PHYSICS INFORMED NEURAL NETWORKS FOR SOLVING DIRAC EQUATION IN (1+1) DIMENSION

Abstract

The Dirac equation plays a fundamental role in quantum physics and its exact solutions are of utmost importance. In this study we solved Linear and Nonlin ear Dirac equation in (1+1) dimension and obtained analytical solutions. Moreover we have implemented Physics Informed Neural Networks to get approximate solutions of Linear and Nonlinear Dirac equation in (1+1) dimension. During the experiments we observed that Physics Informed Neural Networks are not capable of providing good solutions for any given time and faced the problem of choosing appropriate weights for each loss function. Therefore, architecture of multilayer feedforward neural networks for approximating solutions of Dirac equation needs further investigation