Data-driven acceleration of photonic simulations

Rahul Trivedi,Martin F Schubert,Jesse Lu,Jelena Vuckovic,Logan Su

doi:10.1038/s41598-019-56212-5

Rahul Trivedi, Martin F Schubert + Show 3 more

Open Access

https://doi.org/10.1038/s41598-019-56212-5

Copy DOI

Abstract

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 a large number of correlated devices. In this paper, we investigate the possibility of accelerating electromagnetic simulations using the data collected from such correlated simulations. In particular, we present an approach to accelerate the Generalized Minimal Residual (GMRES) algorithm for the solution of frequency-domain Maxwell’s equations using two machine learning models (principal component analysis and a convolutional neural network). These data-driven models are trained to predict a subspace within which the solution of the frequency-domain Maxwell’s equations approximately lies. This subspace is then used for augmenting the Krylov subspace generated during the GMRES iterations, thus effectively reducing the size of the Krylov subspace and hence the number of iterations needed for solving Maxwell’s equations. By training the proposed models on a dataset of wavelength-splitting gratings, we show an order of magnitude reduction (~10–50) in the number of GMRES iterations required for solving frequency-domain Maxwell’s equations.

Highlights

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 a large number of correlated devices
We investigate the possibility of accelerating finite difference frequency domain (FDFD) simulation of Maxwell’s equations using data-driven models
This paper is organized as follows - Section 1 outlines the data-driven Generalized Minimal Residual (GMRES) algorithm and Section 2 presents results of applying the data-driven GMRES algorithm using two machine learning models, principal component analysis and convolutional neural networks, to simulate wavelength splitting gratings

Summary

Introduction

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 a large number of correlated devices. We present an approach to accelerate the Generalized Minimal Residual (GMRES) algorithm for the solution of frequency-domain Maxwell’s equations using two machine learning models (principal component analysis and a convolutional neural network). These data-driven models are trained to predict a subspace within which the solution of the frequency-domain Maxwell’s equations approximately lies. A single device optimization requires ~500–1000 electromagnetic simulations, making them the primary computational bottleneck During such a design process, the electromagnetic simulations being performed are on correlated permittivity distributions (e.g. permittivity distributions generated at different steps of a gradient-based design algorithm). We show that data-driven GMRES achieves an order of magnitude speedup against GMRES, and outperforms a number of commonly used data-free preconditioning techniques

Methods

Results

Conclusion