# Virtual twins of nonlinear vibrating multiphysics microstructures: physics-based versus deep learning-based approaches

arXiv: https://arxiv.org/abs/2205.05928 · HTML: https://mlsanity.com/paper/2205.05928/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 85 references that are in the map.
- First posted on arXiv 12 May 2022.

## Builds on (most cited first, 14 of 14)

- [Sparse identification of nonlinear dynamics for model predictive control in the low-data limit](https://mlsanity.com/paper/1711.05501/) (2017)
- [A comprehensive deep learning-based approach to reduced order modeling of nonlinear time-dependent parametrized PDEs](https://mlsanity.com/paper/2001.04001/) (2020)
- [A fast and accurate physics-informed neural network reduced order model with shallow masked autoencoder](https://mlsanity.com/paper/2009.11990/) (2020)
- [POD-DL-ROM: enhancing deep learning-based reduced order models for nonlinear parametrized PDEs by proper orthogonal decomposition](https://mlsanity.com/paper/2101.11845/) (2021)
- [Deep learning-based reduced order models in cardiac electrophysiology](https://mlsanity.com/paper/2006.03040/) (2020)
- [Digital twin, physics-based model, and machine learning applied to damage detection in structures](https://mlsanity.com/paper/2005.14360/) (2020)
- [Machine Learning Approach to Model Order Reduction of Nonlinear Systems via Autoencoder and LSTM Networks](https://mlsanity.com/paper/2109.11213/) (2021)
- [Real-time simulation of parameter-dependent fluid flows through deep learning-based reduced order models](https://mlsanity.com/paper/2106.05722/) (2021)
- [How to Compute Invariant Manifolds and their Reduced Dynamics in High-Dimensional Finite-Element Models](https://mlsanity.com/paper/2103.10264/) (2021)
- [Direct computation of nonlinear mapping via normal form for reduced-order models of finite element nonlinear structures](https://mlsanity.com/paper/2009.12145/) (2020)
- [Model Order Reduction based on Direct Normal Form: Application to Large Finite Element MEMS Structures Featuring Internal Resonance](https://mlsanity.com/paper/2103.10545/) (2021)
- [High order direct parametrisation of invariant manifolds for model order reduction of finite element structures: application to large amplitude vibrations and uncovering of a folding point](https://mlsanity.com/paper/2109.10031/) (2021)
- [Comparison of nonlinear mappings for reduced-order modelling of vibrating structures: normal form theory and quadratic manifold method with modal derivatives](https://mlsanity.com/paper/2007.05067/) (2020)
- [Non-intrusive reduced order modelling for the dynamics of geometrically nonlinear flat structures using three-dimensional finite elements](https://mlsanity.com/paper/2009.11377/) (2020)

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

- [Nonlinear Model Order Reduction of Dynamical Systems in Process Engineering: Review and Comparison](https://mlsanity.com/paper/2506.12819/) (2025)

## Abstract (arXiv)

Micro-Electro-Mechanical-Systems are complex structures, often involving nonlinearites of geometric and multiphysics nature, that are used as sensors and actuators in countless applications. Starting from full-order representations, we apply deep learning techniques to generate accurate, efficient and real-time reduced order models to be used as virtual twin for the simulation and optimization of higher-level complex systems. We extensively test the reliability of the proposed procedures on micromirrors, arches and gyroscopes, also displaying intricate dynamical evolutions like internal resonances. In particular, we discuss the accuracy of the deep learning technique and its ability to replicate and converge to the invariant manifolds predicted using the recently developed direct parametrization approach that allows extracting the nonlinear normal modes of large finite element models. Finally, by addressing an electromechanical gyroscope, we show that the non-intrusive deep learning approach generalizes easily to complex multiphysics problems