Machine learning inverse problem for topological photonics

Laura Pilozzi,Giulia Marcucci,Claudio Conti,Francis A Farrelly

doi:10.1038/s42005-018-0058-8

Laura Pilozzi, Giulia Marcucci + Show 2 more

Open Access

https://doi.org/10.1038/s42005-018-0058-8

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Abstract

Topology opens many new horizons for photonics, from integrated optics to lasers. The complexity of large-scale devices asks for an effective solution of the inverse problem: how best to engineer the topology for a specific application? We introduce a machine-learning approach applicable in general to numerous topological problems. As a toy model, we train a neural network with the Aubry–Andre–Harper band structure model and then adopt the network for solving the inverse problem. Our application is able to identify the parameters of a complex topological insulator in order to obtain protected edge states at target frequencies. One challenging aspect is handling the multivalued branches of the direct problem and discarding unphysical solutions. We overcome this problem by adopting a self-consistent method to only select physically relevant solutions. We demonstrate our technique in a realistic design and by resorting to the widely available open-source TensorFlow library.

Highlights

Topology opens many new horizons for photonics, from integrated optics to lasers
This twist is based on a self-consistent cycle in which a tentative solution obtained from the inverse problem neural network (NN) is run through the direct problem NN in order to ensure that the solution obtained is viable
The inverse problem in topological design is solved by a supervised Machine learning (ML) regression technique

Summary

Introduction

Topology opens many new horizons for photonics, from integrated optics to lasers. The complexity of large-scale devices asks for an effective solution of the inverse problem: how best to engineer the topology for a specific application? We introduce a machine-learning approach applicable in general to numerous topological problems. By 2D topological systems, one can simulate 4D ones, as recently investigated in refs.[17,18] One challenge in this field is to find an effective methodology for the inverse problem in which the target optical properties result from topological characteristics. We introduce a twist in order to ensure that only physically possible solutions are found This twist is based on a self-consistent cycle in which a tentative solution obtained from the inverse problem NN is run through the direct problem NN in order to ensure that the solution obtained is viable. This has the added benefit of checking that multivalued degeneracy has been effectively removed

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