Abstract
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.
Highlights
In chemical engineering, the use of models is indispensable to describe, design and optimize processes—both on a lab and on production scales, both with academic and with industrial backgrounds
Afterwards, we introduce Gaussian process regression (GPR), which is a machine learning method used to approximate functions
We provide two examples from chemical engineering to illustrate the performance of the new Adaptive Discretization Algorithm with Gaussian Process Regression (ADA-GPR) (Section 3) compared to known the vertex direction method (VDM) and YBT algorithm
Summary
The use of models is indispensable to describe, design and optimize processes—both on a lab and on production scales, both with academic and with industrial backgrounds. A precise model f : X → Y gives a good understanding of the underlying phenomenon and is the basis for reliable simulation and optimization results. These models often depend on a variety of parameters θ that need to be estimated from measured data. Experiments were performed and measurements were taken in order to obtain a good estimate. These experiments should be as informative as possible, such that the estimate of the model parameters is most accurate within the measurement errors
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