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

Abstract

Surrogate models for partial differential equations are widely used in the design of metamaterials 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 simulations required by more than an order of magnitude for an NN surrogate model of optical-surface components compared to uniform 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.

Inverse Design of Multi-Input Multi-Output 2-D Metastructured Devices

“…To determine how many design variables should be included, consider that an arbitrary lossless and reciprocal four-port admittance matrix has a maximum of ten degrees of freedom. However, due to field averaging arguments, the degrees of freedom are reduced to effective material parameters in electrically-small structures, [22], [23]. The beamformer can be viewed as a lossless, reciprocal, polarization conserving medium supporting a TE wave in the x-z plane.…”

Deep Learning the Electromagnetic Properties of Metamaterials—A Comprehensive Review

“…Instead of using a pure DL model, surrogate DNNs can also be combined with the above mentioned optimization methods to solve AEM inverse design problems, which we categorically label as a hybrid approach. There are many such reports of hybrid optimization models in the DL AEM literature, [ 14,115,116,119,120,132,135,136,140,141,143,175,176,189,197,208–212 ] which we summarize very generally here while noting that the individual models may vary substantially due to the number of optimization techniques available.…”

“…[ 218 ] It has been shown that training datasets built with this sampling strategy can yield a substantially more accurate model than one built with a conventional policy (e.g., random selection). Very recently (2020) an uncertainty sampling approach was employed for DNN‐based AEM design, [ 210 ] where the authors report that they were able to reduce the quantity of training data by an order of magnitude compared to random sampling.…”

“…To our knowledge ref. [210] is the only work to employ active learning in this context, however this initial work illustrates its potential benefit for reducing data dependency of DNNs. Furthermore, uncertainty sampling is just one of numerous active learning strategies that have been developed in the machine learning literature, [ 218 ] including for DNNs (e.g., [ 220 ] ).…”

Intelligent designs in nanophotonics: from optimization towards inverse creation

“…The systemically designed dual-λ metalens showed the near-diffraction-limited focusing ability and the intensity distributions Moreover, there is increasing attention on the DL-assisted meta-lens design [84]. A specific example can be found from the Pestourie's report [85], where they presented an active-learning algorithm to reduce at least one order of magnitude of the training time for the surrogate model. The demonstrated ten-layer meta-structure (with 100 unit-cells of period 400 nm) could converge light at three wavelengths (405 nm, 540 nm, and 810 nm) into three different focal spots, respectively.…”