# Interpolatory model reduction of dynamical systems with root mean squared error

arXiv: https://arxiv.org/abs/2403.08894 · HTML: https://mlsanity.com/paper/2403.08894/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Mar 2024.

## Built on by (most cited first, 1 of 1)

- [Enhancing Drug Discovery: Autoencoder-Based Latent Space Augmentation for Improved Molecular Solubility Prediction using LatMixSol](https://mlsanity.com/paper/2506.00223/) (2025)

## Abstract (arXiv)

The root mean squared error is an important measure used in a variety of applications such as structural dynamics and acoustics to model averaged deviations from standard behavior. For large-scale systems, simulations of this quantity quickly become computationally prohibitive. Classical model order reduction techniques attempt to resolve this issue via the construction of surrogate models that emulate the root mean squared error measure using an intermediate linear system. However, this approach requires a potentially large number of linear outputs, which can be disadvantageous in the design of reduced-order models. In this work, we consider directly the root mean squared error as the quantity of interest using the concept of quadratic-output models and propose several new model reduction techniques for the construction of appropriate surrogates. We test the proposed methods on a model for the vibrational response of a plate with tuned vibration absorbers.