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Deep learning for the design of photonic structures


Innovative approaches and tools play an important role in shaping design, characterization and optimization for the field of photonics. As a subset of machine learning that learns multilevel abstraction of data using hierarchically structured layers, deep learning offers an efficient means to design photonic structures, spawning data-driven approaches complementary to conventional physics- and rule-based methods. Here, we review recent progress in deep-learning-based photonic design by providing the historical background, algorithm fundamentals and key applications, with the emphasis on various model architectures for specific photonic tasks. We also comment on the challenges and perspectives of this emerging research direction.

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Fig. 1: Applying deep learning to solve photonic design problems.
Fig. 2: Photonic designs enabled by an MLP model.
Fig. 3: Advanced deep-learning frameworks in optics and photonics.
Fig. 4: Deep-learning-assisted optimization methods.


  1. 1.

    Joannopoulos, J. D., Johnson, S. G., Winn, J. N. & Meade, R. D. Photonic Crystals: Molding the Flow of Light (Princeton Univ. Press, 2011).

  2. 2.

    Smith, D., Pendry, J. & Wiltshire, M. Metamaterials and negative refractive index. Science 305, 788–792 (2004).

    ADS  Google Scholar 

  3. 3.

    Liu, Y. & Zhang, X. Metamaterials: a new frontier of science and technology. Chem. Soc. Rev. 40, 2494–2507 (2011).

    Google Scholar 

  4. 4.

    Cai, W. & Shalaev, V. M. Optical Metamaterials: Fundamentals and Applications (Springer, 2010).

  5. 5.

    Maier, S. A. Plasmonics: Fundamentals and Applications (Springer, 2007).

  6. 6.

    Bohren, C. F. & Huffman, D. R. Absorption and Scattering of Light by Small Particles (Wiley, 2008).

  7. 7.

    Pendry, J. B., Holden, A., Robbins, D. & Stewart, W. Magnetism from conductors and enhanced nonlinear phenomena. IEEE Trans. Microw. Theory Tech. 47, 2075–2084 (1999).

    ADS  Google Scholar 

  8. 8.

    John, S. Strong localization of photons in certain disordered dielectric superlattices. Phys. Rev. Lett. 58, 2486–2489 (1987).

    ADS  Google Scholar 

  9. 9.

    Molesky, S. et al. Inverse design in nanophotonics. Nat. Photon. 12, 659–670 (2018).

    ADS  Google Scholar 

  10. 10.

    Li, W., Meng, F., Chen, Y., Li, Y. & Huang, X. Topology optimization of photonic and phononic crystals and metamaterials: a review. Adv. Theory Simul. 2, 1900017 (2019).

    Google Scholar 

  11. 11.

    Campbell, S. D. et al. Review of numerical optimization techniques for meta-device design. Opt. Mater. Express 9, 1842–1863 (2019).

    ADS  Google Scholar 

  12. 12.

    LeCun, Y., Bengio, Y. & Hinton, G. Deep learning. Nature 521, 436–444 (2015).

    ADS  Google Scholar 

  13. 13.

    Krizhevsky, A., Sutskever, I. & Hinton, G. E. ImageNet classification with deep convolutional neural networks. In Proc. 25th Int. Conf. Neural Information Processing Systems 1097–1105 (NIPS, 2012).

  14. 14.

    Cho, K. et al. Learning phrase representations using RNN encoder–decoder for statistical machine translation. In Proc. 2014 Conf. Empirical Methods in Natural Language Processing (EMNLP) 1724–1734 (2014).

  15. 15.

    Hinton, G. et al. Deep neural networks for acoustic modeling in speech recognition: the shared views of four research groups. IEEE Signal Proc. Mag. 29, 82–97 (2012).

    ADS  Google Scholar 

  16. 16.

    Socher, R., Chen, D., Manning, C. D. & Ng, A. Reasoning with neural tensor networks for knowledge base completion. In NIPS’13: Proc. 26th Int. Conf. Neural Information Processing Systems 926–934 (NIPS, 2013).

  17. 17.

    Silver, D. et al. Mastering the game of Go with deep neural networks and tree search. Nature 529, 484–489 (2016).

    ADS  Google Scholar 

  18. 18.

