# Nonlinear Model Order Reduction of Dynamical Systems in Process Engineering: Review and Comparison

arXiv: https://arxiv.org/abs/2506.12819 · HTML: https://mlsanity.com/paper/2506.12819/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 49 of its 311 references that are in the map.
- First posted on arXiv 15 Jun 2025.

## Builds on (most cited first, 30 of 49)

- [Deep learning for universal linear embeddings of nonlinear dynamics](https://mlsanity.com/paper/1712.09707/) (2017)
- [Machine Learning for Fluid Mechanics](https://mlsanity.com/paper/1905.11075/) (2019)
- [Embed to Control: A Locally Linear Latent Dynamics Model for Control from Raw Images](https://mlsanity.com/paper/1506.07365/) (2015)
- [Linearly-Recurrent Autoencoder Networks for Learning Dynamics](https://mlsanity.com/paper/1712.01378/) (2017)
- [Sobolev Training for Neural Networks](https://mlsanity.com/paper/1706.04859/) (2017)
- [Linear predictors for nonlinear dynamical systems: Koopman operator meets model predictive control](https://mlsanity.com/paper/1611.03537/) (2016)
- [Dynamic mode decomposition with control](https://mlsanity.com/paper/1409.6358/) (2014)
- [A comprehensive deep learning-based approach to reduced order modeling of nonlinear time-dependent parametrized PDEs](https://mlsanity.com/paper/2001.04001/) (2020)
- [Latent-space Physics: Towards Learning the Temporal Evolution of Fluid Flow](https://mlsanity.com/paper/1802.10123/) (2018)
- [Lift & Learn: Physics-informed machine learning for large-scale nonlinear dynamical systems](https://mlsanity.com/paper/1912.08177/) (2019)
- [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 convolutional recurrent autoencoders for learning low-dimensional feature dynamics of fluid systems](https://mlsanity.com/paper/1808.01346/) (2018)
- [Optimal construction of Koopman eigenfunctions for prediction and control](https://mlsanity.com/paper/1810.08733/) (2018)
- [Global Deterministic Optimization with Artificial Neural Networks Embedded](https://mlsanity.com/paper/1801.07114/) (2018)
- [Operator inference for non-intrusive model reduction of systems with non-polynomial nonlinear terms](https://mlsanity.com/paper/2002.09726/) (2020)
- [Koopman operator-based model reduction for switched-system control of PDEs](https://mlsanity.com/paper/1710.06759/) (2017)
- [Quadratic Approximation Manifold for Mitigating the Kolmogorov Barrier in Nonlinear Projection-Based Model Order Reduction](https://mlsanity.com/paper/2204.02462/) (2022)
- [Reduced order modeling of parametrized systems through autoencoders and SINDy approach: continuation of periodic solutions](https://mlsanity.com/paper/2211.06786/) (2022)
- [Learning to Linearize Under Uncertainty](https://mlsanity.com/paper/1506.03011/) (2015)
- [Geometric Autoencoders -- What You See is What You Decode](https://mlsanity.com/paper/2306.17638/) (2023)
- [An autoencoder-based reduced-order model for eigenvalue problems with application to neutron diffusion](https://mlsanity.com/paper/2008.10532/) (2020)
- [Data-Driven Model Predictive Control using Interpolated Koopman Generators](https://mlsanity.com/paper/2003.07094/) (2020)
- [Learning Nonlinear Projections for Reduced-Order Modeling of Dynamical Systems using Constrained Autoencoders](https://mlsanity.com/paper/2307.15288/) (2023)
- [Canonical and Noncanonical Hamiltonian Operator Inference](https://mlsanity.com/paper/2304.06262/) (2023)
- [Nonlinear Model Order Reduction via Lifting Transformations and Proper Orthogonal Decomposition](https://mlsanity.com/paper/1808.02086/) (2018)
- [Koopman Form of Nonlinear Systems with Inputs](https://mlsanity.com/paper/2207.12132/) (2022)
- [Deep Koopman Learning of Nonlinear Time-Varying Systems](https://mlsanity.com/paper/2210.06272/) (2022)
- [Preserving Lagrangian structure in nonlinear model reduction with application to structural dynamics](https://mlsanity.com/paper/1401.8044/) (2014)
- [Generalized Quadratic Embeddings for Nonlinear Dynamics using Deep Learning](https://mlsanity.com/paper/2211.00357/) (2022)
- [How to Compute Invariant Manifolds and their Reduced Dynamics in High-Dimensional Finite-Element Models](https://mlsanity.com/paper/2103.10264/) (2021)

## Abstract (arXiv)

Computationally cheap yet accurate dynamical models are a key requirement for real-time capable nonlinear optimization and model-based control. When given a computationally expensive high-order prediction model, a reduction to a lower-order simplified model can enable such real-time applications. Herein, we review nonlinear model order reduction methods and provide a comparison of method characteristics. Additionally, we discuss both general-purpose methods and tailored approaches for chemical process systems and we identify similarities and differences between these methods. As machine learning manifold-Galerkin approaches currently do not account for inputs in the construction of the reduced state subspace, we extend these methods to dynamical systems with inputs. In a comparative case study, we apply eight established model order reduction methods to an air separation process model: POD-Galerkin, nonlinear-POD-Galerkin, manifold-Galerkin, dynamic mode decomposition, Koopman theory, manifold learning with latent predictor, compartment modeling, and model aggregation. Herein, we do not investigate hyperreduction, i.e., reduction of floating point operations. Based on our findings, we discuss strengths and weaknesses of the model order reduction methods.