Optimal Experimental Design Supported by Machine Learning Regression Models

Modern industry heavily relies on accurate mathematical models to optimize processes. Models are obtained by performing experiments and adapting the model parameters to the measured data. Optimal experimental design (OED) provides methods to obtain precise parameter estimates for mathematical models with as few experiments as possible, which in turn saves costs and time. Classical algorithms for OED require pre-computations on a finite design grid or repeated solutions of a nonlinear program. Both methods need a large amount of model evaluations, which can be computationally expensive and make classical OED unviable for complex and time-dependent models. Utilizing Gaussian process-based regression surrogate models we can approximate the sensitivity function needed in the OED algorithms. This results in a Bayes-like sampling and solution approach for the OED. We show the effectiveness of the machine learning approach by applying the algorithm to several models from chemical process engineering. For small-scale models the method obtains similar results, and for large-scale models the method drastically outperforms classical OED algorithms.