    Sanchez-Lengeling, B. & Aspuru-Guzik, A. Inverse molecular design using machine learning: generative models for matter engineering. Science 361, 360–365 (2018).

    ADS  Google Scholar 

  19. 19.

    Goh, G. B., Hodas, N. O. & Vishnu, A. Deep learning for computational chemistry. J. Comput. Chem. 38, 1291–1307 (2017).

    Google Scholar 

  20. 20.

    Zahavy, T. et al. Deep learning reconstruction of ultrashort pulses. Optica 5, 666–673 (2018).

    ADS  Google Scholar 

  21. 21.

    Baldi, P., Sadowski, P. & Whiteson, D. Searching for exotic particles in high-energy physics with deep learning. Nat. Commun. 5, 4308 (2014).

    ADS  Google Scholar 

  22. 22.

    Carrasquilla, J. & Melko, R. G. Machine learning phases of matter. Nat. Phys. 13, 431–434 (2017).

    Google Scholar 

  23. 23.

    White, A., Khial, P., Salehi, F., Hassibi, B. & Hajimiri, A. A silicon photonics computational lensless active-flat-optics imaging system. Sci. Rep. 10, 1869 (2020).

    Google Scholar 

  24. 24.

    Rivenson, Y. et al. Deep learning microscopy. Optica 4, 1437–1443 (2017).

    ADS  Google Scholar 

  25. 25.

    Goodfellow, I., Bengio, Y. & Courville, A. Deep Learning (MIT Press, 2016).

  26. 26.

    McClelland, J. L., McNaughton, B. L. & O’Reilly, R. C. Why there are complementary learning systems in the hippocampus and neocortex: insights from the successes and failures of connectionist models of learning and memory. Psychol. Rev. 102, 419–457 (1995).

    Google Scholar 

  27. 27.

    Rumelhart, D. E., Hinton, G. E. & Williams, R. J. Learning representations by back-propagating errors. Nature 323, 533–536 (1986).

    ADS  MATH  Google Scholar 

  28. 28.

    Hinton, G. E., Osindero, S. & Teh, Y.-W. A fast learning algorithm for deep belief nets. Neural Comput. 18, 1527–1554 (2006).

    MathSciNet  MATH  Google Scholar 

  29. 29.

    Russakovsky, O. et al. ImageNet Large Scale Visual Recognition Challenge. Int. J. Comput. Vis. 115, 211–252 (2015).

    MathSciNet  Google Scholar 

  30. 30.

    Zhang, Q.-J., Gupta, K. C. & Devabhaktuni, V. K. Artificial neural networks for RF and microwave design-from theory to practice. IEEE Trans. Microw. Theory Tech. 51, 1339–1350 (2003).

    ADS  Google Scholar 

  31. 31.

    Patnaik, A., Mishra, R., Patra, G. & Dash, S. An artificial neural network model for effective dielectric constant of microstrip line. IEEE Trans. Antennas Propag. 45, 1697 (1997).

    ADS  Google Scholar 

  32. 32.

    Watson, P. M. & Gupta, K. C. EM-ANN models for microstrip vias and interconnects in dataset circuits. IEEE Trans. Microw. Theory Tech. 44, 2495–2503 (1996).

    ADS  Google Scholar 

  33. 33.

    Kabir, H., Wang, Y., Yu, M. & Zhang, Q.-J. Neural network inverse modeling and applications to microwave filter design. IEEE Trans. Microw. Theory Tech. 56, 867–879 (2008).

    ADS  Google Scholar 

  34. 34.

    Zaabab, A. H., Zhang, Q.-J. & Nakhla, M. A neural network modeling approach to circuit optimization and statistical design. IEEE Trans. Microw. Theory Tech. 43, 1349–1358 (1995).

    ADS  Google Scholar 

  35. 35.

    Southall, H. L., Simmers, J. A. & O’Donnell, T. H. Direction finding in phased arrays with a neural network beamformer. IEEE Trans. Antennas Propag. 43, 1369–1374 (1995).

    ADS  Google Scholar 

  36. 36.

    Nair, V. & Hinton, G. E. Rectified linear units improve restricted Boltzmann machines. In Proc. 27th Int. Conf. Machine Learning (ICML-10) 807–814 (2010).

  37. 37.

