Neural networks for inverse design of phononic crystals

Chen-Xu Liu,Gui-Lan Yu,Guan-Yuan Zhao

doi:10.1063/1.5114643

Abstract

Intelligent design of one-dimensional (1D) phononic crystals (PCs) by neural networks (NNs) is proposed. Two neural network models, supervised neural network (S-NN) and unsupervised neural network (U-NN), are used to realize the inverse design of PCs, concerning both geometric and physical parameter designs. Performances of the two models are compared and discussed. The results show that the bandgaps of the designed PCs by the two NNs are highly consistent with the target bandgaps. For the design of single or two parameters, the performances of the two NNs are excellent; while for the case of three-parameter design, U-NN works much better than S-NN due to the impact of non-uniqueness on S-NN. The present work confirms the feasibility of inverse design of PCs by NNs, and provides a useful reference for the application of NNs in the intelligent inverse design of 2D or 3D PCs.

Highlights

In 1987, Yablonovitch and John independently proposed the concept of photonic crystals.1,2 Four years later, Yablonovitch verified the existence of photonic bandgaps by experiments
The results show that the inverse design of phononic crystals (PCs) can be successfully realized by using neural networks (NNs)
The structure of the supervised neural network (S-NN) is “4-40-20-10-1”, where “4” is the dimension of the inputs, “40”, “20”, and “10” are the number of the neurons in each hidden layer, and “1” is the dimension of the outputs; The structure of the unsupervised neural network (U-NN) is “4-20-20-10-1-20-20-10-4”, where the first “4” is the dimension of the inputs, the last “4” is the dimension of the outputs, “1” is the number of the neuron in the intermediate layer, and the remaining numbers are the number of the neurons in their corresponding hidden layers

Summary

Introduction

In 1987, Yablonovitch and John independently proposed the concept of photonic crystals. Four years later, Yablonovitch verified the existence of photonic bandgaps by experiments. Yablonovitch verified the existence of photonic bandgaps by experiments. There exists a certain frequency range in which elastic waves are suppressed or prohibited to propagate in a periodic composite structure. This structure was termed as a phononic crystal (PC). Methods for solving PCs have been fully developed in recent 20 years, such as the transfer matrix method, plane wave expansion method, finite difference time domain method, multi-scattering theory and finite element method, etc. The advancement and improvement of these methods have greatly promoted the study of PCs. it is difficult to make inverse design to meet the target bandgaps by these forward solving methods. Researchers often have to go through repeated trial and error calculations to achieve the desired design, which consumes a lot of time and manpower as well as material resources

Objectives

Results

Conclusion