pith. sign in

arxiv: 2606.25226 · v1 · pith:3UKSW4EUnew · submitted 2026-06-23 · 📡 eess.IV · physics.optics

Dimension expansion for simulation-efficient nanophotonic neural networks

Shuo Huang , Mahsa Torfeh , Lujia Zhong , Michelle L. Povinelli , Owen D. Miller , Chia Wei Hsu This is my paper

Pith reviewed 2026-06-25 21:33 UTC · model grok-4.3

classification 📡 eess.IV physics.optics
keywords inverse designnanophotonicsmetalensneural networkdimension expansionelectromagnetic simulationY-splitterunsupervised learning
0
0 comments X

The pith

Expanding target parameters into high-dimensional inputs cuts nanophotonic simulation costs by half while matching adjoint optimization.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper introduces the Dimension Expansion Network to handle inverse design of nanophotonic devices where design goals are low-dimensional but the structures themselves are high-dimensional. It converts compact target parameters into structured high-dimensional conditioning representations before feeding them into a generator network. Training occurs end-to-end with differentiable electromagnetic simulations, eliminating any need for precomputed datasets or libraries. On metalens tasks the approach reaches focal intensities comparable to adjoint methods, uses roughly half the simulations, and generalizes across large numbers of targets in one shared focal region. On Y-splitter tasks it produces arbitrary power ratios from only 21 training examples while maintaining broadband performance.

Core claim

DEN addresses the mismatch between low-dimensional design objectives and high-dimensional nanophotonic structures by transforming compact target parameters into structured, high-dimensional conditioning representations before inverse design. This improves target expressivity and conditioning quality for structure generation. The model is trained end-to-end using differentiable electromagnetic simulations, removing the need for any pre-generated dataset. Validation on free-form metalens and asymmetric Y-splitter problems shows focal intensities comparable to adjoint-based optimization, approximately 50 percent lower simulation cost, generalization across tens to thousands of focal targets, an

What carries the argument

Dimension Expansion Network (DEN), which converts compact target parameters into structured high-dimensional conditioning representations to improve expressivity and conditioning for structure generation.

If this is right

  • Metalens designs reach focal intensities comparable to adjoint-based optimization.
  • Simulation cost drops by approximately 50 percent for metalens design.
  • The network generalizes across tens to thousands of focal targets within one shared focal region.
  • Y-splitter designs produce arbitrary power-splitting ratios from only 21 training targets.
  • Dimension expansion increases structural diversity and reduces mode-collapse-like behavior.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same conditioning strategy could be tested on other continuous inverse-design problems that share the low-dimensional objective versus high-dimensional structure mismatch.
  • Ablation results on sensitivity and diversity suggest the expansion step may help stabilize training when the target space becomes very large.
  • Because training requires no external dataset, the framework can be applied directly to new device classes once differentiable simulators are available.

Load-bearing premise

Expanding compact target parameters into structured high-dimensional conditioning representations improves target expressivity and conditioning quality for structure generation.

What would settle it

Train an otherwise identical network without the dimension-expansion step on the same metalens task and check whether focal intensities, simulation cost, and generalization across focal targets remain comparable.

Figures

Figures reproduced from arXiv: 2606.25226 by Chia Wei Hsu, Lujia Zhong, Mahsa Torfeh, Michelle L. Povinelli, Owen D. Miller, Shuo Huang.

