Manifold Learning for Knowledge Discovery and Intelligent Inverse Design of Photonic Nanostructures: Breaking the Geometric Complexity

Abstract

Here, we present a new approach based on manifold learning for knowledge discovery and inverse design with minimal complexity in photonic nanostructures. Our approach builds on studying submanifolds of responses of a class of nanostructures with different design complexities in the latent space to obtain valuable insight about the physics of device operation to guide a more intelligent design. In contrast to the current methods for inverse design of photonic nanostructures, which are limited to preselected and usually overcomplex structures, we show that our method allows evolution from an initial design toward the simplest structure while solving the inverse problem.

Metric Learning: Harnessing the Power of Machine Learning in Nanophotonics

“…Thus, our approach can also provide the range of feasible responses and can help in identifying whether a desired response is feasible from the selected structure with the given design parameter. 37,39 ■ CONCLUSION Our results clearly show the importance of a proper metric on interpretability of the ML results, especially when we reduce the dimensionality of the data; they also show the shortcomings of the commonly used metrics (i.e., MSE and MAE) in capturing the important features of the responses and that will affect the performance of any inverse-design or knowledgediscovery tool. With ML approaches becoming more widespread in the field of nanophotonic design and knowledge discovery, the results in this paper justify an urgent need for more detailed investigation of metric learning, especially for feature-based nanophotonic design and investigation.…”

“…In addition to solving inverse problems, ML approaches have shown promising potential for knowledge discovery in nanophotonics through interpretable models, dimensionality reduction, and manifold learning. − This has great importance since the input–output relation and the role of design parameters can be well understood, and helpful insight can be provided about the underlying physics of light-matter interaction in these nanophotonic structures. Considering the high redundancy in the input-output relation of photonic nanostructures, these approaches reduce the dimensionality and embed the input-output data into lower-dimensional design and response spaces.…”

Normalizing Flows for Efficient Inverse Design of Thermophotovoltaic Emitters

“…Machine learning enables computers to learn how to solve design problems automatically from data, and has been shown to be highly versatile and efficient as an inverse design method . Some deep learning-based inverse methods include generative adversarial networks (GANs), variational autoencoders (VAEs), adversarial autoencoders (AAEs), and the neural adjoint (NA). − Recently, these techniques have been adopted for designs of highly efficient absorbers/emitters for TPV applications. However, from the view of probability density estimation, GANs and VAEs lack the capacity to optimize exact likelihood, which may weaken their generating performance and probabilistic interpretability…”

New paradigms in manifold learning for knowledge discovery and inverse design of photonic nanostructures

“…However, due to the high dimensionality of the data of nanostructures and the lack of information about the complexity of the input-output relation, very complex NN architectures are being used. This makes interpretation of the models and understanding the hidden patters cumbersome and unnecessarily increases the computational complexity of the model [9][10][11][12][13].…”