Physics-aware surrogate-based optimization with transfer mapping gaussian processes: For bio-inspired flow tailoring

This paper presents a physics-aware surrogate-based approach (aka PhySBO) for computationally efficient optimization of complex systems. This approach is founded on a new hybrid model. This hybrid model combines partial physics and Gaussian process models in a specialized manner that facilitates more generalizable output predictions compared to pure data-driven models (aka surrogate models) and standard low-fidelity-physics/surrogate ensemble models. More specifically, this hybrid modeling approach called OPTMA exploits the potential relationship between the inputs to the partial physics model and the inputs to the full physics model, where this relationship is mapped by a transfer Gaussian process model (GP). The PhySBO method is applied to design surface riblets for bio-inspired passive flow tailoring, where costly CFD simulations are needed to gather high-fidelity samples. In this case, a potential flow solver acting on a 2D airfoil is used as the partial physics model. Here the transfer GP model transforms the inputs from the geometric riblet features on the original 3D ribleted NACA airfoil to geometric and incoming-flow features for the partial physics model. The OPTMA model is estimated to provide 10⁵ times reduction in computing time. Results show the proposed hybrid model is twice as accurate and robust (when tested on unseen sam-ples) compared to a pure data-driven model, when the number of training samples is small and the training and test samples come from different distribution. This shows the generalizability capacity of the OPTMA architecture (the median of error is ∼0.5%). Based on the OPTMA (hybrid) model, the PhySBO framework is able to converge upon an optimum design with substantial computational efficiency, while providing an optimum that is validated to be 99.73% accurate w.r.t. corresponding high-fidelity estimate.