Active learning for photonic crystals

TL;DR

This paper introduces an active learning approach using analytic LL-BNNs to efficiently predict photonic band gaps, significantly reducing the required training data while maintaining accuracy.

Contribution

It presents a novel integration of analytic LL-BNNs with active learning for photonic crystal design, enabling faster and more data-efficient surrogate modeling.

Findings

Achieved up to 2.7x reduction in training data compared to random sampling.

Uncertainty-driven sampling concentrates resources on high-uncertainty regions.

Facilitates rapid, scalable surrogate modeling for photonic crystal optimization.

Abstract

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.