    Srivastava, N., Hinton, G., Krizhevsky, A., Sutskever, I. & Salakhutdinov, R. Dropout: a simple way to prevent neural networks from overfitting. J. Machine Learning Res. 15, 1929–1958 (2014).

    MathSciNet  MATH  Google Scholar 

  38. 38.

    Ioffe, S. & Szegedy, C. Batch normalization: accelerating deep network training by reducing internal covariate shift. In Proc. 32nd Int. Conf. Machine Learning 448–456 (PMLR, 2015).

  39. 39.

    Hochreiter, S. & Schmidhuber, J. Long short-term memory. Neural Comput. 9, 1735–1780 (1997).

    Google Scholar 

  40. 40.

    Goodfellow, I. et al. Generative adversarial nets. In NIPS’14: Proc. 27th Int. Conf. Neural Information Processing Systems 2672–2680 (NIPS, 2014).

  41. 41.

    Kingma, D. P. & Welling, M. Auto-encoding variational Bayes. In Proc. 2nd Int. Conf. Learning Representations (ICLR, 2014); preprint at

  42. 42.

    Haykin, S. S. Neural Networks and Learning Machines (Prentice Hall, 2009).

  43. 43.

    Malkiel, I. et al. Plasmonic nanostructure design and characterization via deep learning. Light Sci. Appl. 7, 60 (2018).

    ADS  Google Scholar 

  44. 44.

    Ma, W., Cheng, F. & Liu, Y. Deep-learning-enabled on-demand design of chiral metamaterials. ACS Nano 6, 6326–6334 (2018).

    Google Scholar 

  45. 45.

    Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018).

    Google Scholar 

  46. 46.

    Peurifoy, J. et al. Nanophotonic particle simulation and inverse design using artificial neural networks. Sci. Adv. 4, eaar4206 (2018).

    ADS  Google Scholar 

  47. 47.

    Pilozzi, L., Farrelly, F. A., Marcucci, G. & Conti, C. Machine learning inverse problem for topological photonics. Commun. Phys. 1, 57 (2018).

    Google Scholar 

  48. 48.

    Tahersima, M. H. et al. Deep neural network inverse design of integrated photonic power splitters. Sci. Rep. 9, 1368 (2019).

    ADS  Google Scholar 

  49. 49.

    Hemmatyar, O., Abdollahramezani, S., Kiarashinejad, Y., Zandehshahvar, M. & Adibi, A. Full color generation with Fano-type resonant HfO2 nanopillars designed by a deep-learning approach. Nanoscale 11, 21266–21274 (2019).

    Google Scholar 

  50. 50.

    Sajedian, I., Badloe, T. & Rho, J. Optimisation of colour generation from dielectric nanostructures using reinforcement learning. Opt. Express 27, 5874–5883 (2019).

    ADS  Google Scholar 

  51. 51.

    Chen, Y., Zhu, J., Xie, Y., Feng, N. & Liu, Q. H. Smart inverse design of graphene-based photonic metamaterials by an adaptive artificial neural network. Nanoscale 11, 9749–9755 (2019).

    Google Scholar 

  52. 52.

    Nadell, C. C., Huang, B., Malof, J. M. & Padilla, W. J. Deep learning for accelerated all-dielectric metasurface design. Opt. Express 27, 27523–27535 (2019).

    ADS  Google Scholar 

  53. 53.

    Qiu, T. et al. Deep learning: a rapid and efficient route to automatic metasurface design. Adv. Sci. 6, 1900128 (2019).

    Google Scholar 

  54. 54.

    Zhang, T. et al. Efficient spectrum prediction and inverse design for plasmonic waveguide systems based on artificial neural networks. Photonics Res. 7, 368–380 (2019).

    Google Scholar 

  55. 55.

    Asano, T. & Noda, S. Optimization of photonic crystal nanocavities based on deep learning. Opt. Express 26, 32704–32717 (2018).

    ADS  Google Scholar 

  56. 56.

    Alagappan, G. & Png, C. E. Modal classification in optical waveguides using deep learning. J. Mod. Opt. 66, 557–561 (2019).

    ADS  Google Scholar 

  57. 57.

    Alagappan, G. & Png, C. E. Deep learning models for effective refractive indices in silicon nitride waveguides. J. Opt. 21, 035801 (2019).

    ADS  Google Scholar 

  58. 58.

