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Learning reduced-order Quadratic-Linear models in Process Engineering using Operator Inference

Ion Victor Gosea, Luisa Peterson, Pawan Goyal, Jens Bremer, Kai Sundmacher, Peter Benner

TL;DR

The paper tackles the challenge of efficiently modeling high-dimensional process dynamics by using non-intrusive Operator Inference (OpInf) to learn reduced-order models from time-domain data. OpInf exploits quadratic structure in the reduced state to fit A_hat, H_hat, and C_hat via regression on projected snapshots, producing accurate ROMs without access to the full-order model. In a CO2 methanation reactor test, the OpInf ROM with rank 7 captures 99.9% of the energy with minimal Frobenius error (~0.45%) and substantial computational speedups (~0.46% of full-model time), demonstrating potential for fast digital twins in industrial settings. The work highlights the practicality of OpInf for processing complex, nonlinear dynamics and suggests extensions to handle variable inputs and control terms for multi-query and digital-twin applications.

Abstract

In this work, we address the challenge of efficiently modeling dynamical systems in process engineering. We use reduced-order model learning, specifically operator inference. This is a non-intrusive, data-driven method for learning dynamical systems from time-domain data. The application in our study is carbon dioxide methanation, an important reaction within the Power-to-X framework, to demonstrate its potential. The numerical results show the ability of the reduced-order models constructed with operator inference to provide a reduced yet accurate surrogate solution. This represents an important milestone towards the implementation of fast and reliable digital twin architectures.

Learning reduced-order Quadratic-Linear models in Process Engineering using Operator Inference

TL;DR

The paper tackles the challenge of efficiently modeling high-dimensional process dynamics by using non-intrusive Operator Inference (OpInf) to learn reduced-order models from time-domain data. OpInf exploits quadratic structure in the reduced state to fit A_hat, H_hat, and C_hat via regression on projected snapshots, producing accurate ROMs without access to the full-order model. In a CO2 methanation reactor test, the OpInf ROM with rank 7 captures 99.9% of the energy with minimal Frobenius error (~0.45%) and substantial computational speedups (~0.46% of full-model time), demonstrating potential for fast digital twins in industrial settings. The work highlights the practicality of OpInf for processing complex, nonlinear dynamics and suggests extensions to handle variable inputs and control terms for multi-query and digital-twin applications.

Abstract

In this work, we address the challenge of efficiently modeling dynamical systems in process engineering. We use reduced-order model learning, specifically operator inference. This is a non-intrusive, data-driven method for learning dynamical systems from time-domain data. The application in our study is carbon dioxide methanation, an important reaction within the Power-to-X framework, to demonstrate its potential. The numerical results show the ability of the reduced-order models constructed with operator inference to provide a reduced yet accurate surrogate solution. This represents an important milestone towards the implementation of fast and reliable digital twin architectures.
Paper Structure (8 sections, 8 equations, 3 figures)

This paper contains 8 sections, 8 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Data-driven methods
  3. The method under investigation: Operator Inference
  4. General description
  5. Solving the optimization problem
  6. Application under study
  7. Numerical results
  8. Conclusion and outlook

Figures (3)

  • Figure 1: 3D plots for CO$_2$ conversion (left) and temperature (right) over time and reactor length.
  • Figure 2: Representation of the singular value decay and the cumulative energy encompassed by the primary dominant modes.
  • Figure 3: Flattened 3D representation comparing the true response with the inferred model, highlighting deviations in both conversion (first row) and temperature (second row).