Research On Application Of Convolutional Neural Network In FDTD Algorithm

The Finite-Difference Time-Domain method(FDTD)is an important numerical algorithm in electromagnetic research.With the deepening of electromagnetic research,the calculation scale of the FDTD algorithm has been expanded,and the algorithm’s demand for calculation efficiency is also increasing.FDTD algorithm can use parallel computing,graphics processing unit(GPU)or other methods to improve computing efficiency.Some of these methods are extremely efficient when using half-precision and single-precision calculations,while do not support double-precision calculations.In addition,it is worth exploring whether deep learning can be applied to electromagnetic calculations and improve the calculation efficiency of traditional algorithms.Considering the above problems,this thesis uses convolutional neural network(CNN)to solve electromagnetic problems by constructing FDTD-CNN model and solving partial differential equation(PDE)by using data laws.These two methods are used to solve the electromagnetic problem,and then discuss the accuracy and stability of FDTD and FDTD-CNN model in half-precision and single-precision mode,and the influence of the data set on the FDTD-CNN model.The main works are as follows:1.The FDTD-CNN models suitable for electromagnetic propagation calculation are constructed.In one dimension,through two examples of free space and plasma photonic crystals,the computational feasibility and generalization reusability of the model are verified.Then,the computational resources and time consumed by the conventional FDTD method and CNN model are analyzed.Absorbing boundary CNN model is separated from FDTD-CNN model in 2D,which reduces the difficulty of training and improves the efficiency of training.Moreover,absorbing boundary CNN model can be used to the calculation of conventional FDTD,which has strong flexibility.2.From the point of data law,CNN is used to solve partial differential equation(PDE)to solve electromagnetic problems.First,a CNN model is constructed to learn the laws in PDE data,and then the Poisson equation is directly solved according to the laws learned by the model,which verifies the ability of CNN to solve PDE by data laws.The above two methods prove that CNN can bring new ideas for numerical modeling of electromagnetic computing and improve the computational efficiency of traditional algorithms.More importantly,it also provides effective means for the analysis and reuse of massive electromagnetic data accumulated over a long period of time.3.The influence of floating-point precision on the conventional FDTD method is analyzed,and the results of single-precision FDTD method are proved to be reliable.At the same time,it is proved that GPU and other acceleration methods that do not support double-precision calculation can be used in the FDTD algorithm.The half-precision is not suitable for FDTD because of its poor precision.Secondly,by comparing and analyzing the results of the conventional FDTD and CNN models,it is verified that the calculation of the CNN model is accurate and reliable.Finally,through comparative experiments on the default data set and the doped data set,the influence of the data set on the accuracy of the CNN model is analyzed.