Figure 1
Figure 1. Figure 1: The proposed dimension expansion network (DEN). (a) Structure generation using the trained network under multiple design targets. (b) Training process of the network. The scalar target, such as efficiency or focal￾point coordinates, is first embedded into a high-dimensional image and then fed into the neural network. The loss is calculated by directly comparing the actual output of the designed structure, … view at source ↗
Figure 2
Figure 2. Figure 2: Comparison with existing neural-network-based metalens design methods. We compare existing work and our metalens design outcomes on two axes: (1) the design region’s size, V , measured in half-wavelength boxes/cubes (d is the simulation dimension): V /(λ/2)d ; (2) the number of optimized structures or simulations used to generate training data and train the network. “Forward simulation” are methods that on… view at source ↗
Figure 3
Figure 3. Figure 3: Comparison between DEN and adjoint optimization (via L-BFGS) for metalens design. (a) Schematic illustration of the metalens design task. (b) Three design examples with different target focal-point coordinates and their corresponding output fields. (c) Comparison between DEN and L-BFGS in terms of focal intensity at the full width at half maximum (FWHM) and the number of simulations required to generate th… view at source ↗
Figure 4
Figure 4. Figure 4: Inverse design of Y-splitters using DEN. The model is trained at λ = 1550 nm. (a) Design configuration. The design region consists of a 30 × 30 = 900 pixel square. Light is injected at the yellow line and measured at the blue line. (b) Six representative test examples with different target splitting ratios not used during training. The corresponding Poynting flux distributions and output cross-sectional Po… view at source ↗
Figure 5
Figure 5. Figure 5: Dimension expansion enables effective inverse design even with a simple multilayer perceptron (MLP) backbone. (a) Performance of MLP-based models without dimension expansion. Performance degrades as the number of model parameters increases or as the focal region becomes larger. (b) Performance of MLP-based models with dimension expansion. The generated structures exhibit improved focusing performance, and … view at source ↗
Figure 6
Figure 6. Figure 6: Mechanism of dimension expansion (DEN). (a) Network architecture without dimension expansion. (b) Focal intensity as a function of the target-region size D, showing performance degradation and eventual collapse without dimension expansion. (c) Representative failure cases for D = 2.67 µm without dimension expansion. (d) Comparison of learned conditioning representations. DEN produces more diverse and spati… view at source ↗
Figure 7
Figure 7. Figure 7: Comparison with existing metalens design methods. We compared the minimum design step size (in ∆Vmin/(λ) d , where ∆Vmin is the minimum step size measured in units consistent with the design dimensionality and d is the number of independent design axes) and the number of optimized structures or simulations used to generate training data and train the network. “Forward simulation” are methods that only use … view at source ↗
Figure 8
Figure 8. Figure 8: Network structure for design generation from the input image. The proposed framework employs an attention-based U-Net architecture to generate nanophotonic structures from the dimension-expanded inputs. The net￾work consists of encoder blocks (Ei), decoder blocks (Di), skip connections, a bottleneck attention module (M), and an output head (H). Residual connections are incorporated within each block to fac… view at source ↗
Figure 9
Figure 9. Figure 9: Training data selection for the Y-splitter design task. We firstly randomly selected 9 amplitude splitting ratios between 1% : 99% and 49% : 51%. Then the two boundary cases, 0% : 100% and 50% : 50%, are added. We then calculate the corresponding power splitting ratios and use these ratios as the training data. The symmetric data of the selected power splitting ratios are also used in the training. The Y-s… view at source ↗
Figure 10
Figure 10. Figure 10: Examples of metalens structures generated by DEN for D = 2.67 µm and λ = 500 nm. The target focal points span different horizontal (fx) and vertical (fy) coordinates within the focal region. For each target loca￾tion, DEN directly predicts a corresponding binary-like refractive-index distribution and focuses light to the desired position. The red crosses indicate the target focal points. The generated str… view at source ↗
Figure 11
Figure 11. Figure 11: Scalability to dense per-pixel target sampling. Distribution comparisons of the focal intensity for sparse and dense target-space sampling under different target-region sizes D. The light violins show the distributions of the generated structures, while the markers and error bars indicate the mean and standard deviation, respectively. Even when the number of target focal points increases from sparse grids… view at source ↗
Figure 12
Figure 12. Figure 12: Additional analysis of the projection MLPs with and without dimension expansion (DE). (a) Dis￾tributions of MLP weights k and biases b with DE. The weights and biases remain well balanced across different layers. (b) Distributions of MLP weights and biases without DE. The bias distributions exhibit long tails (red arrows), indicating increased reliance on large biases rather than informative target-depend… view at source ↗
read the original abstract

Inverse design of nanophotonic structures is challenging due to the large design space, nonlinear structure-response relationships, and the high computational cost of iterative electromagnetic simulations. Existing deep-learning approaches typically rely on large precomputed datasets or libraries of optimized structures, which limits scalability to continuous and complex inverse-design tasks. We introduce a Dimension Expansion Network (DEN), a fully unsupervised, simulation-efficient framework for nanophotonic inverse design. DEN addresses the mismatch between low-dimensional design objectives and high-dimensional nanophotonic structures by transforming compact target parameters into structured, high-dimensional conditioning representations before inverse design. This improves target expressivity and conditioning quality for structure generation. The model is trained end-to-end using differentiable electromagnetic simulations, removing the need for any pre-generated dataset. We validate DEN on free-form metalens and asymmetric Y-splitter design problems. For metalens design, DEN achieves focal intensities comparable to adjoint-based optimization while reducing simulation cost by approximately 50% and generalizing across tens to thousands of focal targets within a shared focal region. For Y-splitter design, DEN accurately produces arbitrary power-splitting ratios using only 21 training targets and demonstrates robust broadband performance. Ablation studies and representation analyses show that dimension expansion enhances sensitivity to target variations, increases structural diversity, and reduces mode-collapse-like behavior. Overall, DEN provides a scalable conditioning strategy for inverse design with low-dimensional objectives, enabling efficient photonic design across large continuous target spaces.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

0 major / 3 minor

Summary. The manuscript introduces a Dimension Expansion Network (DEN) for unsupervised, simulation-efficient inverse design of nanophotonic structures. DEN transforms compact low-dimensional target parameters into structured high-dimensional conditioning representations to improve expressivity for structure generation. The model is trained end-to-end against differentiable electromagnetic simulations without any precomputed dataset. Validation is reported on free-form metalens design (comparable focal intensity to adjoint optimization, ~50% simulation cost reduction, generalization across tens to thousands of targets) and asymmetric Y-splitter design (accurate arbitrary power-splitting ratios from only 21 training targets, robust broadband performance). Ablation studies and representation analyses are presented to support the benefits of dimension expansion in sensitivity, diversity, and avoidance of mode-collapse-like behavior.

