Data-driven nonlinear parametric model order reduction framework using deep hierarchical variational autoencoder

A data-driven parametric model order reduction (MOR) method using a deep artificial neural network is proposed. The present network, a least-squares hierarchical variational autoencoder (LSH-VAE), is capable of performing nonlinear MOR for the parametric interpolation of a nonlinear dynamic system w...

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Bibliographic Details
Published in:Engineering with computers Vol. 40; no. 4; pp. 2385 - 2400
Main Authors: Lee, SiHun, Lee, Sangmin, Jang, Kijoo, Cho, Haeseong, Shin, SangJoon
Format: Journal Article
Language:English
Published: London Springer London 01.08.2024
Springer Nature B.V
Subjects:
Accuracy
Artificial neural networks
CAE) and Design
Calculus of Variations and Optimal Control; Optimization
Classical Mechanics
Computer Science
Computer-Aided Engineering (CAD
Control
Degrees of freedom
Dynamical systems
Fluid flow
Fluid-structure interaction
Interpolation
Limit cycle oscillations
Math. Applications in Chemistry
Mathematical and Computational Engineering
Model reduction
Nonlinear dynamics
Nonlinear systems
Original Article
Systems Theory
Three dimensional analysis
Three dimensional flow
Multiphysics analysis
Variational autoencoder
Parametric interpolation
Nonlinear model order reduction
Machine learning
ISSN:0177-0667, 1435-5663
Online Access:Get full text
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Summary:A data-driven parametric model order reduction (MOR) method using a deep artificial neural network is proposed. The present network, a least-squares hierarchical variational autoencoder (LSH-VAE), is capable of performing nonlinear MOR for the parametric interpolation of a nonlinear dynamic system with a significant number of degrees of freedom. LSH-VAE differs from existing networks in two major respects: a deep hierarchical structure and a hybrid weighted, probabilistic loss function. The enhancements result in significantly improved accuracy and stability compared with conventional nonlinear MOR methods, autoencoders, and variational autoencoders. In LSH-VAE, the parametric MOR framework is based on the spherically linear interpolation of the latent manifold. The present framework is validated and evaluated on three nonlinear and multiphysics dynamic systems. First, the present framework is evaluated on the fluid–structure interaction benchmark problem to assess its efficiency and accuracy. Then, a highly nonlinear aeroelastic phenomenon, limit cycle oscillation, is analyzed. Finally, the framework is applied to three-dimensional fluid flow to demonstrate its capability to efficiently analyze a significantly large number of degrees of freedom. The superior performance of LSH-VAE is emphasized by comparing its results against those of widely used nonlinear MOR methods, a convolutional autoencoder, and β -VAE. The proposed framework exhibits significantly enhanced accuracy compared with that of conventional methods, while the computational efficiency continues to remain significantly higher.
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ISSN:0177-0667
1435-5663
DOI:10.1007/s00366-023-01916-6