  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 3,000, 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).