    Kiarashinejad, Y., Abdollahramezani, S., Zandehshahvar, M., Hemmatyar, O. & Adibi, A. Deep learning reveals underlying physics of light-matter interactions in nanophotonic devices. Adv. Theory Simul. 2, 1900088 (2019).

    Google Scholar 

  59. 59.

    Comin, A. & Hartschuh, A. Efficient optimization of SHG hotspot switching in plasmonic nanoantennas using phase-shaped laser pulses controlled by neural networks. Opt. Express 26, 33678–33686 (2018).

    ADS  Google Scholar 

  60. 60.

    Li, L. et al. DeepNIS: deep neural network for nonlinear electromagnetic inverse scattering. IEEE Trans. Antennas Propag. 67, 1819–1825 (2018).

    ADS  Google Scholar 

  61. 61.

    Turpin, A., Vishniakou, I. & Seelig, J. D. Light scattering control in transmission and reflection with neural networks. Opt. Express 26, 30911–30929 (2018).

    ADS  Google Scholar 

  62. 62.

    Zhang, Q. et al. Machine‐learning designs of anisotropic digital coding metasurfaces. Adv. Theory Simul. 2, 1800132 (2019).

    ADS  Google Scholar 

  63. 63.

    Li, L. et al. Machine-learning reprogrammable metasurface imager. Nat. Commun. 10, 1082 (2019).

    ADS  Google Scholar 

  64. 64.

    Maksov, A. et al. Deep learning analysis of defect and phase evolution during electron beam-induced transformations in WS2. npj Comput. Mater. 5, 12 (2019).

    ADS  Google Scholar 

  65. 65.

    Xie, T. & Grossman, J. C. Crystal graph convolutional neural networks for an accurate and interpretable prediction of material properties. Phys. Rev. Lett. 120, 145301 (2018).

    ADS  Google Scholar 

  66. 66.

    He, K., Zhang, X., Ren, S. & Sun, J. Deep residual learning for image recognition. In Proc. 2016 IEEE Conf. Computer Vision and Pattern Recognition (IEEE, 2016).

  67. 67.

    Szegedy, C. et al. Going deeper with convolutions. In Proc. IEEE Conf. Computer Vision and Pattern Recognition (IEEE, 2015).

  68. 68.

    Sajedian, I., Kim, J. & Rho, J. Finding the optical properties of plasmonic structures by image processing using a combination of convolutional neural networks and recurrent neural networks. Microsyst. Nanoeng. 5, 27 (2019).

    ADS  Google Scholar 

  69. 69.

    Zhou, Q., Yang, C., Liang, A., Zheng, X. & Chen, Z. Low computationally complex recurrent neural network for high speed optical fiber transmission. Opt. Commun. 441, 121–126 (2019).

    ADS  Google Scholar 

  70. 70.

    Liu, Z., Raju, L., Zhu, D. & Cai, W. A hybrid strategy for the discovery and design of photonic nanostructures. IEEE Trans. Emerg. Sel. Top. Circuits Systems 10, 126–135 (2020).

    ADS  Google Scholar 

  71. 71.

    Ma, W., Cheng, F., Xu, Y., Wen, Q. & Liu, Y. Probabilistic representation and inverse design of metamaterials based on a deep generative model with semi-supervised learning strategy. Adv. Mater. 31, 201901111 (2019).

    Google Scholar 

  72. 72.

    So, S. & Rho, J. Designing nanophotonic structures using conditional deep convolutional generative adversarial networks. Nanophotonics 8, 1255–1261 (2019).

    Google Scholar 

  73. 73.

    Liu, Z., Zhu, D., Rodrigues, S. P., Lee, K.-T. & Cai, W. Generative model for the inverse design of metasurfaces. Nano Lett. 18, 6570–6576 (2018).

    ADS  Google Scholar 

  74. 74.

    Liu, Z. et al. Compounding meta-atoms into meta-molecules with hybrid artificial intelligence techniques. Adv. Mater. 32, 1904790 (2019).

    Google Scholar 

  75. 75.

    Wiecha, P. R. & Muskens, O. L. Deep learning meets nanophotonics: a generalized accurate predictor for near fields and far fields of arbitrary 3D nanostructures. Nano Lett. 20, 329–338 (2019).

    ADS  Google Scholar 

  76. 76.

