Physics-Aware Multifidelity Bayesian Optimization: a Generalized Formulation

TL;DR

This work introduces Physics-Aware Multifidelity Bayesian Optimization (PA-MFBO), a framework that embeds prior physical domain knowledge into multifidelity Bayesian optimization to accelerate black-box optimization with expensive high-fidelity models. PA-MFBO combines a multifidelity Gaussian process (MFGP) with a physics-aware acquisition function $U_{PA}$ that multiplies the data-driven $U_{EI}$ by physics-based factors, including correlation, uncertainty reduction, cost, and a physics bias encoded by a vector of domain variables $\psi$. The authors demonstrate PA-MFBO on two engineering problems—the cross-regime transonic airfoil design and composite plate health monitoring—showing that physics-aware bias yields faster convergence, better final designs (up to ~24% drag reduction), and exact damage identification at substantially lower computational budgets than standard MFBO or single-fidelity methods. These results highlight the practical value of incorporating explicit physical priors into MFBO to reduce data requirements and computational cost while improving robustness and accuracy in complex, real-world engineering tasks.

Abstract

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.

Figures (9)

• Figure 1: Drag coefficient of the RAE-2822 airfoil varying the element scale of the CFD computational mesh. The markers indicate the drag coefficients computed adopting the element scale of the high-fidelity $ES=2.5$, mid-fidelity $ES=12$, and low-fidelity $ES=20$ aerodynamic model.
• Figure 2: (a) high-fidelity discretization of the computational domain, and (b) high-fidelity pressure coefficient contours for the RAE-2822 airfoil.
• Figure 3: (a) mid-fidelity discretization of the computational domain, and (b) mid-fidelity pressure coefficient contours for the RAE-2822 airfoil.
• Figure 4: (a) low-fidelity discretization of the computational domain, and (b) low-fidelity pressure coefficient contours for the RAE-2822 airfoil.
• Figure 5: Statistics over 25 runs of the minimum drag coefficient $C_d^{*}$ obtained with the competing algorithms.