# Neural Autoencoder-Based Structure-Preserving Model Order Reduction and Control Design for High-Dimensional Physical Systems

arXiv: https://arxiv.org/abs/2312.06256 · HTML: https://mlsanity.com/paper/2312.06256/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 30 references that are in the map.
- First posted on arXiv 11 Dec 2023.

## Builds on (most cited first, 16 of 16)

- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [Hamiltonian Neural Networks](https://mlsanity.com/paper/1906.01563/) (2019)
- [Lagrangian Neural Networks](https://mlsanity.com/paper/2003.04630/) (2020)
- [A Gentle Introduction to Deep Learning for Graphs](https://mlsanity.com/paper/1912.12693/) (2019)
- [Challenges and Outlook in Robotic Manipulation of Deformable Objects](https://mlsanity.com/paper/2105.01767/) (2021)
- [Bayesian parameter estimation using conditional variational autoencoders for gravitational-wave astronomy](https://mlsanity.com/paper/1909.06296/) (2019)
- [High-order Differentiable Autoencoder for Nonlinear Model Reduction](https://mlsanity.com/paper/2102.11026/) (2021)
- [Model Based Control of Soft Robots: A Survey of the State of the Art and Open Challenges](https://mlsanity.com/paper/2110.01358/) (2021)
- [Combining Physics and Deep Learning to learn Continuous-Time Dynamics Models](https://mlsanity.com/paper/2110.01894/) (2021)
- [Soft Robots Modeling: a Structured Overview](https://mlsanity.com/paper/2112.03645/) (2021)
- [Physics-informed Neural Networks to Model and Control Robots: a Theoretical and Experimental Investigation](https://mlsanity.com/paper/2305.05375/) (2023)
- [Gaussian Process Port-Hamiltonian Systems: Bayesian Learning with Physics Prior](https://mlsanity.com/paper/2305.09017/) (2023)
- [Applying Machine Learning to Study Fluid Mechanics](https://mlsanity.com/paper/2110.02083/) (2021)
- [Physically Consistent Learning of Conservative Lagrangian Systems with Gaussian Processes](https://mlsanity.com/paper/2206.12272/) (2022)
- [Using Spectral Submanifolds for Nonlinear Periodic Control](https://mlsanity.com/paper/2209.06573/) (2022)

## Built on by (most cited first, 7 of 7)

- [Input-to-State Stable Coupled Oscillator Networks for Closed-form Model-based Control in Latent Space](https://mlsanity.com/paper/2409.08439/) (2024)
- [A Riemannian Framework for Learning Reduced-order Lagrangian Dynamics](https://mlsanity.com/paper/2410.18868/) (2024)
- [Data-driven identification of latent port-Hamiltonian systems](https://mlsanity.com/paper/2408.08185/) (2024)
- [Learning Hamiltonian Dynamics at Scale: A Differential-Geometric Approach](https://mlsanity.com/paper/2509.24627/) (2025)
- [Data-driven Model Reduction for Soft Robots via Lagrangian Operator Inference](https://mlsanity.com/paper/2407.08840/) (2024)
- [Nonlinear Model Order Reduction of Dynamical Systems in Process Engineering: Review and Comparison](https://mlsanity.com/paper/2506.12819/) (2025)
- [Structure-preserving Lift & Learn: Scientific machine learning for nonlinear conservative partial differential equations](https://mlsanity.com/paper/2507.00301/) (2025)

## Abstract (arXiv)

This work concerns control-oriented and structure-preserving learning of low-dimensional approximations of high-dimensional physical systems, with a focus on mechanical systems. We investigate the integration of neural autoencoders in model order reduction, while at the same time preserving Hamiltonian or Lagrangian structures. We focus on extensively evaluating the considered methodology by performing simulation and control experiments on large mass-spring-damper networks, with hundreds of states. The empirical findings reveal that compressed latent dynamics with less than 5 degrees of freedom can accurately reconstruct the original systems' transient and steady-state behavior with a relative total error of around 4%, while simultaneously accurately reconstructing the total energy. Leveraging this system compression technique, we introduce a model-based controller that exploits the mathematical structure of the compressed model to regulate the configuration of heavily underactuated mechanical systems.