    Jiang, J. & Fan, J. A. Global optimization of dielectric metasurfaces using a physics-driven neural network. Nano Lett. 19, 5366–5372 (2019).

    ADS  Google Scholar 

  77. 77.

    Bogdanov, S. I., Boltasseva, A. & Shalaev, V. M. Overcoming quantum decoherence with plasmonics. Science 364, 532–533 (2019).

    ADS  Google Scholar 

  78. 78.

    Linic, S., Christopher, P. & Ingram, D. B. Plasmonic-metal nanostructures for efficient conversion of solar to chemical energy. Nat. Mater. 10, 911–921 (2011).

    ADS  Google Scholar 

  79. 79.

    Ilic, O. & Atwater, H. A. Self-stabilizing photonic levitation and propulsion of nanostructured macroscopic objects. Nat. Photon. 13, 289–295 (2019).

    ADS  Google Scholar 

  80. 80.

    Li, J. et al. Addressable metasurfaces for dynamic holography and optical information encryption. Sci. Adv. 4, eaar6768 (2018).

    ADS  Google Scholar 

  81. 81.

    Jiang, J. et al. Free-form diffractive metagrating design based on generative adversarial networks. ACS Nano 13, 8872–8878 (2019).

    Google Scholar 

  82. 82.

    Kudyshev, Z. A., Kildishev, A. V., Shalaev, V. M. & Boltasseva, A. Machine-learning-assisted metasurface design for high-efficiency thermal emitter optimization. Appl. Phys. Rev. 7, 021407 (2020).

    ADS  Google Scholar 

  83. 83.

    Melati, D. et al. Mapping the global design space of nanophotonic components using machine learning pattern recognition. Nat. Commun. 10, 4775 (2019).

    ADS  Google Scholar 

  84. 84.

    Watanabe, T., Ayata, M., Koch, U., Fedoryshyn, Y. & Leuthold, J. Perpendicular grating coupler based on a blazed antiback-reflection structure. J. Light. Technol. 35, 4663–4669 (2017).

    ADS  Google Scholar 

  85. 85.

    Bar-Sinai, Y., Hoyer, S., Hickey, J. & Brenner, M. P. Learning data-driven discretizations for partial differential equations. Proc. Natl Acad. Sci. USA 116, 15344–15349 (2019).

    MathSciNet  MATH  Google Scholar 

  86. 86.

    Rudy, S. H., Brunton, S. L., Proctor, J. L. & Kutz, J. N. Data-driven discovery of partial differential equations. Sci. Adv. 3, e1602614 (2017).

    ADS  Google Scholar 

  87. 87.

    Han, J., Jentzen, A. & Weinan, E. Solving high-dimensional partial differential equations using deep learning. Proc. Natl Acad. Sci. USA 115, 8505–8510 (2018).

    MathSciNet  MATH  Google Scholar 

  88. 88.

    Trivedi, R., Su, L., Lu, J., Schubert, M. F. & Vuckovic, J. Data-driven acceleration of photonic simulations. Sci. Rep. 9, 19728 (2019).

    ADS  Google Scholar 

  89. 89.

    Qu, Y., Jing, L., Shen, Y., Qiu, M. & Soljacic, M. Migrating knowledge between physical scenarios based on artificial neural networks. ACS Photonics 6, 1168–1174 (2019).

    Google Scholar 

  90. 90.

    Liu, C.-X., Yu, G.-L. & Zhao, G.-Y. Neural networks for inverse design of phononic crystals. AIP Adv. 9, 085223 (2019).

    ADS  Google Scholar 

  91. 91.

    Ma, W. & Liu, Y. M. A data-efficient self-supervised deep learning model for design and characterization of nanophotonic structures. Sci. China Phys. Mech. Astron. 63, 284212 (2020).

    Google Scholar 

  92. 92.

    Sirignano, J. & Spiliopoulos, K. DGM: a deep learning algorithm for solving partial differential equations. J. Comput. Phys. 375, 1339–1364 (2018).

    ADS  MathSciNet  MATH  Google Scholar 

  93. 93.

    Raissi, M. & Karniadakis, G. E. Hidden physics models: machine learning of nonlinear partial differential equations. J. Comput. Phys. 357, 125–141 (2018).

    ADS  MathSciNet  MATH  Google Scholar 

  94. 94.

