Sekulic, I.; Schaible, J.; Müller, G.; Plock, M.; Burger, S.; Gaaloul, N.; Schneider, P.-I.: Physics-informed Bayesian optimization of expensive-to-evaluate black-box functions. Machine Learning : Science and Technology 6 (2025), p. 040503/1-20
10.1088/2632-2153/ae1f5f
Open Access Version
Abstract:
Bayesian optimization with Gaussian process surrogates is a popular approach for optimizing expensive-to-evaluate functions in terms of time, energy, or computational resources. Typically, a Gaussian process 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 Gaussian processes 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.