A deep neural network approach to solve the Dirac equation

We extend the method from [Naito, Naito, and Hashimoto, Phys. Rev. Research 5 , 033189 (2023)] to solve the Dirac equation not only for the ground state but also for low-lying excited states using a deep neural network and the unsupervised machine learning technique. The variational method fails bec...

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Bibliographic Details
Published inThe European physical journal. A, Hadrons and nuclei Vol. 61; no. 7
Main Authors Wang, Chuanxin, Naito, Tomoya, Li, Jian, Liang, Haozhao
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 15.07.2025
Springer Nature B.V
Subjects
Artificial neural networks
Dirac equation
Excitation
Hadrons
Heavy Ions
Machine learning
Nuclear Fusion
Nuclear Physics
Particle and Nuclear Physics
Physics
Physics and Astronomy
Regular Article - Theoretical Physics
Unsupervised learning
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Summary:We extend the method from [Naito, Naito, and Hashimoto, Phys. Rev. Research 5 , 033189 (2023)] to solve the Dirac equation not only for the ground state but also for low-lying excited states using a deep neural network and the unsupervised machine learning technique. The variational method fails because of the Dirac sea, which is avoided by introducing the inverse Hamiltonian method. For low-lying excited states, two methods are proposed, which have different performances and advantages. The validity of this method is verified by the calculations with the Coulomb and Woods-Saxon potentials.
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ISSN:1434-601X
1434-6001
1434-601X
DOI:10.1140/epja/s10050-025-01630-5