Technology Category
Machine Learning: Learning with ManifoldsSearch and Optimization: Mixed Discrete/Continuous SearchReasoning under Uncertainty: Stochastic Optimization
Nonlinear Model Order Reduction of Dynamical Systems in Process Engineering: Review and Comparison
🤖 AI Summary
To address the dual demand for low computational overhead and high-fidelity dynamic models in real-time nonlinear optimization and model predictive control (MPC) for process engineering, this paper systematically reviews and empirically compares eight classes of nonlinear model order reduction (MOR) methods. We propose a novel manifold-Galerkin extension framework tailored to input-driven dynamical systems—marking the first generalization of manifold-Galerkin methods to controlled nonlinear systems. A unified theoretical analysis is provided, characterizing foundational principles, applicability boundaries, and accuracy-efficiency-robustness trade-offs across both generic and process-specific MOR techniques. Quantitative evaluation is conducted on a high-fidelity air separation unit model, assessing methods along four dimensions: approximation accuracy, computational efficiency, robustness to operating condition shifts, and interpretability. The results yield a practical, application-oriented MOR method selection guideline for industrial dynamic modeling.
Technology Category
Application Category
📝 Abstract
Computationally cheap yet accurate enough dynamical models are vital 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 state-of-the-art nonlinear model order reduction methods and provide a theoretical comparison of method properties. Additionally, we discuss both general-purpose methods and tailored approaches for (chemical) process systems and we identify similarities and differences between these methods. As 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 (reduction of FLOPS). Based on our findings, we discuss strengths and weaknesses of the model order reduction methods.
Problem
Research questions and friction points this paper is trying to address.
Review and compare nonlinear model order reduction methods
Extend manifold-Galerkin methods for systems with inputs
Evaluate methods on air separation process model
Innovation
Methods, ideas, or system contributions that make the work stand out.
Extends manifold-Galerkin methods to handle input systems
Compares eight nonlinear model reduction techniques
Focuses on real-time optimization and control applications
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