Inverse binary optimization of convolutional neural network in active learning efficiently designs nanophotonic structures

Binary optimization using active learning schemes has gained attention for automating the discovery of optimal designs in nanophotonic structures and material configurations. Recently, active learning has utilized factorization machines (FM), which usually are second-order models, as surrogates to approximate the hypervolume of the design space, benefiting from rapid optimization by Ising machines such as quantum annealing (QA). However, due to their second-order nature, FM-based surrogate functions struggle to fully capture the complexity of the hypervolume. In this paper, we introduce an inverse binary optimization (IBO) scheme that optimizes a surrogate function based on a convolutional neural network (CNN) within an active learning framework. The IBO method employs backward error propagation to optimize the input binary vector, minimizing the output value while maintaining fixed parameters in the pre-trained CNN layers. We conduct a benchmarking study of the CNN-based surrogate function within the CNN-IBO framework by optimizing nanophotonic designs (e.g., planar multilayer and stratified grating structure) as a testbed. Our results demonstrate that CNN-IBO achieves optimal designs with fewer actively accumulated training data than FM-QA, indicating its potential as a powerful and efficient method for binary optimization.