Bayesian Design of Experiments: Implementation, Validation and Application to Chemical Kinetics

Abstract

Bayesian experimental design (BED) is a tool for guiding experiments founded on the principle of expected information gain. I.e., which experiment design will inform the most about the model can be predicted before experiments in a laboratory are conducted. BED is also useful when specific physical questions arise from the model which are answered from certain experiments but not from other experiments. BED can take two forms, and these two forms are expressed in three example models in this work. The first example takes the form of a Bayesian linear regression, but also this example is a benchmark for checking numerical and analytical solutions. One of two parameters is an estimator of the synthetic experimental data, and the BED task is choosing among which of the two parameters to inform (limited experimental observability). The second example is a chemical reaction model with a parameter space of informed reaction free energy and temperature. The temperature is an independent experimental design variable explored for information gain. The second and third examples are of the form of adjusting an independent variable in the experimental setup. The third example is a catalytic membrane reactor similar to a plug-flow reactor. For this example, a grid search over the independent variables, temperature and volume, for the greatest information gain is conducted. Also, maximum information gain is conducted is optimized with two algorithms: the differential evolution algorithm and steepest ascent, both of which benefitted in terms of initial guess from the grid search.