    Raissi, M., Perdikaris, P. & Karniadakis, G. E. Physics-informed neural networks: a deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations. J. Comput. Phys. 378, 686–707 (2019).

    ADS  MathSciNet  MATH  Google Scholar 

  95. 95.

    Hansen, N., Müller, S. D. & Koumoutsakos, P. Reducing the time complexity of the derandomized evolution strategy with covariance matrix adaptation (CMA-ES). Evol. Comput. 11, 1–18 (2003).

    Google Scholar 

  96. 96.

    Hegde, R. S. Photonics inverse design: pairing deep neural networks with evolutionary algorithms. IEEE J. Sel. Top. Quant. Electron. 26, (2019).

  97. 97.

    Guler, U., Boltasseva, A. & Shalaev, V. M. Refractory plasmonics. Science 344, 263–264 (2014).

    ADS  Google Scholar 

  98. 98.

    Marino, G. et al. Spontaneous photon-pair generation from a dielectric nanoantenna. Optica 6, 1416–1422 (2019).

    ADS  Google Scholar 

  99. 99.

    Zhang, Q., Yu, H., Barbiero, M., Wang, B. & Gu, M. Artificial neural networks enabled by nanophotonics. Light Sci. Appl. 8, 42 (2019).

    ADS  Google Scholar 

  100. 100.

    Khoram, E. et al. Nanophotonic media for artificial neural inference. Photonics Res. 7, 823–827 (2019).

    Google Scholar 

  101. 101.

    Shen, Y. et al. Deep learning with coherent nanophotonic circuits. Nat. Photon. 11, 441–446 (2017).

    ADS  Google Scholar 

  102. 102.

    Feldmann, J., Youngblood, N., Wright, C., Bhaskaran, H. & Pernice, W. All-optical spiking neurosynaptic networks with self-learning capabilities. Nature 569, 208–214 (2019).

    ADS  Google Scholar 

  103. 103.

    Hughes, T. W., Minkov, M., Shi, Y. & Fan, S. Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5, 864–871 (2018).

    ADS  Google Scholar 

  104. 104.

    Lin, X. et al. All-optical machine learning using diffractive deep neural networks. Science 361, 1004–1008 (2018).

    ADS  MathSciNet  MATH  Google Scholar 

  105. 105.

    Bao, Q. et al. Monolayer graphene as a saturable absorber in a mode-locked laser. Nano Res. 4, 297–307 (2011).

    Google Scholar 

  106. 106.

    Tait, A. N. et al. Silicon photonic modulator neuron. Phys. Rev. Appl. 11, 064043 (2019).

    ADS  Google Scholar 

  107. 107.

    Williamson, I. A. et al. Reprogrammable electro-optic nonlinear activation functions for optical neural networks. IEEE J. Sel. Top. Quant. Electron. 26, (2019).

  108. 108.

    Shastri, B. J. et al. Spike processing with a graphene excitable laser. Sci. Rep. 6, 19126 (2016).

    ADS  Google Scholar 

  109. 109.

    Tait, A. N. et al. Neuromorphic photonic networks using silicon photonic weight banks. Sci. Rep. 7, 7430 (2017).

    ADS  Google Scholar 

  110. 110.

    Estakhri, N. M., Edwards, B. & Engheta, N. Inverse-designed metastructures that solve equations. Science 363, 1333–1338 (2019).

    ADS  MathSciNet  MATH  Google Scholar 

  111. 111.

    Hughes, T. W., Williamson, I. A., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Sci. Adv. 5, eaay6946 (2019).

    ADS  Google Scholar 

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Y.L. acknowledges financial support from the US National Science Foundation (NSF) (ECCS-1916839) and the Office of Naval Research (N00014-16-1-2409). W.C. acknowledges support from the Office of Naval Research (N00014-17-1-2555) and the NSF (DMR-2004749). The Purdue team acknowledges financial support from DARPA/DSO (HR00111720032, Z.A.K.), the US National Science Foundation (ECCS-2029553, A.B.) and the Air Force Office of Scientific Research (AFOSR) (FA9550-20-1-0124, A.B.).

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Ma, W., Liu, Z., Kudyshev, Z.A. et al. Deep learning for the design of photonic structures. Nat. Photonics 15, 77–90 (2021).

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