Obey validity limits of data-driven models through topological data analysis and one-class classification

• Published in: Optimization and engineering Vol. 23; no. 2; pp. 855 - 876
• Main Authors: Schweidtmann, Artur M., Weber, Jana M., Wende, Christian, Netze, Linus, Mitsos, Alexander
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.06.2022; Springer Nature B.V
• Subjects: Clusters; Computational geometry; Control; Convexity; Data analysis; Design optimization; Domains; Engineering; Environmental Management; Financial Engineering; Homology; Mathematics; Mathematics and Statistics; Operations Research/Decision Theory; Optimization; Research Article; Support vector machines; Systems Theory; Topology; Training; Validity; Persistent homology; Topological data analysis; One-class support vector machine; Machine-learning; Deterministic global optimization
• ISSN: 1389-4420; 1573-2924; 1573-2924
• DOI: 10.1007/s11081-021-09608-0

Data-driven models are becoming increasingly popular in engineering, on their own or in combination with mechanistic models. Commonly, the trained models are subsequently used in model-based optimization of design and/or operation of processes. Thus, it is critical to ensure that data-driven models are not evaluated outside their validity domain during process optimization. We propose a method to learn this validity domain and encode it as constraints in process optimization. We first perform a topological data analysis using persistent homology identifying potential holes or separated clusters in the training data. In case clusters or holes are identified, we train a one-class classifier, i.e., a one-class support vector machine, on the training data domain and encode it as constraints in the subsequent process optimization. Otherwise, we construct the convex hull of the data and encode it as constraints. We finally perform deterministic global process optimization with the data-driven models subject to their respective validity constraints. To ensure computational tractability, we develop a reduced-space formulation for trained one-class support vector machines and show that our formulation outperforms common full-space formulations by a factor of over 3000, making it a viable tool for engineering applications. The method is ready-to-use and available open-source as part of our MeLOn toolbox ( https://git.rwth-aachen.de/avt.svt/public/MeLOn ).