用不确定性选样本，让光子晶体设计少算2.7倍数据仍准确

Active learning for photonic crystals explores the integration of analytic approximate Bayesian last layer neural networks (LL-BNNs) with uncertainty-driven sample selection to accelerate photonic band gap prediction. We employ an analytic LL-BNN formulation, corresponding to the infinite Monte Carlo sample limit, to obtain uncertainty estimates that are strongly correlated with the true predictive error on unlabeled candidate structures. These uncertainty scores drive an active learning strategy that prioritizes the most informative simulations during training. Applied to the task of predicting band gap sizes in two-dimensional, two-tone photonic crystals, our approach achieves up to a 2.7x reduction on average in required training data compared to a random sampling baseline while maintaining predictive accuracy. The efficiency gains arise from concentrating computational resources on high uncertainty regions of the design space rather than sampling uniformly. Given the substantial cost of full band structure simulations, especially in three dimensions, this data efficiency enables rapid and scalable surrogate modeling. Our results suggest that analytic LL-BNN based active learning can substantially accelerate topological optimization and inverse design workflows for photonic crystals, and more broadly, offers a general framework for data efficient regression across scientific machine learning domains.