Physics-Aware Multifidelity Bayesian Optimization: a Generalized
  Formulation
Francesco Di Fiore Laura Mainini
The adoption of high-fidelity models for many-query optimization problems is
majorly limited by the significant computational cost required for their
evaluation at every query. Multifidelity Bayesian methods (MFBO) allow to
include costly high-fidelity responses for a sub-selection of queries only, and
use fast lower-fidelity models to accelerate the optimization process.
State-of-the-art methods rely on a purely data-driven search and do not include
explicit information about the physical context. This paper acknowledges that
prior knowledge about the physical domains of engineering problems can be
leveraged to accelerate these data-driven searches, and proposes a generalized
formulation for MFBO to embed a form of domain awareness during the
optimization procedure. In particular, we formalize a bias as a multifidelity
acquisition function that captures the physical structure of the domain. This
permits to partially alleviate the data-driven search from learning the domain
properties on-the-fly, and sensitively enhances the management of multiple
sources of information. The method allows to efficiently include high-fidelity
simulations to guide the optimization search while containing the overall
computational expense. Our physics-aware multifidelity Bayesian optimization is
presented and illustrated for two classes of optimization problems frequently
met in science and engineering, namely design optimization and health
monitoring problems.