Significance. If the central performance and efficiency claims hold under scrutiny, the work provides a scalable conditioning strategy that reduces dependence on large precomputed datasets and enables continuous target spaces in nanophotonic inverse design. The explicit use of differentiable EM simulations as the training signal and the reported generalization results constitute concrete strengths that could influence practical design workflows.

minor comments (3)
  1. The abstract states focal intensities are 'comparable' to adjoint-based optimization; the results section should include quantitative metrics (e.g., mean and standard deviation over multiple runs) and direct side-by-side values to support this claim.
  2. The ~50% simulation cost reduction is a key efficiency claim; the methods or results section should explicitly define the baseline (number of simulations, adjoint iterations, etc.) and how the count is performed to allow reproduction.
  3. Figure captions and axis labels in the ablation studies should clarify the exact conditioning representations compared (e.g., direct vs. expanded) to make the sensitivity and diversity improvements immediately interpretable.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the detailed summary of our manuscript on the Dimension Expansion Network (DEN) and for the positive assessment of its contributions to simulation-efficient nanophotonic inverse design. The recommendation of minor revision is noted. No specific major comments were provided in the report, so we have no individual points to address at this stage. We remain available to incorporate any additional feedback if the editor or referee provides further details.

Circularity Check

0 steps flagged

No significant circularity

full rationale

The derivation relies on an end-to-end differentiable loop that directly optimizes against external electromagnetic simulations rather than any self-generated or fitted targets. Dimension expansion is introduced as an architectural choice to improve conditioning, with no equations or claims reducing the output to the input by construction. Performance claims are benchmarked against adjoint optimization (an independent method) and use only 21 training targets for the Y-splitter case. No self-citation load-bearing steps, fitted-input predictions, or ansatz smuggling appear in the provided text. The framework is therefore self-contained against external simulation signals.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

No concrete free parameters, axioms, or invented entities are identifiable from the abstract alone; the method description does not specify any fitted constants or new postulated entities.

pith-pipeline@v0.9.1-grok · 5800 in / 1113 out tokens · 43871 ms · 2026-06-25T21:33:47.945778+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

99 extracted references · 4 linked inside Pith

  1. [1]

    Nanophotonics: Shrinking light-based technology

    A Femius Koenderink, Andrea Al `u, and Albert Polman. Nanophotonics: Shrinking light-based technology. Science, 348(6234):516–521, 2015

    2015

  2. [2]

    Metamaterial, plasmonic and nanophotonic devices.Reports on Progress in Physics, 80(3):036401, 2017

    Francesco Monticone and Andrea Alu. Metamaterial, plasmonic and nanophotonic devices.Reports on Progress in Physics, 80(3):036401, 2017

    2017

  3. [3]

    Broadband multifunctional efficient meta-gratings based on dielectric waveguide phase shifters.Nano letters, 15(10):6709–6715, 2015

    Mohammadreza Khorasaninejad and Federico Capasso. Broadband multifunctional efficient meta-gratings based on dielectric waveguide phase shifters.Nano letters, 15(10):6709–6715, 2015

    2015

  4. [4]

    Numerical optimization methods for metasurfaces.Laser & Photonics Reviews, 14(10):1900445, 2020

    Mahmoud MR Elsawy, St ´ephane Lanteri, R ´egis Duvigneau, Jonathan A Fan, and Patrice Genevet. Numerical optimization methods for metasurfaces.Laser & Photonics Reviews, 14(10):1900445, 2020

    2020

  5. [5]

    Waveguiding in blazed-binary diffractive elements.JOSA A, 16(10):2517–2520, 1999

    Philippe Lalanne. Waveguiding in blazed-binary diffractive elements.JOSA A, 16(10):2517–2520, 1999

    1999

  6. [6]

    In- verse design in nanophotonics.Nature Photonics, 12(11):659–670, 2018

    Sean Molesky, Zin Lin, Alexander Y Piggott, Weiliang Jin, Jelena Vuckovi ´c, and Alejandro W Rodriguez. In- verse design in nanophotonics.Nature Photonics, 12(11):659–670, 2018. 13

    2018

  7. [7]

    Advances in optical metalenses.Nature Photonics, 17(1):16–25, 2023

    Amir Arbabi and Andrei Faraon. Advances in optical metalenses.Nature Photonics, 17(1):16–25, 2023

    2023

  8. [8]

    Deep learning to accelerate scatterer-to-field mapping for inverse design of dielectric metasurfaces.ACS Photonics, 8(2):481–488, 2021

    Maksym V Zhelyeznyakov, Steve Brunton, and Arka Majumdar. Deep learning to accelerate scatterer-to-field mapping for inverse design of dielectric metasurfaces.ACS Photonics, 8(2):481–488, 2021

    2021

  9. [9]

    Progress of infrared guided-wave nanophotonic sensors and devices.Nano Convergence, 7(1):12, 2020

    Yiming Ma, Bowei Dong, and Chengkuo Lee. Progress of infrared guided-wave nanophotonic sensors and devices.Nano Convergence, 7(1):12, 2020

    2020

  10. [10]

    Advances and applications of nanophotonic biosensors.Nature nanotechnology, 17(1):5–16, 2022

    Hatice Altug, Sang-Hyun Oh, Stefan A Maier, and Ji ˇr´ı Homola. Advances and applications of nanophotonic biosensors.Nature nanotechnology, 17(1):5–16, 2022

    2022

  11. [11]

    Metasurface-driven oled displays beyond 10,000 pixels per inch

    Won-Jae Joo, Jisoo Kyoung, Majid Esfandyarpour, Sung-Hoon Lee, Hyun Koo, Sunjin Song, Young-Nam Kwon, Seok Ho Song, Jun Cheol Bae, Ara Jo, et al. Metasurface-driven oled displays beyond 10,000 pixels per inch. Science, 370(6515):459–463, 2020

    2020

  12. [12]

