# Active learning for photonic crystals

arXiv: https://arxiv.org/abs/2601.16287 · HTML: https://mlsanity.com/paper/2601.16287/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 15 of its 24 references that are in the map.
- First posted on arXiv 22 Jan 2026.

## Builds on (most cited first, 15 of 15)

- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [Deep Bayesian Active Learning with Image Data](https://mlsanity.com/paper/1703.02910/) (2017)
- [Deep Batch Active Learning by Diverse, Uncertain Gradient Lower Bounds](https://mlsanity.com/paper/1906.03671/) (2019)
- [BatchBALD: Efficient and Diverse Batch Acquisition for Deep Bayesian Active Learning](https://mlsanity.com/paper/1906.08158/) (2019)
- [Deep Evidential Regression](https://mlsanity.com/paper/1910.02600/) (2019)
- [Batch Active Learning at Scale](https://mlsanity.com/paper/2107.14263/) (2021)
- [Variational Bayesian Last Layers](https://mlsanity.com/paper/2404.11599/) (2024)
- [Bayesian Batch Active Learning as Sparse Subset Approximation](https://mlsanity.com/paper/1908.02144/) (2019)
- [Batch Active Learning Using Determinantal Point Processes](https://mlsanity.com/paper/1906.07975/) (2019)
- [Active learning of deep surrogates for PDEs: Application to metasurface design](https://mlsanity.com/paper/2008.12649/) (2020)
- [Black-Box Batch Active Learning for Regression](https://mlsanity.com/paper/2302.08981/) (2023)
- [Making Better Use of Unlabelled Data in Bayesian Active Learning](https://mlsanity.com/paper/2404.17249/) (2024)
- [Efficacy of Bayesian Neural Networks in Active Learning](https://mlsanity.com/paper/2104.00896/) (2021)
- [Surrogate- and invariance-boosted contrastive learning for data-scarce applications in science](https://mlsanity.com/paper/2110.08406/) (2021)

## Abstract (arXiv)

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.