Physics-informed Bayesian optimization of expensive-to-evaluate black-box functions

Abstract Bayesian optimization with Gaussian process (GP) surrogates is a popular approach for optimizing expensive-to-evaluate functions in terms of time, energy, or computational resources. Typically, a GP models a scalar objective derived from observed data. However, in many real-world applications, the objective is a combination of multiple outputs from physical experiments or simulations. Converting these multidimensional observations into a single scalar can lead to information loss, slowing convergence and yielding suboptimal results. To address this, we propose to use multi-output GPs to learn the full vector of observations directly, before mapping them to the scalar objective via an inexpensive analytical function. This physics-informed approach retains more information from the underlying physical processes, improving surrogate model accuracy. As a result, the approach accelerates optimization and produces better final designs compared to standard implementations.