    Metasurface eyepiece for augmented reality.Nature communications, 9(1): 1–10, 2018

    Gun-Yeal Lee, Jong-Young Hong, SoonHyoung Hwang, Seokil Moon, Hyeokjung Kang, Sohee Jeon, Hwi Kim, Jun-Ho Jeong, and Byoungho Lee. Metasurface eyepiece for augmented reality.Nature communications, 9(1): 1–10, 2018

    2018

  13. [13]

    Optical meta-waveguides for integrated photonics and beyond.Light: Science & Applications, 10(1):1–44, 2021

    Yuan Meng, Yizhen Chen, Longhui Lu, Yimin Ding, Andrea Cusano, Jonathan A Fan, Qiaomu Hu, Kaiyuan Wang, Zhenwei Xie, Zhoutian Liu, et al. Optical meta-waveguides for integrated photonics and beyond.Light: Science & Applications, 10(1):1–44, 2021

    2021

  14. [14]

    Optical buffer performance enhancement using particle swarm optimization in ring-shape-hole photonic crystal waveguide.Optik, 124(23):5989–5993, 2013

    Seyed Mohammad Mirjalili, Kambiz Abedi, and Seyedali Mirjalili. Optical buffer performance enhancement using particle swarm optimization in ring-shape-hole photonic crystal waveguide.Optik, 124(23):5989–5993, 2013

    2013

  15. [15]

    Concurrent design of quasi-random photonic nanostructures.Proceedings of the National Academy of Sciences, 114(33):8734–8739, 2017

    Won-Kyu Lee, Shuangcheng Yu, Clifford J Engel, Thaddeus Reese, Dongjoon Rhee, Wei Chen, and Teri W Odom. Concurrent design of quasi-random photonic nanostructures.Proceedings of the National Academy of Sciences, 114(33):8734–8739, 2017

    2017

  16. [16]

    Adaptive genetic algorithm for optical meta- surfaces design.Scientific reports, 8(1):11040, 2018

    Samad Jafar-Zanjani, Sandeep Inampudi, and Hossein Mosallaei. Adaptive genetic algorithm for optical meta- surfaces design.Scientific reports, 8(1):11040, 2018

    2018

  17. [17]

    Particle swarm optimized ultra-compact polarization beam splitter on silicon-on-insulator.Photonics and Nanostructures-Fundamentals and Applications, 32:19–23, 2018

    Qichao Lu, Wei Wei, Xin Yan, Bing Shen, Yanbin Luo, Xia Zhang, and Xiaomin Ren. Particle swarm optimized ultra-compact polarization beam splitter on silicon-on-insulator.Photonics and Nanostructures-Fundamentals and Applications, 32:19–23, 2018

    2018

  18. [18]

    Heuristic methods and performance bounds for photonic design.Optics Express, 29(2):2827–2854, 2021

    Guillermo Angeris, Jelena Vuˇckovi´c, and Stephen Boyd. Heuristic methods and performance bounds for photonic design.Optics Express, 29(2):2827–2854, 2021

    2021

  19. [19]

    Inverse design of terahertz optical power splitters using the particle swarm optimization method.Journal of Electromagnetic Engineering and Science, 23(2):139–144, 2023

    Kiyanoush Goudarzi, Han-eol Lee, Doyoung Kim, Ikmo Park, and Haewook Han. Inverse design of terahertz optical power splitters using the particle swarm optimization method.Journal of Electromagnetic Engineering and Science, 23(2):139–144, 2023

    2023

  20. [20]

    Topology optimization for nano-photonics.Laser & Photonics Reviews, 5(2):308–321, 2011

    Jakob Søndergaard Jensen and Ole Sigmund. Topology optimization for nano-photonics.Laser & Photonics Reviews, 5(2):308–321, 2011

    2011

  21. [21]

    Adjoint shape optimiza- tion applied to electromagnetic design.Optics express, 21(18):21693–21701, 2013

    Christopher M Lalau-Keraly, Samarth Bhargava, Owen D Miller, and Eli Yablonovitch. Adjoint shape optimiza- tion applied to electromagnetic design.Optics express, 21(18):21693–21701, 2013

    2013

  22. [22]

    Adjoint method and inverse design for nonlinear nanophotonic devices.ACS Photonics, 5(12):4781–4787, 2018

    Tyler W Hughes, Momchil Minkov, Ian AD Williamson, and Shanhui Fan. Adjoint method and inverse design for nonlinear nanophotonic devices.ACS Photonics, 5(12):4781–4787, 2018

    2018

  23. [23]

    High-NA achromatic metalenses by inverse design.Optics Express, 28(5): 6945–6965, 2020

    Haejun Chung and Owen D Miller. High-NA achromatic metalenses by inverse design.Optics Express, 28(5): 6945–6965, 2020

    2020

  24. [24]

    Large-scale parametrized metasur- face design using adjoint optimization.Acs Photonics, 8(2):455–463, 2021

    Mahdad Mansouree, Andrew McClung, Sarath Samudrala, and Amir Arbabi. Large-scale parametrized metasur- face design using adjoint optimization.Acs Photonics, 8(2):455–463, 2021

    2021

  25. [25]

    High- performance hybrid time/frequency-domain topology optimization for large-scale photonics inverse design.Op- tics Express, 30(3):4467–4491, 2022

