Active learning of deep surrogates for PDEs: Application to metasurface design

TL;DR

This paper introduces an active learning approach to efficiently train neural network surrogates for PDE-based photonic device modeling, significantly reducing training data and accelerating optimization.

Contribution

The paper presents a novel active learning algorithm that decreases training data requirements for deep surrogates in PDE applications, especially for large design regions.

Findings

Training data reduced by over an order of magnitude.

Surrogate evaluation is over 100 times faster than direct PDE solve.

Accelerates large-scale photonic device optimization.

Abstract

Surrogate models for partial-differential equations are widely used in the design of meta-materials to rapidly evaluate the behavior of composable components. However, the training cost of accurate surrogates by machine learning can rapidly increase with the number of variables. For photonic-device models, we find that this training becomes especially challenging as design regions grow larger than the optical wavelength. We present an active learning algorithm that reduces the number of training points by more than an order of magnitude for a neural-network surrogate model of optical-surface components compared to random samples. Results show that the surrogate evaluation is over two orders of magnitude faster than a direct solve, and we demonstrate how this can be exploited to accelerate large-scale engineering optimization.