Hyper-Reduced Autoencoders for Efficient and Accurate Nonlinear Model Reductions

2023/03/16 by Jorio Cocola, Cocola, Jorio, John Tencer +7 · 2 citations
Computer Science · Physics and Astronomy · #Computational Physics (physics.comp-ph) #Computational Physics and Python Applications #FOS: Computer and information sciences #FOS: Mathematics #FOS: Physical sciences #Gaussian Processes and Bayesian Inference #Machine Learning (cs.LG) #Model Reduction and Neural Networks #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.2303.09630

openalex publication_date 2023/03/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Projection-based model order reduction on nonlinear manifolds has been recently proposed for problems with slowly decaying Kolmogorov n-width such as advection-dominated ones. These methods often use neural networks for manifold learning and showcase improved accuracy over traditional linear subspace-reduced order models. A disadvantage of the previously proposed methods is the potential high computational costs of training the networks on high-fidelity solution snapshots. In this work, we propose and analyze a novel method that overcomes this disadvantage by training a neural network only on subsampled versions of the high-fidelity solution snapshots. This method coupled with collocation-based hyper-reduction and Gappy-POD allows for efficient and accurate surrogate models. We demonstrate the validity of our approach on a 2d Burgers problem.

Cited by

• Kernel manifolds: nonlinear-augmentation dimensionality reduction using reproducing kernel Hilbert spaces
• A hyperreduced manifold learning approach to nonlinear model order reduction for the homogenisation of hyperelastic RVEs

Related

• Efficient nonlinear manifold reduced order model
• A fast and accurate physics-informed neural network reduced order model with shallow masked autoencoder
• Nonlinear-manifold reduced order models with domain decomposition
• Non-linear manifold ROM with Convolutional Autoencoders and Reduced Over-Collocation method
• Explicable hyper-reduced order models on nonlinearly approximated solution manifolds of compressible and incompressible Navier-Stokes equations