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Model-Based Design of Experiments for High-Dimensional Inputs Supported by Machine-Learning Methods

Fraunhofer Institute for Industrial Mathematics (ITWM), 67663 Kaiserslautern, Germany
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Academic Editor: Federico Galvani
Processes 2021, 9(3), 508; https://doi.org/10.3390/pr9030508
Received: 26 January 2021 / Revised: 25 February 2021 / Accepted: 8 March 2021 / Published: 11 March 2021
Algorithms that compute locally optimal continuous designs often rely on a finite design space or on the repeated solution of difficult non-linear programs. Both approaches require extensive evaluations of the Jacobian Df of the underlying model. These evaluations are a heavy computational burden. Based on the Kiefer-Wolfowitz Equivalence Theorem, we present a novel design of experiments algorithm that computes optimal designs in a continuous design space. For this iterative algorithm, we combine an adaptive Bayes-like sampling scheme with Gaussian process regression to approximate the directional derivative of the design criterion. The approximation allows us to adaptively select new design points on which to evaluate the model. The adaptive selection of the algorithm requires significantly less evaluations of Df and reduces the runtime of the computations. We show the viability of the new algorithm on two examples from chemical engineering. View Full-Text
Keywords: optimal experimental design; Gaussian process regression; Bayes-like sampling; chemical engineering optimal experimental design; Gaussian process regression; Bayes-like sampling; chemical engineering
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MDPI and ACS Style

Seufert, P.; Schwientek, J.; Bortz, M. Model-Based Design of Experiments for High-Dimensional Inputs Supported by Machine-Learning Methods. Processes 2021, 9, 508. https://doi.org/10.3390/pr9030508

AMA Style

Seufert P, Schwientek J, Bortz M. Model-Based Design of Experiments for High-Dimensional Inputs Supported by Machine-Learning Methods. Processes. 2021; 9(3):508. https://doi.org/10.3390/pr9030508

Chicago/Turabian Style

Seufert, Philipp, Jan Schwientek, and Michael Bortz. 2021. "Model-Based Design of Experiments for High-Dimensional Inputs Supported by Machine-Learning Methods" Processes 9, no. 3: 508. https://doi.org/10.3390/pr9030508

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