Designing modern photonic devices often involves traversing a large parameter space via an optimization procedure, gradient based or otherwise, and typically results in the designer performing electromagnetic simulations of correlated devices. In this paper, we present an approach to accelerate the Generalized Minimal Residual (GMRES) algorithm for the solution of frequency-domain Maxwells equations using two machine learning models (principal component analysis and a convolutional neural network) trained on simulations of correlated devices. These data-driven models are trained to predict a subspace within which the solution of the frequency-domain Maxwells equations lie. This subspace can then be used for augmenting the Krylov subspace generated during the GMRES iterations. By training the proposed models on a dataset of grating wavelength-splitting devices, we show an order of magnitude reduction ($sim 10 - 50$) in the number of GMRES iterations required for solving frequency-domain Maxwells equations.
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