Galerkin Method Based On Deep Learning

Deep learning has been a great success in computer vision and other artificial intelligence tasks.The basis for this success is a new approximation function method,from the additive constructs widely used in approximation theory to the combinatorial constructs used in deep neural networks.This means that models based on deep neural networks can be useful in situations involving constructors.Inspired by the depth Ritz method,Dr.Yuan cheng proposed the depth Galerkin method,which is based on the use of neural network representation of functions in the context of the Galerkin method.This paper continues this work.The main work includes the following aspects:1.The research development history of deep learning and the important research significance of deep neural network are summarized,and then the deep learning framework TensorFlow of Google is introduced and explained.2.introduces the ritz-galerkin method in detail.Finite element method;Deep feedforward network,including activation function and back propagation algorithm;Optimization in depth model,including small-batch algorithm,stochastic gradient descent and introduction of Adam algorithm;Monte carlo method.3.introduces the Galerkin method based on deep learning.We selected the diversity of test function space,using Google TensorFlow deep learning framework structure trial function,and select the appropriate update algorithm of discrete integral rules and parameters set up good model,we choose to solve Poisson equations boundary value problems of second as the research object,and gives the one-dimensional and two-dimensional numerical example and experiment results show that the loss function is down to 10-5,which shows that the method can successfully obtain numerical solutions with fewer parameters.