PHYSICS INFORMED NEURAL NETWORKS FOR SOLVING DIRAC EQUATION IN (1+1) DIMENSION
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Date
2021-05-13
Authors
Bazarkhanova, Aigerim
Journal Title
Journal ISSN
Volume Title
Publisher
Nazarbayev University School of Sciences and Humanities
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
Description
Keywords
Dirac equation, Type of access: Open Access
Citation
Bazarkhanova, A. (2021). Physics Informed Neural Networks for solving Dirac equation in (1+1) dimension (Unpublished master`s thesis). Nazarbayev University, Nur-Sultan, Kazakhstan