Application Of Machine Learning In Optical Impurity Detection And Differential Equations

The purpose of machine learning is to automatically obtain the corresponding theory from the data,through the use of reasoning,model fitting and learning from samples,and is particularly suited to the lack of general theories and large-scale data sets.Physics is a subject that studies the most general laws of motion and the basic structure of matter.Although it is in two different professional fields with machine learning,there are many similarities in the thinking of dealing with problems.Therefore,machine learning can be used to solve the problems of unclear theoretical framework,complicated systems,and unsatisfactory simulation results in the process of physics research,thereby promoting the continuous development of physics research.This paper mainly combines the machine learning algorithm to solve the impurity detection problem in the classical optical experiment and solve the nonlinear partial differential equation.Firstly,we introduce the related concepts of machine learning and deep learning,expound the forward propagation algorithm and back propagation algorithm of fully connected neural network and the basic structure of convolutional neural network.Secondly,we combine machine learning algorithms with classical optics to study the detection of impurities on optical surfaces based on deep learning.Finally,we investigate the use of deep neural networks to solve differential equations,introduce traditional numerical methods for solving differential equations and the solution framework based on deep neural networks,focusing on calculating the general form of partial differential equation solutions,and proposing the use of the method to solve the partial differential equation of one-dimensional harmonic oscillators and Gross-Pitaevskii equation,and by analysing the shortcomings of the current network,proposing a series of corrections and obtaining significant enhancements and improvements are made.The research results show that:(1)The neural network can successfully extract the location information of the impurities loaded in the optical signal,the prediction accuracy can reach 100%,and make more accurate judgment on the location of the impurities in the generalization test,the overall accuracy is above 75%,after comparing the convolutional neural network and the fully connected neural network,it shows that the convolutional neural network performs better;(2)the deep neural network can provide new ideas and solutions for solving differential equations,and can obtain the result which is highly close to the analytical solution.