Physics-Aware Multifidelity Bayesian Optimization: a Generalized Formulation

Optimization problems are ubiquitous in science and engineering applications [1]. Those also include the support to engineering tasks that are in increasing demand to meet sustainability goals such as the identification of the best design configurations to maximize the performance and minimize the environmental impact of novel engineering solutions, and the detection and identification of damages or faults to monitor the health condition of complex systems to maximize their useful life and minimize waste of resources. Over the last decades, the increase of computing power and the advances in computational modelling capabilities made available computer-based models for the accurate analysis and simulation of complex physical systems. This is the case of computational schemes for the numerical solution of governing partial differential equations as computational fluid dynamic solvers to represent viscous fluids, and finite element methods for the analysis of mechanical structures, heath transfer and electromagnetic phenomena. In principle, this computer-based representations can provide a remarkable contribution to enhance the search and identification task in simulation-based optimization. Unfortunately, the extensive adoption of these high-fidelity models during the optimization procedure is hampered by the significant computational cost and time required for their evaluation, potentially in the order of months for a single evaluation on high performance computing platforms. This issue becomes more challenging for many-query optimization problems where the demand for model evaluations grows exponentially with the number of parameters to optimize. The use of low-fidelity models constitutes a popular approach to reduce the computational resources associated with the solution of optimization problems. Low-fidelity representations introduce assumptions about the physics and/or approximate the solution of the governing equations, and relief the computational expenditure for the evaluation of the response of the system.