    Alec M Hammond, Ardavan Oskooi, Mo Chen, Zin Lin, Steven G Johnson, and Stephen E Ralph. High- performance hybrid time/frequency-domain topology optimization for large-scale photonics inverse design.Op- tics Express, 30(3):4467–4491, 2022. 14

    2022

  26. [26]

    Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer

    Alexander Y Piggott, Jesse Lu, Konstantinos G Lagoudakis, Jan Petykiewicz, Thomas M Babinec, and Jelena Vuˇckovi´c. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature photonics, 9(6):374–377, 2015

    2015

  27. [27]

    Topology optimization approaches: A comparative review.Structural and multi- disciplinary optimization, 48(6):1031–1055, 2013

    Ole Sigmund and Kurt Maute. Topology optimization approaches: A comparative review.Structural and multi- disciplinary optimization, 48(6):1031–1055, 2013

    2013

  28. [28]

    Inverse design in photonics by topology optimization: tutorial.Journal of the Optical Society of America B, 38(2):496–509, 2021

    Rasmus E Christiansen and Ole Sigmund. Inverse design in photonics by topology optimization: tutorial.Journal of the Optical Society of America B, 38(2):496–509, 2021

    2021

  29. [29]

    Multimode grating couplers via foundry-compliant inverse design.arXiv preprint arXiv:2604.28058, 2026

    Hao Li, Nazar Pyvovar, Zhaowei Dai, and Owen D Miller. Multimode grating couplers via foundry-compliant inverse design.arXiv preprint arXiv:2604.28058, 2026

    Pith/arXiv arXiv 2026

  30. [30]

    Deep learning in nano-photonics: inverse design and beyond.Photonics Research, 9(5):B182–B200, 2021

    Peter R Wiecha, Arnaud Arbouet, Christian Girard, and Otto L Muskens. Deep learning in nano-photonics: inverse design and beyond.Photonics Research, 9(5):B182–B200, 2021

    2021

  31. [31]

    Deep learning the electromagnetic properties of metamaterials—a comprehensive review.Advanced Functional Materials, 31(31):2101748, 2021

    Omar Khatib, Simiao Ren, Jordan Malof, and Willie J Padilla. Deep learning the electromagnetic properties of metamaterials—a comprehensive review.Advanced Functional Materials, 31(31):2101748, 2021

    2021

  32. [32]

    Deep learning for the design of photonic structures.Nature Photonics, 15(2):77–90, 2021

    Wei Ma, Zhaocheng Liu, Zhaxylyk A Kudyshev, Alexandra Boltasseva, Wenshan Cai, and Yongmin Liu. Deep learning for the design of photonic structures.Nature Photonics, 15(2):77–90, 2021

    2021

  33. [33]

    Deep neural networks for the evaluation and design of photonic devices.Nature Reviews Materials, 6(8):679–700, 2021

    Jiaqi Jiang, Mingkun Chen, and Jonathan A Fan. Deep neural networks for the evaluation and design of photonic devices.Nature Reviews Materials, 6(8):679–700, 2021

    2021

  34. [34]

    Free-form optimization of nanophotonic devices: from classical methods to deep learning.Nanophotonics, 11(9):1809– 1845, 2022

    Juho Park, Sanmun Kim, Daniel Wontae Nam, Haejun Chung, Chan Y Park, and Min Seok Jang. Free-form optimization of nanophotonic devices: from classical methods to deep learning.Nanophotonics, 11(9):1809– 1845, 2022

    2022

  35. [35]

    Artificial intelligence in meta-optics.Chemical Reviews, 122(19):15356–15413, 2022

    Mu Ku Chen, Xiaoyuan Liu, Yanni Sun, and Din Ping Tsai. Artificial intelligence in meta-optics.Chemical Reviews, 122(19):15356–15413, 2022

    2022

  36. [36]

    Non-volatile double-tunable vortex metalens design based on sb2s3 using deep neural network and particle swarm optimization algorithm.Optics Communications, 560:130453, 2024

    Yuqing Zhang, Yiyi Zhang, Jin Deng, Zihan Shen, Zhicheng Wang, Yilu Wu, Yuqi Hu, Chengzhi Huang, Jiagui Wu, and Junbo Yang. Non-volatile double-tunable vortex metalens design based on sb2s3 using deep neural network and particle swarm optimization algorithm.Optics Communications, 560:130453, 2024

    2024

  37. [37]

    High efficiency visible achromatic metalens design via deep learning.Advanced Optical Materials, 11(18):2300394, 2023

    Feilou Wang, Shiqiang Zhao, Yongzheng Wen, Jingbo Sun, and Ji Zhou. High efficiency visible achromatic metalens design via deep learning.Advanced Optical Materials, 11(18):2300394, 2023

    2023

  38. [38]

    Deep convolutional neural networks to predict mutual coupling effects in metasurfaces.Advanced Optical Materials, 10(3):2102113, 2022

    Sensong An, Bowen Zheng, Mikhail Y Shalaginov, Hong Tang, Hang Li, Li Zhou, Yunxi Dong, Mohammad Haerinia, Anuradha Murthy Agarwal, Clara Rivero-Baleine, et al. Deep convolutional neural networks to predict mutual coupling effects in metasurfaces.Advanced Optical Materials, 10(3):2102113, 2022

    2022

  39. [39]

    Design of multifunctional tunable dual-layer metalens based on deep learning.Optics Express, 33(10):21979–21998, 2025

