Pendry, J. B. et al. Controlling electromagnetic fields. Science 312, 1780–1782 (2006).
Google Scholar
Schurig, D. et al. Metamaterial electromagnetic cloak at microwave frequencies. Science 314, 977–980 (2006).
Google Scholar
Veselago, V. G. et al. Electrodynamics of substances with simultaneously negative electrical and magnetic permeabilities. Sov. Phys. Uspekhi 10, 504–514 (1968).
Google Scholar
Pendry, J. B., Holden, A. J., Stewart, W. J. & Youngs, I. Extremely low frequency plasmons in metallic mesostructures. Phys. Rev. Lett. 76, 4773–4776 (1996).
Google Scholar
Pendry, J. B., Holden, A. J., Robbins, D. J. & Stewart, W. J. Magnetism from conductors and enhanced nonlinear phenomena. IEEE Trans. Microw. Theory Tech. 47, 2075–2084 (1999).
Google Scholar
Yu, N. et al. Light propagation with phase discontinuities: generalized laws of reflection and refraction. Science 334, 333–337 (2011).
Google Scholar
Yu, N. & Capasso, F. Flat optics with designer metasurfaces. Nat. Mater. 13, 139–150 (2014).
Google Scholar
Liu, M. et al. Multifunctional metasurfaces enabled by simultaneous and independent control of phase and amplitude for orthogonal polarization states. Light: Sci. Appl. 10, 107 (2021).
Google Scholar
Wang, S. et al. Arbitrary polarization conversion dichroism metasurfaces for all-in-one full Poincaré sphere polarizers. Light: Sci. Appl. 10, 24 (2021).
Google Scholar
So, S., Badloe, T., Noh, J., Bravo-Abad, J. & Rho, J. Deep learning enabled inverse design in nanophotonics. Nanophotonics 9, 1041–1057 (2020).
Google Scholar
Wang, Y. et al. High-efficiency broadband achromatic metalens for near-IR biological imaging window. Nat. Commun. 12, 5560 (2021).
Google Scholar
Qian, C. et al. Deep-learning-enabled self-adaptive microwave cloak without human intervention. Nat. Photonics 14, 383–390 (2020).
Google Scholar
Song, Q. et al. Ptychography retrieval of fully polarized holograms from geometric-phase metasurfaces. Nat. Commun. 11, 2651 (2020).
Google Scholar
Zhang, L. et al. Space-time-coding digital metasurfaces. Nat. Commun. 9, 4334 (2018).
Google Scholar
Rubin, N. A. et al. Matrix Fourier optics enables a compact full-Stokes polarization camera. Science 365, eaax1839 (2019).
Google Scholar
Wang, Z., Zhang, H., Zhao, H., Cui, T. J. & Li, L. Intelligent electromagnetic metasurface camera: system design and experimental results. Nanophotonics 11, 2011–2024 (2022).
Google Scholar
Li, H.-Y. et al. Intelligent electromagnetic sensing with learnable data acquisition and processing. Patterns 1, 100006 (2020).
Google Scholar
Zhang, L. et al. A wireless communication scheme based on space- and frequency-division multiplexing using digital metasurfaces. Nat. Electron. 4, 218–227 (2021).
Google Scholar
Zhao, J. et al. Programmable time-domain digital coding metasurface for nonlinear harmonic manipulation and new wireless communication systems. Natl Sci. Rev. 6, 231–238 (2019).
Google Scholar
Gradoni, G. et al. Smart radio environments. Preprint at https://arxiv.org/abs/2111.08676 (2021).
Xiao, C. et al. Ultrabroadband and band-selective thermal meta-emitters by machine learning. Nature 643, 80–88 (2025).
Google Scholar
Budhu, J. & Grbic, A. Fast and accurate optimization of metasurfaces with gradient descent and the Woodbury matrix identity. IEEE Trans. Antennas Propag. 71, 7679–7683 (2023).
Google Scholar
Mansouree, M. et al. Multifunctional 2.5D metastructures enabled by adjoint optimization. Optica 7, 77–84 (2020).
Google Scholar
Brown, T. & Mojabi, P. Cascaded metasurface design using electromagnetic inversion with gradient-based optimization. IEEE Trans. Antennas Propag. 70, 2033–2045 (2022).
Google Scholar
Xu, D. et al. Efficient design of a dielectric metasurface with transfer learning and genetic algorithm. Opt. Mater. Express 11, 1852–1862 (2021).
Google Scholar
Thompson, J. R. Particle swarm optimization of polymer-embedded broadband metasurface reflectors. Opt. Express 298, 43421–43434 (2021).
Google Scholar
Wu, N. et al. Intelligent nanophotonics: when machine learning sheds light. eLight 5, 5 (2025).
Google Scholar
Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nat. Rev. Mater. 6, 679–700 (2021).
Google Scholar
Ma, W. et al. Deep learning for the design of photonic structures. Nat. Photonics 15, 77–90 (2021).
Google Scholar
An, S. et al. A Deep learning approach for objective-driven all-dielectric metasurface design. ACS Photonics 6, 3196–3207 (2019).
Google Scholar
Zhang, Q. Machine-learning designs of anisotropic digital coding metasurfaces. Adv. Theory Simul. 2, 1800132 (2019).
Google Scholar
Tang, Y. et al. Physics-informed recurrent neural network for time dynamics in optical resonances. Nat. Comput. Sci. 2, 169–178 (2022).
Google Scholar
Khatib, O., Ren, S., Malof, J. & Padilla, W. J. Learning the physics of all-dielectric metamaterials with deep Lorentz neural networks. Adv. Opt. Mater. 10, 2200097 (2022).
