Probability-Density-Based Deep Learning Paradigm for the Fuzzy Design of Functional Metastructures

Abstract

In quantum mechanics, a norm-squared wave function can be interpreted as the probability density that describes the likelihood of a particle to be measured in a given position or momentum. This statistical property is at the core of the fuzzy structure of microcosmos. Recently, hybrid neural structures raised intense attention, resulting in various intelligent systems with far-reaching influence. Here, we propose a probability-density-based deep learning paradigm for the fuzzy design of functional metastructures. In contrast to other inverse design methods, our probability-density-based neural network can efficiently evaluate and accurately capture all plausible metastructures in a high-dimensional parameter space. Local maxima in probability density distribution correspond to the most likely candidates to meet the desired performances. We verify this universally adaptive approach in but not limited to acoustics by designing multiple metastructures for each targeted transmission spectrum, with experiments unequivocally demonstrating the effectiveness and generalization of the inverse design.

Deep Learning Enabled Design of Complex Transmission Matrices for Universal Optical Components

“…This large computational overhead limits the range of parameters that can be easily explored, reducing the flexibility of the method. However, the required data to train networks on new, yet similar, problems might be significantly reduced using procedures such as transfer learning, whereas variable input dimensions might be realized with so-called attention-based concepts. , Accordingly, research in the context of photonics is still scarce; hence, such techniques are interesting as the subject of follow-up work. Future work will also look at expanding the geometrical design space, which includes increasing the number of input and output channels to ultimately achieve large-scale, multi-input, multi-output (MIMO), programmable devices.…”

Information metasurfaces and intelligent metasurfaces

“…The main defect of this process is that the preceding simulation samples have not been fully used, and a brand-new procedure needs to be called if the optimization target is changed. From here, it would be very natural to think about exploiting the powerful learning capacity of deep-learning methods to make full use of the existing data to accelerate the whole design process [180][181][182][183][184][185] . Existing data could be gathered from past simulation work, and most researchers would choose to specifically make a training dataset by simulations and/or experiments for the learning process.…”

“…To solve the steady and one-to-many problems of inverse ANNs, Luo et al [183] developed a special inverse ANN structure called a probability-density-based network (PDN). Instead of directly outputting meta-structure parameters, PDN generates a mixture of Gaussian distributions represented by mixing the coefficient, mean, and standard deviation of the output Gaussian, which indicates the likelihood of each structure parameter.…”

“…In 2018, Inampudi and Mosallaei developed a meta-element design method using the neural network for surface metal structures based on polygonal patterns [137] . The structural intelligent design method was also extended to acoustic metamaterials [138] , where the cylindrical structure is divided into five layers with different radii to obtain desired transmission coefficients, which are analyzed by a probability-density-based neural network. In addition to being used for the automatic design of metasurface elements, the machine-learning algorithm was also integrated into information metasurfaces to perform more intelligent tasks.…”

Acoustic Structure Inverse Design and Optimization Using Deep Learning

“…Moreover, DL has become a radically new approach in the context of photonic and electromagnetic design, such as approximation of light scattering from plasmonic nanostructures [19][20][21][22] and inverse design of the electromagnetic metasurface structure 23 , over the past few years. Recently, DL has also been used to solve the inverse problem of the variable cross-sectional acoustic structure 24 and twodimensional acoustic cloaking 25 . However, both the researches trained the deep neural networks (DNNs) for specific structures, which are hard to be extended to other acoustic structures.…”