100049, PR China
Yi Liu
Affiliation:
State Key Laboratory of Nonlinear Mechanics, Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, PR China School of Engineering Science, University of Chinese Academy of Sciences, Beijing 100049, PR China
Xinyi He
Affiliation:
State Key Laboratory of Nonlinear Mechanics, Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, PR China School of Engineering Science, University of Chinese Academy of Sciences, Beijing 100049, PR China
Shuyi Feng
Affiliation:
Department of Structural Heart Disease, National Center for Cardiovascular Disease, PR China Fuwai Hospital, Chinese Academy of Medical Sciences and Peking Union Medical College, Beijing, PR China
Shizhao Wang*
Affiliation:
State Key Laboratory of Nonlinear Mechanics, Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, PR China School of Engineering Science, University of Chinese Academy of Sciences, Beijing 100049, PR China
*
Corresponding author: Shizhao Wang, [email protected]
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Abstract

The greatest challenge in pressure reconstruction from the measured velocity fields is that the error of material acceleration is significantly contaminated due to error propagation. Particularly for flows with moving boundaries, accurate boundary velocities are difficult to obtain due to error propagation, and a complex boundary processing technique is needed to treat the moving boundaries. The present work proposes a machine-learning-based method to determine the pressure for incompressible flows with moving boundaries. The proposed network consists of two neural networks: one network, named the boundary network, is used to track the Lagrangian boundary points; the other physics-informed neural network, named the flow network, is adopted to approximate the flow fields. These two networks are coupled by imposing boundary conditions. We further propose a new dynamic weight strategy for the loss terms to guarantee convergence and stability. The performance of the proposed method is validated by two examples: the flow over an oscillating cylinder and the flow around a swimming fish. The proposed method can accurately determine the pressure fields and boundary motion from synthetic particle image velocimetry (PIV) flow fields. Moreover, this method can also predict the boundary and pressure at a given instant without supervised data. Finally, this method was applied to reconstruct the pressure from the two-dimensional and three-dimensional PIV velocities of the left ventricle. All of the results indicate that the proposed method can accurately reconstruct the pressure fields for flows with moving boundaries and is a novel method for surface pressure estimation.

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Mathematical Foundations: Machine learning Mathematical Foundations: General fluid mechanics
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JFM Papers
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Journal of Fluid Mechanics , Volume 1008 , 10 April 2025 , A21
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© The Author(s), 2025. Published by Cambridge University Press

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