Research ArticleCOMPUTER SCIENCE

Nanophotonic particle simulation and inverse design using artificial neural networks

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Science Advances  01 Jun 2018:
Vol. 4, no. 6, eaar4206
DOI: 10.1126/sciadv.aar4206
  • Fig. 1 The NN architecture has as its inputs the thickness of each shell of the nanoparticle, and as its output the scattering cross section at different wavelengths of the scattering spectrum.

    Our actual NN has four hidden layers.

  • Fig. 2 NN results on spectrum approximation.

    (A) Training loss for the eight-shell case. The loss has sharp declines occasionally, suggesting that the NN is finding a pattern about the data at each point. (B) Comparison of NN approximation to the real spectrum, with the closest training examples shown here. One training example is the most similar particle larger than desired, and the other is the most similar particle smaller than desired. These results were consistent across many different spectra.

  • Fig. 3 Inverse design for an eight-shell nanoparticle.

    The legend gives the dimensions of the particle, and the blue is the desired spectrum. The NN is seen to solve the inverse design much more accurately.

  • Fig. 4 Spectra produced by using our approach as an optimization tool.

    (A) Scattering at a narrow range close to a single wavelength. Here, we force the NN to find a total geometry that scatters around a single peak, using alternating layers of silver and silica. (B) Scattering across a broadband of wavelengths. The legend specifies the thickness of each shell in nanometers, alternating silica and silver shells. The network here was restricted to fewer layers of material (only five shells) but given a broader region of shell sizes than previously (from 10 to 70 nm).

  • Fig. 5 Comparison of forward runtime versus complexity of the nanoparticle.

    The simulation becomes infeasible to run many times for large particles, while the NN’s time increases much more slowly. Conceptually, this is logical as the NN is using pure matrix multiplication—and the matrices do not get much bigger—while the simulation must approximate higher and higher orders. The scale is log-log. The simulation was fit with a quadratic fit, while the NN was a linear fit. See the Supplementary Materials for more details and inverse design speed comparison.

  • Table 1 Network architecture and cross-validation results for various sizes of nanoparticles.

    The common architecture throughout is a four-layer densely connected network. The errors are presented as the mean percent off per point on the spectrum (subtracting the output by desired and dividing by the magnitude). The validation set was used to select the best model; the test was never seen until final evaluation. The errors are close, suggesting that not much overfitting is occurring, although the effects become more pronounced for more shells.

    Nanoparticle
    shells
    Neurons
    per layer
    MRE
    (train)
    MRE
    (validation)
    MRE
    (test)
    82501.4%1.5%1.5%
    72250.98%1.0%1.0%
    62250.97%1.0%1.0%
    52000.45%0.46%0.46%
    41250.60%0.60%0.60%
    31000.32%0.33%0.32%
    21000.29%0.30%0.29%

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/4/6/eaar4206/DC1

    section S1. Details for the comparison of NNs with inverse design algorithms

    section S2. J aggregates

    fig. S1. Comparison of inverse design runtime versus complexity of the nanoparticle.

    fig. S2. Comparison of NN approximation to the real spectrum for a particle made with a J-aggregate material.

    fig. S3. Optimization of scattering at a particular wavelength using the J-aggregate material.

  • Supplementary Materials

    This PDF file includes:

    • section S1. Details for the comparison of NNs with inverse design algorithms
    • section S2. J aggregates
    • fig. S1. Comparison of inverse design runtime versus complexity of the nanoparticle.
    • fig. S2. Comparison of NN approximation to the real spectrum for a particle made with a J-aggregate material.
    • fig. S3. Optimization of scattering at a particular wavelength using the J-aggregate material.

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