Global optimization of processes through machine learning

Machine learning models can learn complex relationships from data and have led to breakthrough results in various domains. In chemical engineering, machine learning models have great potential for process optimization when combined with mechanistic model equations. However, machine learning models frequently lead to large-scale nonlinear optimization problems where deterministic global optimization is desirable but often intractable. In this dissertation, the global solution of optimization problems with machine learning models embedded is accelerated by orders of magnitude through the development of reduced-space formulations and tight relaxations. The reduced-space formulations are proposed for optimization problems with trained (deep and shallow) artificial neural networks and Gaussian processes embedded. The approach formulates the machine learning models in their original variable space which reduces the number of variables to be branched on compared to the standard full-space formulation. To obtain convex and concave relaxations, we propagate McCormick relaxations through the models which lead to smaller sizes of subproblems compared to the commonly used auxiliary variable method. Moreover, we develop tight relaxations for activation functions of neural networks, for acquisition functions used in Bayesian optimization, and for covariance functions used in Gaussian processes. Our approach greatly improves computational performance compared to the standard full-space formulations and thus enables global optimization for the rational design of ion-separation membranes, energy processes, and chemical processes using machine learning models. To ensure validity of the machine learning models during optimization, we learn the training data domain and encode it as constraints in process optimization. For this, we perform a topological data analysis using persistent homology identifying potential holes or separated clusters in the training data. Then, we train a one-class classifier on the training data domain or construct the convex hull and encode it as constraints in the subsequent process optimization. The developed methods are available in our open-source ``MeLOn - Machine Learning Models for Optimization'' toolbox, which is a submodule to our global solver ``MAiNGO - McCormick-based Algorithm for mixed-integer Nonlinear Global Optimization''. To further accelerate the learning of complex relationships, this work investigates information and knowledge representations for chemical engineering data. We study complex molecular structures as input data for physicochemical property prediction. In particular, we investigate higher-order physical graph neural networks that enable end-to-end learning of physicochemical properties from the molecular graph. We use the method for the prediction of the ignition quality of biofuels. In light of limited experimental data, a combination of multi-task learning, transfer learning, and ensemble learning is used, which results in competitive performance compared to state-of-the-art QSPR models. Furthermore, we identify physical pooling functions based on the molecular size dependency of physicochemical properties. Integrating this physical knowledge into the model structure can be understood as a hybrid modeling approach that improves generalization capabilities and reduces data requirements.