    Yu Wang, Yue Wang, Guohui Yang, Kuang Zhang, Xing Yang, Chunhui Wang, and Yu Zhang. Design of multifunctional tunable dual-layer metalens based on deep learning.Optics Express, 33(10):21979–21998, 2025

    2025

  40. [40]

    Design of a deep learning-based metalens color router for rgb-nir sensing.Nanomaterials, 14(23):1973, 2024

    Hua Mu, Yu Zhang, Zhenyu Liang, Haoqi Gao, Haoli Xu, Bingwen Wang, Yangyang Wang, and Xing Yang. Design of a deep learning-based metalens color router for rgb-nir sensing.Nanomaterials, 14(23):1973, 2024

    1973

  41. [41]

    Multi-angle focusing metalens designed via kan deep learning for expanding the reception field of mems lidar

    Yue Wang, Yu Wang, Zeyang Zhang, Chunhui Wang, Kuang Zhang, Xing Yang, Guohui Yang, and Yu Zhang. Multi-angle focusing metalens designed via kan deep learning for expanding the reception field of mems lidar. ACS Photonics, 2025

    2025

  42. [42]

    Soumyashree S Panda, Sushil Kumar, Devdutt Tripathi, and Ravi S Hegde. Deep learning aids simultaneous structure–material design discovery: a case study on designing phase change material metasurfaces.Journal of Nanophotonics, 17(3):036006–036006, 2023

    2023

  43. [43]

    Nanophotonic structure inverse design for switching application using deep learning.Scientific Reports, 14(1):21094, 2024

    Ehsan Adibnia, Majid Ghadrdan, and Mohammad Ali Mansouri-Birjandi. Nanophotonic structure inverse design for switching application using deep learning.Scientific Reports, 14(1):21094, 2024

    2024

  44. [44]

    Nanophotonic particle simulation and inverse design using artificial neural networks.Science Advances, 4(6):eaar4206, 2018

    John Peurifoy, Yichen Shen, Li Jing, Yi Yang, Fidel Cano-Renteria, Brendan G DeLacy, John D Joannopoulos, Max Tegmark, and Marin Solja ˇci´c. Nanophotonic particle simulation and inverse design using artificial neural networks.Science Advances, 4(6):eaar4206, 2018. 15

    2018

  45. [45]

    Deep neural network inverse design of integrated photonic power splitters.Scientific Reports, 9(1):1368, 2019

    Mohammad H Tahersima, Keisuke Kojima, Toshiaki Koike-Akino, Devesh Jha, Bingnan Wang, Chungwei Lin, and Kieran Parsons. Deep neural network inverse design of integrated photonic power splitters.Scientific Reports, 9(1):1368, 2019

    2019

  46. [46]

    Maziar Raissi, Paris Perdikaris, and George E Karniadakis. Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations.Journal of Computational physics, 378:686–707, 2019

    2019

  47. [47]

    Physics- informed machine learning.Nature Reviews Physics, 3(6):422–440, 2021

    George Em Karniadakis, Ioannis G Kevrekidis, Lu Lu, Paris Perdikaris, Sifan Wang, and Liu Yang. Physics- informed machine learning.Nature Reviews Physics, 3(6):422–440, 2021

    2021

  48. [48]

    Deeponet: Learning nonlinear operators for identifying dif- ferential equations based on the universal approximation theorem of operators.arXiv preprint arXiv:1910.03193, 2019

    Lu Lu, Pengzhan Jin, and George Em Karniadakis. Deeponet: Learning nonlinear operators for identifying dif- ferential equations based on the universal approximation theorem of operators.arXiv preprint arXiv:1910.03193, 2019

    Pith/arXiv arXiv 1910

  49. [49]

    Fourier neural operator for parametric partial differential equations.arXiv preprint arXiv:2010.08895, 2020

    Zongyi Li, Nikola Kovachki, Kamyar Azizzadenesheli, Burigede Liu, Kaushik Bhattacharya, Andrew Stuart, and Anima Anandkumar. Fourier neural operator for parametric partial differential equations.arXiv preprint arXiv:2010.08895, 2020

    Pith/arXiv arXiv 2010

  50. [50]

    Neural operator: Learning maps between function spaces with applications to pdes

    Nikola Kovachki, Zongyi Li, Burigede Liu, Kamyar Azizzadenesheli, Kaushik Bhattacharya, Andrew Stuart, and Anima Anandkumar. Neural operator: Learning maps between function spaces with applications to pdes. Journal of Machine Learning Research, 24(89):1–97, 2023

    2023

  51. [51]

    Probabilistic inverse design of metasurfaces using mixture density neural networks.Journal of Physics: Photonics, 7(1):015007, 2024

    Mahsa Torfeh and Chia Wei Hsu. Probabilistic inverse design of metasurfaces using mixture density neural networks.Journal of Physics: Photonics, 7(1):015007, 2024

    2024

  52. [52]

    Neural network inverse modeling and applications to microwave filter design.IEEE Transactions on Microwave Theory and Techniques, 56(4):867–879, 2008

    Humayun Kabir, Ying Wang, Ming Yu, and Qi-Jun Zhang. Neural network inverse modeling and applications to microwave filter design.IEEE Transactions on Microwave Theory and Techniques, 56(4):867–879, 2008

    2008

  53. [53]

