# Deep learning approach based on dimensionality reduction for designing electromagnetic nanostructures

arXiv: https://arxiv.org/abs/1902.03865 · HTML: https://mlsanity.com/paper/1902.03865/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Feb 2019.

## Built on by (most cited first, 12 of 12)

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- [Inverse deep learning methods and benchmarks for artificial electromagnetic material design](https://mlsanity.com/paper/2112.10254/) (2021)
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- [Manifold Learning for Knowledge Discovery and Intelligent Inverse Design of Photonic Nanostructures: Breaking the Geometric Complexity](https://mlsanity.com/paper/2102.04454/) (2021)
- [HiLAB: A Hybrid Inverse-Design Framework](https://mlsanity.com/paper/2505.17491/) (2025)
- [A deep learning approach for inverse design of the metasurface for dual-polarized waves](https://mlsanity.com/paper/2105.08508/) (2021)
- [Mixed Integer Neural Inverse Design](https://mlsanity.com/paper/2109.12888/) (2021)
- [Machine learning for knowledge acquisition and accelerated inverse-design for non-Hermitian systems](https://mlsanity.com/paper/2204.13376/) (2022)
- [Inverse Design of Metamaterials with Manufacturing-Guiding Spectrum-to-Structure Conditional Diffusion Model](https://mlsanity.com/paper/2506.07083/) (2025)
- [Data driven design of optical resonators](https://mlsanity.com/paper/2202.03578/) (2021)
- [Physics Enhanced Deep Surrogates for the Phonon Boltzmann Transport Equation](https://mlsanity.com/paper/2512.05976/) (2025)
- [Bayesian Optimization for Function-Valued Responses under Min-Max Criteria](https://mlsanity.com/paper/2512.07868/) (2025)

## Abstract (arXiv)

In this paper, we demonstrate a computationally efficient new approach based on deep learning (DL) techniques for analysis, design, and optimization of electromagnetic (EM) nanostructures. We use the strong correlation among features of a generic EM problem to considerably reduce the dimensionality of the problem and thus, the computational complexity, without imposing considerable errors. By employing the dimensionality reduction concept using the more recently demonstrated autoencoder technique, we redefine the conventional many-to-one design problem in EM nanostructures into a one-to-one problem plus a much simpler many-to-one problem, which can be simply solved using an analytic formulation. This approach reduces the computational complexity in solving both the forward problem (i.e., analysis) and the inverse problem (i.e., design) by orders of magnitude compared to conventional approaches. In addition, it provides analytic formulations that, despite their complexity, can be used to obtain intuitive understanding of the physics and dynamics of EM wave interaction with nanostructures with minimal computation requirements. As a proof-of-concept, we applied such an efficacious method to design a new class of on-demand reconfigurable optical metasurfaces based on phase-change materials (PCM). We envision that the integration of such a DL-based technique with full-wave commercial software packages offers a powerful toolkit to facilitate the analysis, design, and optimization of the EM nanostructures as well as explaining, understanding, and predicting the observed responses in such structures.