# S-OPT: A Points Selection Algorithm for Hyper-Reduction in Reduced Order Models

arXiv: https://arxiv.org/abs/2203.16494 · HTML: https://mlsanity.com/paper/2203.16494/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Mar 2022.

## Built on by (most cited first, 8 of 8)

- [SVD Perspectives for Augmenting DeepONet Flexibility and Interpretability](https://mlsanity.com/paper/2204.12670/) (2022)
- [gLaSDI: Parametric Physics-informed Greedy Latent Space Dynamics Identification](https://mlsanity.com/paper/2204.12005/) (2022)
- [GPLaSDI: Gaussian Process-based Interpretable Latent Space Dynamics Identification through Deep Autoencoder](https://mlsanity.com/paper/2308.05882/) (2023)
- [A Comprehensive Review of Latent Space Dynamics Identification Algorithms for Intrusive and Non-Intrusive Reduced-Order-Modeling](https://mlsanity.com/paper/2403.10748/) (2024)
- [Physics-informed active learning with simultaneous weak-form latent space dynamics identification](https://mlsanity.com/paper/2407.00337/) (2024)
- [Reduced-order modeling for parameterized PDEs via implicit neural representations](https://mlsanity.com/paper/2311.16410/) (2023)
- [State Estimation Using Sparse DEIM and Recurrent Neural Networks](https://mlsanity.com/paper/2410.15982/) (2024)
- [Hyper-Reduced Autoencoders for Efficient and Accurate Nonlinear Model Reductions](https://mlsanity.com/paper/2303.09630/) (2023)

## Abstract (arXiv)

While projection-based reduced order models can reduce the dimension of full order solutions, the resulting reduced models may still contain terms that scale with the full order dimension. Hyper-reduction techniques are sampling-based methods that further reduce this computational complexity by approximating such terms with a much smaller dimension. The goal of this work is to introduce a points selection algorithm developed by Shin and Xiu [SIAM J. Sci. Comput., 38 (2016), pp. A385--A411], as a hyper-reduction method. The selection algorithm is originally proposed as a stochastic collocation method for uncertainty quantification. Since the algorithm aims at maximizing a quantity S that measures both the column orthogonality and the determinant, we refer to the algorithm as S-OPT. Numerical examples are provided to demonstrate the performance of S-OPT and to compare its performance with an over-sampled Discrete Empirical Interpolation (DEIM) algorithm. We found that using the S-OPT algorithm is shown to predict the full order solutions with higher accuracy for a given number of indices.