Deep learning approach based on dimensionality reduction for designing electromagnetic nanostructures

Abstract: 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.

• The paper presents a deep learning approach utilizing autoencoders for dimensionality reduction to significantly improve computational efficiency in designing electromagnetic nanostructures.
• The proposed method was successfully applied to design reconfigurable optical metasurfaces, achieving high design fidelity demonstrated by minimal mean squared error.
• This work offers a new paradigm for AI-assisted design in computational nanophotonics and can be extended to tackle complex design challenges in other scientific domains.

Deep Learning for Electromagnetic Nanostructure Design via Dimensionality Reduction

The paper discusses an innovative deep learning approach leveraging dimensionality reduction for the design and optimization of electromagnetic (EM) nanostructures. This methodology offers computational efficiency by transforming complex many-to-one design problems into simplified one-to-one issues, complemented by a straightforward many-to-one problem. Employing autoencoders, a notable machine learning technique, the authors effectively reduce the problem's dimensionality, mitigating computational complexity while maintaining accuracy.

Overview of the Approach

The research introduces a dual strategy encompassing both the forward (analysis) and inverse (design) problems in EM nanostructures:

• Dimensionality Reduction of Problem Spaces: The authors split the conventional design problem into manageable parts. By engaging autoencoders, they minimize the dimensionality of both the design and response spaces. Through training, autoencoders encode high-dimensional data into lower-dimensional forms without substantial loss of information, enabling efficient navigation through the design parameters.
• Transformation of Problem Landscapes: This dimensionality reduction facilitates the transformation of intricate many-to-one design landscapes into simpler, tractable forms. The deep learning model subsequently solves these transformed problems, leading to reduced computational demand by orders of magnitude.

Results and Implications

As a practical demonstration, the authors applied their novel technique to engineer a class of reconfigurable optical metasurfaces using phase-change materials (PCMs). These metasurfaces demonstrate significant promise in areas like amplitude modulation across a broadband spectrum, showcasing the model's capability in real-world applications. Notably, the achieved design for maximum absorption had a minimal mean squared error (MSE), indicating high design fidelity.

Theoretical and Practical Significance

This work not only advances the theoretical understanding of EM wave interactions with nanostructures but also proposes a practical toolkit for tackling complex design problems previously insurmountable with traditional methods. By providing analytical formulations from the DR approach, insight into the underlying physics of wave-matter interactions is afforded, facilitating a deeper understanding of nanostructure functionalities.

The efficacy of integrating deep learning with existing full-wave simulation tools is underscored, suggesting a new paradigm for future AI developments in technical design disciplines. This methodological framework can be extrapolated to other complex scientific and engineering challenges across diverse domains requiring optimized design solutions.

Future Outlook

The research opens new avenues for further exploration in AI-assisted nanostructure design. The prospect of applying similar dimensionality reduction techniques to other high-dimensional scientific problems is promising. Future work could focus on refining the general approach to enhance the robustness of the architecture in different contexts, especially where constraints and requirements vary.

In conclusion, this paper presents a significant contribution to the field of computational nanophotonics by unlocking new design methodologies through the potent capabilities of deep learning. The integration of dimensionality reduction establishes a cornerstone for both theoretical advancements and practical applications, driving the evolution of next-generation EM nanostructures.