Evaluation of derivatives in PDEs by using neural network

Abstract

The explanation model using the existing partial differential equation (PDE) is very important for utilizing big data obtained from various new phenomena such as new corona infection. The academic question in this research is “how can a partial differential equation be derived from given big data?” In this research, we clarify whether PDE can be derived more accurately than big data if we can construct an appropriate deep learning model that explains the given big data. If the neural network model is accurate enough, the chain rule can be used to compute the exact partial derivative term sampling, automatic differentiation was performed in the class called Gradient Tape of Tensor Flow, and the relationship between PDE derivation accuracy and partial differential term accuracy was clarified.