# Hyper-Reduced Autoencoders for Efficient and Accurate Nonlinear Model Reductions

arXiv: https://arxiv.org/abs/2303.09630 · HTML: https://mlsanity.com/paper/2303.09630/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 18 references that are in the map.
- First posted on arXiv 16 Mar 2023.

## Builds on (most cited first, 9 of 9)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [A fast and accurate physics-informed neural network reduced order model with shallow masked autoencoder](https://mlsanity.com/paper/2009.11990/) (2020)
- [Analyzing noise in autoencoders and deep networks](https://mlsanity.com/paper/1406.1831/) (2014)
- [On the Inherent Regularization Effects of Noise Injection During Training](https://mlsanity.com/paper/2102.07379/) (2021)
- [S-OPT: A Points Selection Algorithm for Hyper-Reduction in Reduced Order Models](https://mlsanity.com/paper/2203.16494/) (2022)
- [Non-linear manifold ROM with Convolutional Autoencoders and Reduced Over-Collocation method](https://mlsanity.com/paper/2203.00360/) (2022)
- [A Tailored Convolutional Neural Network for Nonlinear Manifold Learning of Computational Physics Data using Unstructured Spatial Discretizations](https://mlsanity.com/paper/2006.06154/) (2020)
- [Pressio: Enabling projection-based model reduction for large-scale nonlinear dynamical systems](https://mlsanity.com/paper/2003.07798/) (2020)

## Abstract (arXiv)

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.