# Machine Learning Approach to Model Order Reduction of Nonlinear Systems via Autoencoder and LSTM Networks

arXiv: https://arxiv.org/abs/2109.11213 · HTML: https://mlsanity.com/paper/2109.11213/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Sep 2021.

## Built on by (most cited first, 16 of 16)

- [A Review of Machine Learning Methods Applied to Structural Dynamics and Vibroacoustic](https://mlsanity.com/paper/2204.06362/) (2022)
- [Discussing the Spectrum of Physics-Enhanced Machine Learning; a Survey on Structural Mechanics Applications](https://mlsanity.com/paper/2310.20425/) (2023)
- [Neural modal ordinary differential equations: Integrating physics-based modeling with neural ordinary differential equations for modeling high-dimensional monitored structures](https://mlsanity.com/paper/2207.07883/) (2022)
- [Emulating the dynamics of complex systems using autoregressive models on manifolds (mNARX)](https://mlsanity.com/paper/2306.16335/) (2023)
- [Adaptive learning of effective dynamics: Adaptive real-time, online modeling for complex systems](https://mlsanity.com/paper/2304.01732/) (2023)
- [RefreshNet: Learning Multiscale Dynamics through Hierarchical Refreshing](https://mlsanity.com/paper/2401.13282/) (2024)
- [Autoencoder-based non-intrusive model order reduction in continuum mechanics](https://mlsanity.com/paper/2509.02237/) (2025)
- [Virtual twins of nonlinear vibrating multiphysics microstructures: physics-based versus deep learning-based approaches](https://mlsanity.com/paper/2205.05928/) (2022)
- [Physics-based Reduced Order Modeling for Uncertainty Quantification of Guided Wave Propagation using Bayesian Optimization](https://mlsanity.com/paper/2307.09661/) (2023)
- [Data-driven identification of nonlinear dynamical systems with LSTM autoencoders and Normalizing Flows](https://mlsanity.com/paper/2503.03977/) (2025)
- [Reduced-order modeling of Hamiltonian dynamics based on symplectic neural networks](https://mlsanity.com/paper/2508.11911/) (2025)
- [Enhancing Computational Efficiency in Multiscale Systems Using Deep Learning of Coordinates and Flow Maps](https://mlsanity.com/paper/2407.00011/) (2024)
- [Data-driven Modeling of Parameterized Nonlinear Fluid Dynamical Systems with a Dynamics-embedded Conditional Generative Adversarial Network](https://mlsanity.com/paper/2412.17978/) (2024)
- [Probabilistic function-on-function nonlinear autoregressive model for emulation and reliability analysis of stochastic dynamical systems](https://mlsanity.com/paper/2602.01929/) (2026)
- [Deep Learning-Based Metamodeling of Nonlinear Stochastic Dynamic Systems under Parametric and Predictive Uncertainty](https://mlsanity.com/paper/2603.12012/) (2026)
- [Variational LSTM with Augmented Inputs: Nonlinear Response History Metamodeling with Aleatoric and Epistemic Uncertainty](https://mlsanity.com/paper/2604.01587/) (2026)

## Abstract (arXiv)

In analyzing and assessing the condition of dynamical systems, it is necessary to account for nonlinearity. Recent advances in computation have rendered previously computationally infeasible analyses readily executable on common computer hardware. However, in certain use cases, such as uncertainty quantification or high precision real-time simulation, the computational cost remains a challenge. This necessitates the adoption of reduced-order modelling methods, which can reduce the computational toll of such nonlinear analyses. In this work, we propose a reduction scheme relying on the exploitation of an autoencoder as means to infer a latent space from output-only response data. This latent space, which in essence approximates the system's nonlinear normal modes (NNMs), serves as an invertible reduction basis for the nonlinear system. The proposed machine learning framework is then complemented via the use of long short term memory (LSTM) networks in the reduced space. These are used for creating an nonlinear reduced-order model (ROM) of the system, able to recreate the full system's dynamic response under a known driving input.