Machine-learning algorithms are powerful tools in developing reliable models to relate the design space of a nanophotonic structure to its response space. They can be used not only to simplify the inverse design problem but also to provide valuable insight about the physics of light-matter interaction. This talk will provide a new approach through combining manifold-learning algorithms for reducing the dimensionality of the problem with metric-learning techniques for more insightful mapping of the input-output relation to the dimensionality-reduced (or the latent) space. In addition to covering the fundamental properties of the presented algorithms, their applications to both the inverse design and the knowledge discovery in state-of-the-art metaphotonic structures will be discussed.
This work presents a comprehensive investigation aimed at identifying the most streamlined neural network architecture for the inverse design of nanophotonic structures. In pursuit of this objective, we delve into the statistical and computational complexities inherent in neural network design, contextualized within the realm of nanophotonic structures, as defined by their design complexity, e.g., the number of constituent parameters. The study encompasses two critical dimensions: statistical complexity, where we explore the optimal quantity of training data, and computational complexity, where our aim is the study of the required computation and model complexity for accurately modeling the input-output relation in a class of nanophotonic structures. Through the integration of these two facets, we will determine the simplest neural network configuration for the given class of nanophotonic structures, facilitating efficient and accurate inverse design, and understanding the effect of design parameters on the output response complexity. In addition to reporting the details of this novel technique, we will show its implementation for two important classes of nanophotonic devices.
In the realm of nanophotonics, establishing the intricate relationship between design parameters and the ultimate response of a given nanophotonic devices stands as a formidable challenge. The prevalent utilization of numerical solutions to Maxwell's equations, whether through in-house codes or commercial software, often conceals the underlying physics. In this talk, we present machine-learning (ML) algorithms for elucidating the connection between design parameters and device response. We discuss two distinct ML methods to discern the roles and significance of individual design parameters, namely SHAP (SHapley Additive exPlanations) values and Pruning. By scrutinizing two diverse nano-devices using these complementary techniques, this talk sheds light on the compelling insights derived from this innovative approach.
In this work, we present a new approach based on metric learning for defining new similarity measures that are well-matched for design tasks in nanophotonics. Majority of the existing approaches use mean squared error (MSE) or mean absolute error (MAE) as the similarity measure to compare the desired and optimal spectra while it is clear that point-wise distance cannot capture the important features of the responses. Here, our goal is to use deep metric learning to provide a systematic approach for defining new metrics in nanophotonics.
This talk is focused on using the intelligent aspects of machine learning (ML) for both the understanding of the subtle properties of nanophotonic devices and their inverse design to achieve a desired response. It will be shown that by reducing the dimensionality of the problem using manifold learning techniques and simplifying the resulting networks using pruning, the computation complexity of the underlying artificial intelligence (AI) algorithms will be considerably reduced. Furthermore, by optimally defining the loss function (or the metric) for AI algorithms, priceless information about the properties of photonic nanostructures can be uncovered while facilitating the better visualization of the input-output relationship in these nanostructures. In addition, the resulting manifold-learning algorithms can be optimally trained to facilitate the inverse design of such nanostructures while minimizing the structural complexity. This talk will provide the foundation for both knowledge discovery and design in photonic nanostructures using manifold learning and metric learning and their application to the highly desired metaphotonic structures as an example platform.
Here, we present a new approach based on manifold learning for inverse design and knowledge discovery in nanophotonics. We present the unique capabilities of manifold learning approaches for reducing the dimensionality of the high-dimensional relationships in photonic nanostructures. We show how this can help to understand the underlying patterns in the responses of such nanostructures. Such a visualization in the low-dimensional space enables knowledge discovery and studying the underlying physics of nanostructures and can facilitate the inverse design. We also use this method to study the role of the design parameters and design a class of nanostructure while reducing the design complexity.
We present a new machine learning (ML)-based approach for efficient inverse design of nanophotonic structures. Generating training data for a ML method is the most computationally expensive step in the ML-based inverse design and knowledge discovery, and it becomes cumbersome when the number of design parameters and the complexity of the structure increase. Here we show how to optimize the training process and considerably reduce the computation requirements without increasing error in order to efficiently model the input-output relationship in a nanophotonic structure and solve the inverse design problem.
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