Application of Definite Solution of Partial Differential Equation in Deep Learning

Abstract

With the continuous development of human knowledge and the rapid expansion of knowledge data, the traditional learning methods have been unable to meet the needs of the development of human knowledge. In this case, some scholars proposed the theory of deep learning on the basis of the layered operation of human brain. At present, deep learning has been widely applied in various fields, such as image processing, speech recognition and emotion classification. Partial differential equation (pde) is a common mathematical analysis method, which can effectively extract data features, which is consistent with the characteristics of deep learning. Therefore, it is feasible to apply the definite solution of partial differential equation to deep learning. The purpose of this paper is to promote the further development of deep learning by studying the application of partial differential equation in deep learning. This paper first summarizes the concepts of deep learning and partial differential equations, then analyzes the wavelet method of the definite solution problem, and then discusses the feasibility of applying the wavelet method to deep learning. Finally, the development of deep learning based on wavelet analysis is discussed. The research in this paper shows that the solution of the definite solution problem of partial differential equations can take three-dimensional space as the starting point to reconstruct deep learning in an all-round way, which greatly expands the application scope of deep learning theory.