Hyper-Reduced Autoencoders for Efficient and Accurate Nonlinear Model Reductions
This work addresses computational efficiency for researchers in computational physics and engineering dealing with advection-dominated problems, though it is incremental as it builds on existing nonlinear reduction methods.
The paper tackles the high computational cost of training neural networks on high-fidelity data for nonlinear model reduction by proposing a method that trains on subsampled snapshots, achieving efficient and accurate surrogate models as demonstrated on a 2D Burgers problem.
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.