    Deep learning approach based on dimensionality reduction for designing electromagnetic nanostructures.npj Computational Materials, 6(1):12, 2020

    Yashar Kiarashinejad, Sajjad Abdollahramezani, and Ali Adibi. Deep learning approach based on dimensionality reduction for designing electromagnetic nanostructures.npj Computational Materials, 6(1):12, 2020

    2020

  54. [54]

    Independent bifocal metalens design based on deep learning algebra.IEEE Photonics Technology Letters, 33(8):403–406, 2021

    Yijie Gu, Ran Hao, and Er-Ping Li. Independent bifocal metalens design based on deep learning algebra.IEEE Photonics Technology Letters, 33(8):403–406, 2021

    2021

  55. [55]

    Designing broadband terahertz achromatic metalens based on deep learning.Optics & Laser Technology, 184:112550, 2025

    Qiankun Zhang, Bingxuan Mao, Jialu Li, Xiaohua Xing, Die Zou, Yin Liu, Jianquan Yao, Jianqiang Gu, Pengfei Zhu, and Liang Wu. Designing broadband terahertz achromatic metalens based on deep learning.Optics & Laser Technology, 184:112550, 2025

    2025

  56. [56]

    Wen-Qiang Deng, H Zhu, Yu-Xuan Xie, Zhengji Xu, and Shu-Yan Zhu. Design and optimization of an ultra- wideband millimeter-wave circularly polarized metalens antenna with deep learning method.IEEE Open Journal of Antennas and Propagation, 5(4):823–832, 2024

    2024

  57. [57]

    Metasurfacevit: A generic ai model for metasurface inverse design.arXiv preprint arXiv:2504.14895, 2025

    Jiahao Yan, Jilong Yi, Churong Ma, Yanjun Bao, Qin Chen, and Baojun Li. Metasurfacevit: A generic ai model for metasurface inverse design.arXiv preprint arXiv:2504.14895, 2025

    arXiv 2025

  58. [58]

    Shengmei Ou, Jiakang Xu, Jiming Wang, Yulian Zhu, Xiaorong Gu, Tong Wu, and Youwen Liu. Deep learning- assisted focus engineering for metalens design with high numerical aperture cylindrical vector beams.Photonics and Nanostructures: Fundamentals and Applications, page 101396, 2025

    2025

  59. [59]

    Inverse design of plasmonic metasurfaces by convolutional neural network.Optics Letters, 45(6):1362–1365, 2020

    Ronghui Lin, Yanfen Zhai, Chenxin Xiong, and Xiaohang Li. Inverse design of plasmonic metasurfaces by convolutional neural network.Optics Letters, 45(6):1362–1365, 2020

    2020

  60. [60]

    Plasmonic nanos- tructure design and characterization via deep learning.Light: Science & Applications, 7(1):60, 2018

    Itzik Malkiel, Michael Mrejen, Achiya Nagler, Uri Arieli, Lior Wolf, and Haim Suchowski. Plasmonic nanos- tructure design and characterization via deep learning.Light: Science & Applications, 7(1):60, 2018

    2018

  61. [61]

    Neural network-assisted design of gsst-based achromatic metalens with continuously variable focal heights.Op- tics Communications, 554:130141, 2024

    Rui Qiu, Guanmao Zhang, Shaokai Du, Jie Liu, Hongyu Ji, Kaiyun Bi, Bochuan Xing, and Guangchao Diao. Neural network-assisted design of gsst-based achromatic metalens with continuously variable focal heights.Op- tics Communications, 554:130141, 2024

    2024

  62. [62]

    Deep-learning-enabled on-demand design of chiral metamaterials.ACS Nano, 12(6):6326–6334, 2018

    Wei Ma, Feng Cheng, and Yongmin Liu. Deep-learning-enabled on-demand design of chiral metamaterials.ACS Nano, 12(6):6326–6334, 2018

    2018

  63. [63]

    Training deep neural networks for the inverse design of nanophotonic structures.Acs Photonics, 5(4):1365–1369, 2018

    Dianjing Liu, Yixuan Tan, Erfan Khoram, and Zongfu Yu. Training deep neural networks for the inverse design of nanophotonic structures.Acs Photonics, 5(4):1365–1369, 2018. 16

    2018

  64. [64]

    An improved tandem neural network for the inverse design of nanophotonics devices.Optics Communications, 481:126513, 2021

    Xiaopeng Xu, Chonglei Sun, Yu Li, Jia Zhao, Junlei Han, and Weiping Huang. An improved tandem neural network for the inverse design of nanophotonics devices.Optics Communications, 481:126513, 2021

    2021

  65. [65]

    Generative adversarial nets.Advances in neural information processing sys- tems, 27, 2014

    Ian J Goodfellow, Jean Pouget-Abadie, Mehdi Mirza, Bing Xu, David Warde-Farley, Sherjil Ozair, Aaron Courville, and Yoshua Bengio. Generative adversarial nets.Advances in neural information processing sys- tems, 27, 2014

    2014

  66. [66]

    Auto-encoding variational bayes.arXiv preprint arXiv:1312.6114, 2013

    Diederik P Kingma and Max Welling. Auto-encoding variational bayes.arXiv preprint arXiv:1312.6114, 2013

    Pith/arXiv arXiv 2013

  67. [67]

    Deep learning design for multiwave- length infrared image sensors based on dielectric freeform metasurface.Advanced Optical Materials, 12(10): 2302200, 2024

