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.

翻译：计算成本低廉且精确的动态模型是实现实时非线性优化和基于模型控制的关键前提。当给定计算代价高昂的高阶预测模型时，将其简化为低阶模型可支持此类实时应用。本文系统综述了非线性模型降阶方法，并对各类方法的特征进行了比较分析。同时，我们讨论了通用方法及针对化工过程系统的定制化方法，并辨析了这些方法间的异同。鉴于当前基于机器学习的流形-伽辽金方法在构建降维状态子空间时未考虑输入变量的影响，我们将其扩展至含输入的动力系统。通过对比案例研究，我们将八种成熟的模型降阶方法应用于空分过程模型：POD-Galerkin、非线性POD-Galerkin、流形-Galerkin、动态模态分解、Koopman理论、隐变量预测流形学习、分区建模及模型聚合。需要说明的是，本研究未涉及超降阶（即浮点运算次数的缩减）。基于研究结果，我们系统探讨了各模型降阶方法的优势与局限性。