[Paper Review] A deep learning approach for inverse design of the metasurface for dual-polarized waves

Fardin Ghorbani, Javad Shabanpour+4 more|arXiv (Cornell University)|May 12, 2021

Metamaterials and Metasurfaces Applications37 references52 citations

TL;DR

This paper proposes a deep neural network (DNN)-based inverse design method for metasurfaces that generates unit cell structures for dual-polarized (TE and TM) waves up to 45 GHz. By confining the output to 8 predefined annular meta-atom models, the method reduces computational load and accelerates training, achieving 92% accuracy in generating desired S-parameter responses without iterative optimization.

ABSTRACT

Compared to the conventional metasurface design, machine learning-based methods have recently created an inspiring platform for an inverse realization of the metasurfaces. Here, we have used the Deep Neural Network (DNN) for the generation of desired output unit cell structures in an ultra-wide working frequency band for both TE and TM polarized waves. To automatically generate metasurfaces in a wide range of working frequencies from 4 to 45 GHz, we deliberately design an 8 ring-shaped pattern in such a way that the unit-cells generated in the dataset can produce single or multiple notches in the desired working frequency band. Compared to the general approach, whereby the final metasurface structure may be formed by any randomly distributed "0" and "1", we propose here a restricted output structure. By restricting the output, the number of calculations will be reduced and the learning speed will be increased. Moreover, we have shown that the accuracy of the network reaches 91\%. Obtaining the final unit cell directly without any time-consuming optimization algorithms for both TE and TM polarized waves, and high average accuracy, promises an effective strategy for the metasurface design; thus, the designer is required only to focus on the design goal.

Motivation & Objective

• To address the high computational cost and time consumption of conventional inverse metasurface design methods based on trial-and-error or optimization.
• To enable fast, accurate, and direct generation of metasurface unit cells for both TE and TM polarized waves across a wide frequency band (up to 45 GHz).
• To reduce computational complexity and training time by confining the DNN output to a predefined set of 8 annular meta-atom patterns.
• To achieve high accuracy in reproducing desired S-parameter features (notch frequency, depth, bandwidth) for dual orthogonal polarizations.
• To provide a programmable, efficient, and scalable framework for inverse metasurface design without relying on time-consuming optimization algorithms.

Proposed method

• The DNN is trained to map desired S-parameter targets (notch frequency, depth, bandwidth) for both TE and TM polarized waves to a 48-element output vector representing 8 annular meta-atom configurations.
• The output is constrained to 8 predefined annular models (coded as 000 to 111), limiting the search space and reducing computational complexity.
• Each meta-atom is composed of 4×4 lattices of these 8 annular patterns, forming a 32×32 unit cell with 0.2 mm resolution.
• The network architecture uses 11 layers: 6 dense layers with ReLU activation, 5 dropout layers for regularization, and a final sigmoid layer to output binary (0/1) values.
• The loss function is Mean Squared Error (MSE) between predicted and target S-parameters, minimized using the Adam optimizer.
• Full-wave simulations using CST Microwave Studio and MATLAB integration validate the generated metasurface responses.

Experimental results

Research questions

• RQ1 Can a DNN-based inverse design method generate accurate metasurface unit cells for both TE and TM polarized waves across a wide frequency band (up to 45 GHz)?
• RQ2 How does confining the DNN output to a predefined set of 8 annular meta-atom patterns affect the accuracy, training speed, and computational efficiency of inverse metasurface design?
• RQ3 To what extent can the proposed method eliminate the need for iterative optimization algorithms in metasurface design?
• RQ4 What is the achievable accuracy and inference speed of the DNN in reproducing complex S-parameter responses (e.g., multiple notches) for dual-polarized waves?
• RQ5 How does the proposed method compare in efficiency and accuracy to conventional optimization-based approaches?

Key findings

• The DNN achieved an average accuracy of 92% in generating metasurface unit cells that match the desired S-parameter targets for both TE and TM polarized waves.
• The inference time for generating a single unit cell was only 0.038 seconds, significantly faster than conventional methods that take 700–800 minutes.
• The model size was only 6 MB, enabling efficient deployment and low computational resource usage.
• The training process completed in 19 minutes, demonstrating high training efficiency with the constrained output configuration.
• Full-wave simulations confirmed that the generated metasurfaces successfully achieved the target resonant notches in frequency, depth, and bandwidth for both polarizations.
• The method successfully produced multiple resonances (up to three) in the desired frequency range (4–45 GHz) using the 8 annular meta-atom models.