Bayesian optimization of functional output in inverse problems

Motivated by the parameter identification problem of a reaction-diffusion transport model in a vapor phase infiltration processes, we propose a Bayesian optimization procedure for solving the inverse problem that aims to find an input setting that achieves a desired functional output. The proposed algorithm improves over the standard single-objective Bayesian optimization by (i) utilizing the generalized chi-square distribution as a more appropriate predictive distribution for the squared distance objective function in the inverse problems, and (ii) applying functional principal component analysis to reduce the dimensionality of the functional response data, which allows for efficient approximation of the predictive distribution and the subsequent computation of the expected improvement acquisition function.