    Bo Xiong, Yihao Xu, Wenwen Li, Wei Ma, Tao Chu, and Yongmin Liu. Deep learning design for multiwave- length infrared image sensors based on dielectric freeform metasurface.Advanced Optical Materials, 12(10): 2302200, 2024

    2024

  68. [68]

    Probabilistic representation and inverse design of metamaterials based on a deep generative model with semi-supervised learning strategy.Advanced Materials, 31(35):1901111, 2019

    Wei Ma, Feng Cheng, Yihao Xu, Qinlong Wen, and Yongmin Liu. Probabilistic representation and inverse design of metamaterials based on a deep generative model with semi-supervised learning strategy.Advanced Materials, 31(35):1901111, 2019

    2019

  69. [69]

    Yanhe Lyu, Theng Huat Gan, and Zhi Ning Chen. Te-tm balanced wide-angle metacells for low scan-loss metalens antenna using prior knowledge-guided generative deep learning-enabled method.IEEE Transactions on Antennas and Propagation, 2025

    2025

  70. [70]

    Multifunctional metasurface design with a generative adversarial network

    Sensong An, Bowen Zheng, Hong Tang, Mikhail Y Shalaginov, Li Zhou, Hang Li, Myungkoo Kang, Kathleen A Richardson, Tian Gu, Juejun Hu, et al. Multifunctional metasurface design with a generative adversarial network. Advanced Optical Materials, 9(5):2001433, 2021

    2021

  71. [71]

    A cyclical deep learning based framework for simultaneous inverse and forward design of nanophotonic metasurfaces.Scientific Reports, 10(1):19427, 2020

    Abhishek Mall, Abhijeet Patil, Amit Sethi, and Anshuman Kumar. A cyclical deep learning based framework for simultaneous inverse and forward design of nanophotonic metasurfaces.Scientific Reports, 10(1):19427, 2020

    2020

  72. [72]

    Huakun Xia, Shu-Lin Chen, Yuxin Wang, Yijia Zhao, Heping Jia, Rongcao Yang, and Y . Jay Guo. Deep-learning- assisted intelligent design of terahertz hybrid-functional metasurfaces with freeform patterns.Optics & Laser Technology, 181:112041, 2025

    2025

  73. [73]

    Designing nanophotonic structures using conditional deep convolutional generative adversarial networks.Nanophotonics, 8(7):1255–1261, 2019

    Sunae So and Junsuk Rho. Designing nanophotonic structures using conditional deep convolutional generative adversarial networks.Nanophotonics, 8(7):1255–1261, 2019

    2019

  74. [74]

    Free-form diffractive metagrating design based on generative adversarial networks.ACS Nano, 13(8):8872–8878, 2019

    Jiaqi Jiang, David Sell, Stephan Hoyer, Jason Hickey, Jianji Yang, and Jonathan A Fan. Free-form diffractive metagrating design based on generative adversarial networks.ACS Nano, 13(8):8872–8878, 2019

    2019

  75. [75]

    Robust freeform metasurface design based on progressively growing generative networks.ACS Photonics, 7(8):2098–2104, 2020

    Fufang Wen, Jiaqi Jiang, and Jonathan A Fan. Robust freeform metasurface design based on progressively growing generative networks.ACS Photonics, 7(8):2098–2104, 2020

    2098

  76. [76]

    Inverse design of nanophotonic devices using generative adversarial networks.Engineering Applications of Artificial Intelligence, 115:105259, 2022

    Wonsuk Kim, Soojeong Kim, Minhyeok Lee, and Junhee Seok. Inverse design of nanophotonic devices using generative adversarial networks.Engineering Applications of Artificial Intelligence, 115:105259, 2022

    2022

  77. [77]

    Generative deep learning model for inverse design of integrated nanophotonic devices.Laser & Photonics Reviews, 14(12):2000287, 2020

    Yingheng Tang, Keisuke Kojima, Toshiaki Koike-Akino, Ye Wang, Pengxiang Wu, Youye Xie, Mohammad H Tahersima, Devesh K Jha, Kieran Parsons, and Minghao Qi. Generative deep learning model for inverse design of integrated nanophotonic devices.Laser & Photonics Reviews, 14(12):2000287, 2020

    2020

  78. [78]

    Inverse design of nanophotonic devices using generative adversarial networks with the sim-nn model and self-attention mechanism.Micromachines, 14(3):634, 2023

    Xiaopeng Xu, Yu Li, Liuge Du, and Weiping Huang. Inverse design of nanophotonic devices using generative adversarial networks with the sim-nn model and self-attention mechanism.Micromachines, 14(3):634, 2023

    2023

  79. [79]

    Simulator-based training of generative neural networks for the inverse design of metasurfaces.Nanophotonics, 9(5):1059–1069, 2020

    Jiaqi Jiang and Jonathan A Fan. Simulator-based training of generative neural networks for the inverse design of metasurfaces.Nanophotonics, 9(5):1059–1069, 2020

    2020

  80. [80]

    Attention is all you need.Advances in neural information processing systems, 30, 2017

    Ashish Vaswani, Noam Shazeer, Niki Parmar, Jakob Uszkoreit, Llion Jones, Aidan N Gomez, Łukasz Kaiser, and Illia Polosukhin. Attention is all you need.Advances in neural information processing systems, 30, 2017

    2017

Showing first 80 references.