# Data-Driven Model Reduction and Nonlinear Model Predictive Control of an Air Separation Unit by Applied Koopman Theory

arXiv: https://arxiv.org/abs/2309.05386 · HTML: https://mlsanity.com/paper/2309.05386/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 24 references that are in the map.
- First posted on arXiv 11 Sep 2023.

## Builds on (most cited first, 7 of 7)

- [Deep learning for universal linear embeddings of nonlinear dynamics](https://mlsanity.com/paper/1712.09707/) (2017)
- [Embed to Control: A Locally Linear Latent Dynamics Model for Control from Raw Images](https://mlsanity.com/paper/1506.07365/) (2015)
- [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)
- [Lift & Learn: Physics-informed machine learning for large-scale nonlinear dynamical systems](https://mlsanity.com/paper/1912.08177/) (2019)
- [Identification of MIMO Wiener-type Koopman Models for Data-Driven Model Reduction using Deep Learning](https://mlsanity.com/paper/2201.12669/) (2022)
- [Graph-Based Modeling and Simulation of Complex Systems](https://mlsanity.com/paper/1812.04983/) (2018)

## Built on by (most cited first, 3 of 3)

- [Nonlinear Model Order Reduction of Dynamical Systems in Process Engineering: Review and Comparison](https://mlsanity.com/paper/2506.12819/) (2025)
- [End-to-End Reinforcement Learning of Koopman Models for eNMPC of an Air Separation Unit](https://mlsanity.com/paper/2511.04522/) (2025)
- [Addressing Terminal Constraints in Data-Driven Demand Response Scheduling](https://mlsanity.com/paper/2605.14741/) (2026)

## Abstract (arXiv)

Achieving real-time capability is an essential prerequisite for the industrial implementation of nonlinear model predictive control (NMPC). Data-driven model reduction offers a way to obtain low-order control models from complex digital twins. In particular, data-driven approaches require little expert knowledge of the particular process and its model, and provide reduced models of a well-defined generic structure. Herein, we apply our recently proposed data-driven reduction strategy based on Koopman theory [Schulze et al. (2022), Comput. Chem. Eng.] to generate a low-order control model of an air separation unit (ASU). The reduced Koopman model combines autoencoders and linear latent dynamics and is constructed using machine learning. Further, we present an NMPC implementation that uses derivative computation tailored to the fixed block structure of reduced Koopman models. Our reduction approach with tailored NMPC implementation enables real-time NMPC of an ASU at an average CPU time decrease by 98 %.