Fig. 2: Multi-fidelity Bayesian optimization.

a Quality factor distribution for the two different lengths of PnC resonators (Blue: 3 cm, Green: 3 mm). 25 sets of design parameters were randomly selected, and both results followed a log-normal distribution. b Probability distribution of the 3 cm and 3 mm resonator’s quality factor ratio. The quality factor ratio follows a log-normal distribution. c Shape of the optimized 3 cm resonator. d Evolution of the optimized quality factor with two formulations. MFBO maximizing the log of the quality factor (Transformed MFBO) and single-fidelity Bayesian optimization maximizing the quality factor directly (Regular BO). Transformed MFBO outperformed regular BO. e Iteration history of the transformed MFBO where the shaded blue part represents the first 25 randomly selected simulations for both high and low-fidelity models, and where the green part represents the remaining design iterations where the MFBO method searches the best design and controls what fidelity it wants to evaluate. The abscissa of the plot has units of iteration cost, and its limit was set to 1200. At the end of the optimization process, 122 high-fidelity simulations (each with a relative cost of 8) and 226 low-fidelity simulations (relative cost of 1) were evaluated. All the designs considered during the optimization can be found in the Supplementary Video. f The distance from a previous optimized point to the point considered in that iteration. The red markers indicate when the algorithm has found a higher quality factor until that iteration. d–f Shares the same x-axis corresponding to the design iteration times the cost of each iteration as the optimization process evolves.