Google Scholar
An, S. et al. Multifunctional metasurface design with a generative adversarial network. Adv. Opt. Mater. 9, 2001433 (2021).
Google Scholar
Liu, Z. et al. Compounding meta-atoms into metamolecules with hybrid artificial intelligence techniques. Adv. Mater. 32, 1904790 (2020).
Google Scholar
Liu, Z., Zhu, D., Rodrigues, S. P., Lee, K. Y. & Cai, W. Generative model for the inverse design of metasurfaces. Nano Lett. 18, 6570–6576 (2018).
Google Scholar
Xiong, B. et al. Deep learning design for multiwavelength infrared image sensors based on dielectric freeform metasurface. Adv. Opt. Mater. 12, 2302200 (2024).
Google Scholar
Ma, W. et al. Pushing the limits of functionality-multiplexing capability in metasurface design based on statistical machine learning. Adv. Mater. 34, 2110022 (2022).
Google Scholar
Ma, W. et al. Probabilistic representation and inverse design of metamaterials based on a deep generative model with semi-supervised learning strategy. Adv. Mater. 31, 1901111 (2019).
Google Scholar
Tanriover, I. et al. Deep generative modeling and inverse design of manufacturable free-form dielectric metasurfaces. ACS Photonics 10, 875–883 (2022).
George, E. K. et al. Physics-informed machine learning. Nat. Rev. Phys. 3, 422–440 (2021).
Google Scholar
Lu, L., Jin, P. Z., Pang, G. F., Zhang, Z. Q. & Karniadakis, G. E. Learning nonlinear operators via DeepONet based on the universal approximation theorem of operators. Nat. Mach. Intell. 3, 218 (2021).
Google Scholar
Bastek, J. H. & Kochmann, D. M. Inverse design of nonlinear mechanical metamaterials via video denoising diffusion models. Nat. Mach. Intell. 5, 1466–1475 (2023).
Google Scholar
Jin, H. et al. Mechanical characterization and inverse design of stochastic architected metamaterials using neural operators. Preprint at https://arxiv.org/abs/2311.13812 (2023).
Rao, C. et al. Encoding physics to learn reaction–diffusion processes. Nat. Mach. Intell. 5, 765–779 (2023).
Google Scholar
Li, Z. et al. Learning spatiotemporal dynamics with a pretrained generative model. Nat. Mach. Intell. 6, 1566–1579 (2024).
Google Scholar
Ho, J., Jain, A. & Abbeel, P. Denoising diffusion probabilistic models. In Proc. 34th International Conference on Neural Information Processing Systems Vol. 33 (eds Caron, M. et al.) 6840–6851 (Curran Associates, 2020).
Ho, J. & Salimans, T. Classifier-free diffusion guidance. In NeurIPS 2021 Workshop on Deep Generative Models and Downstream Applications https://openreview.net/pdf?id=qw8AKxfYbI (2021).
Wei, Z. & Chen, X. Physics-inspired learning method for solving full-wave nonlinear inverse scattering problems. IEEE Trans. Antennas Propag. 67, 6138–6148 (2019).
Google Scholar
Wang, Y., Zong, Z., He, S., Song, R. & Wei, Z. Push the generalization limitation of learning approaches by multi-domain weight-sharing for full-wave inverse scattering. IEEE Trans. Geosci. Remote Sens. 61, 2003814 (2023).
Ma, H. et al. A comprehensive survey on NSGA-II for multi-objective optimization and applications. Artif. Intell. Rev. 56, 15217–15270 (2023).
Google Scholar
Jiang, Z. et al. Near-field optical mode engineering-enabled freeform nonlocal metasurfaces. Preprint at http://arxiv.org/abs/2506.15495 (2025).
Mao, C. & Fan, J. A. Accurate and scalable deep Maxwell solvers using multilevel iterative methods. Preprint at http://arxiv.org/abs/2509.03622 (2025).
Lu, H. et al. VDT: general-purpose video diffusion transformers via mask modeling. In Twelfth International Conference on Learning Representations https://openreview.net/forum?id=Un0rgm9f04 (ICLR, 2024).
Peebles, W. & Xie, S. Scalable diffusion models with transformers. In Proc. IEEE/CVF International Conference on Computer Vision (eds Kosecka, J. et al.) 4195–4205 (IEEE, 2023).
Oord, A. V. D. et al. Neural discrete representation learning. In Proc. 31st International Conference on Neural Information Processing Systems Vol. 30 (eds Guyon, I. et al.) 6309–6318 (Curran Associates, 2017).
Kim, S. Implementation of generating diverse high-fidelity images with VQ-VAE-2, in PyTorch. GitHub https://github.com/rosinality/vq-vae-2-pytorch (2020).
Su, J. et al. Roformer: enhanced transformer with rotary position embedding. Neurocomputing 568, 127063 (2024).
Google Scholar
Nichol, A. Q. & Dhariwal, P. Improved denoising diffusion probabilistic models. In Proc. 38th International Conference on Machine Learning Vol. 139 (eds Meila, M. & Zhang, T.) 8162–8171 (PMLR, 2021).
Song, J., Meng, C. & Ermon, S. Denoising diffusion implicit models. In 9th International Conference on Learning Representations https://openreview.net/forum?id=St1giarCHLP (ICLR, 2021).
Li, E. et al. ISEE213/current-diffusion-model: metaAI: v10. Zenodo https://doi.org/10.5281/zenodo.16875307 (2025).
