Multi-fidelity Bayesian optimization of population-robust near-infrared sensors for skeletal muscle oximetry

Designing transcutaneous skeletal muscle oxygenation (SmO2) sensors requires jointly optimizing source--detector geometry and wavelength selection while guaranteeing performance across populations that vary in subcutaneous fat thickness and skin pigmentation. We present a multi-fidelity Bayesian optimization (MFBO) framework that couples Monte Carlo light-transport simulations at two photon-count fidelities to a distributionally robust design objective. An autoregressive Gaussian-process surrogate learns the correlation between inexpensive low-photon-count and accurate high-photon-count simulations, and a cost-aware acquisition function decides both where and at what fidelity to sample. Robustness across the population is enforced with Conditional Value-at-Risk (CVaR) and entropic-risk (ERM) objectives that target worst-case subjects rather than the population average. On a five-layer forearm tissue model with anthropometric variability we find (i) a fidelity regime that is favorable for MFBO where the low-fidelity surrogate is rank-informative (Spearman {rho} = 0.84) but biased, at 100x lower cost; (ii) MFBO attains 23% higher robust sensitivity than a strong high-fidelity single-fidelity baseline at equal budget (p = 0.035), and avoids the optimistic bias that causes low-fidelity-only optimization to collapse when its designs are validated at high fidelity; (iii) CVaR/ERM objectives improve worst-case tail performance by {approx}23% relative to a mean objective without sacrificing average sensitivity; and (iv) discovered designs improve robust tail sensitivity by roughly 3--6x over commercial and heuristic optode layouts, with the largest gains in the high-fat and high-melanin subpopulations. The methodology bridges stochastic light-transport physics with sample-efficient machine-learning optimization and generalizes to cerebral oximetry, photodynamic therapy planning, and wearable physiological monitors.