SCIENCE CHINA Physics, Mechanics & Astronomy, Volume 63 , Issue 8 : 284212(2020) https://doi.org/10.1007/s11433-020-1575-2

A data-efficient self-supervised deep learning model for design and characterization of nanophotonic structures

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  • ReceivedMar 3, 2020
  • AcceptedMay 7, 2020
  • PublishedJun 22, 2020
PACS numbers


With its tremendous success in many machine learning and pattern recognition tasks, deep learning, as one type of data-driven models, has also led to many breakthroughs in other disciplines including physics, chemistry and material science. Nevertheless, the supremacy of deep learning over conventional optimization approaches heavily depends on the huge amount of data collected in advance to train the model, which is a common bottleneck of such a data-driven technique. In this work, we present a comprehensive deep learning model for the design and characterization of nanophotonic structures, where a self-supervised learning mechanism is introduced to alleviate the burden of data acquisition. Taking reflective metasurfaces as an example, we demonstrate that the self-supervised deep learning model can effectively utilize randomly generated unlabeled data during training, with the total test loss and prediction accuracy improved by about 15% compared with the fully supervised counterpart. The proposed self-supervised learning scheme provides an efficient solution for deep learning models in some physics-related tasks where labeled data are limited or expensive to collect.

Funded by

the National Natural Science Foundation of China(Grant,No.,ECCS-1916839)


This work was supported by the National Science Foundation (Grant No. ECCS-1916839).


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  • Figure 1

    (Color online) (a) The proposed deep learning model with self-supervised learning mechanism for both the forward prediction and inverse design of nanophotonic structures. The network architecture of encoder (b) and decoder (c). Conv stands for the convolutional block containing three convolution operations with kernel size of 1×1, 3×3 and 1×1, respectively, each followed by a batch-normalization layer. Pool denotes the pooling layer to halve the lateral dimension while U denotes the up-sampling layer to double the lateral dimension. Fc stands for the fully connected layer.

  • Figure 2

    (Color online) The total loss (a), reconstruction loss (b), and prediction loss (c) of four models (left), together with the loss evolution with training epochs (right).

  • Figure 3

    (Color online) Forward prediction of three samples, bowtie (a), ellipse (b) and split ring (c) from the test dataset. Top panels show the prediction without self-supervised learning (model U0) and bottom panels show the prediction with self-supervised learning (model U_dynamic).

  • Figure 4

    (Color online) Visualization of the latent space by reducing the dimension from 20 to 2 using t-SNE. The distribution of the nanophotonic structures from test dataset encoded by model U0 (a) and model U_dynamic (b), respectively.

  • Figure 5

    (Color online) Inverse design by the U_dynamic model. (a) Required spectra and the ground-truth design. (b)-(f) Retrieved designs and their corresponding reflection spectra.

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