Geometric scientific machine learning: physical modeling and simulation by deep learning

Abstract

In recent years, research on the application of artificial neural networks to the modeling and simulation of physical phenomena has been attracting significant attention. In addition to modeling phenomena without known governing equations, such research is expected to accelerate and improve physical simulations. In this paper, we first explain Hamiltonian neural networks, which is a representative example of such research. Then, two improved models, the neural symplectic form and DGNet, are explained.