# Efficient nonlinear manifold reduced order model

arXiv: https://arxiv.org/abs/2011.07727 · HTML: https://mlsanity.com/paper/2011.07727/

## Key facts

- Cited by 17 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Nov 2020.

## Built on by (most cited first, 17 of 17)

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- [Deep-HyROMnet: A deep learning-based operator approximation for hyper-reduction of nonlinear parametrized PDEs](https://mlsanity.com/paper/2202.02658/) (2022)
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- [Machine Learning in Heterogeneous Porous Materials](https://mlsanity.com/paper/2202.04137/) (2022)
- [Data-driven Nonlinear Parametric Model Order Reduction Framework using Deep Hierarchical Variational Autoencoder](https://mlsanity.com/paper/2307.06816/) (2023)
- [Hybrid neural network reduced order modelling for turbulent flows with geometric parameters](https://mlsanity.com/paper/2107.09591/) (2021)
- [Enhancing Dynamic Mode Decomposition Workflow with In-Situ Visualization and Data Compression](https://mlsanity.com/paper/2208.07767/) (2022)
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## Abstract (arXiv)

Traditional linear subspace reduced order models (LS-ROMs) are able to accelerate physical simulations, in which the intrinsic solution space falls into a subspace with a small dimension, i.e., the solution space has a small Kolmogorov n-width. However, for physical phenomena not of this type, such as advection-dominated flow phenomena, a low-dimensional linear subspace poorly approximates the solution. To address cases such as these, we have developed an efficient nonlinear manifold ROM (NM-ROM), which can better approximate high-fidelity model solutions with a smaller latent space dimension than the LS-ROMs. Our method takes advantage of the existing numerical methods that are used to solve the corresponding full order models (FOMs). The efficiency is achieved by developing a hyper-reduction technique in the context of the NM-ROM. Numerical results show that neural networks can learn a more efficient latent space representation on advection-dominated data from 2D Burgers' equations with a high Reynolds number. A speed-up of up to 11.7 for 2D Burgers' equations is achieved with an appropriate treatment of the nonlinear terms through a hyper-reduction technique.