Binary Black Hole Puncture Initial Data with Physics-Informed Neural Networks
Abstract
We present Pinndorama, a physics-informed neural network (PINN) code for solving the Hamiltonian constraint in the puncture formalism. The networks are trained solely on the governing equation and boundary conditions, without an analytical or perturbative guiding solution, with collocation points sampled in curvilinear coordinates. Training combines two optimization algorithms: an initial stage using adaptive moment estimation (Adam), followed by the self-scaled Broyden quasi-Newton method. We apply this approach to a spherically symmetric test problem with a known exact solution, axisymmetric binary punctures with unequal spins, and a fully three-dimensional GW150914-like configuration with unequal spins and orbital momenta. Comparisons with the NRPyElliptic solver yield relative L2 errors of order 10−8 in axisymmetry and 10−5 in three dimensions. In addition, we reduce the hyperbolic-relaxation time in NRPyElliptic by a factor of approximately $4.6$ by training a parametric network that takes the puncture spin as input and provides a physics-informed initial guess to the solver. These results demonstrate that PINNs can provide accurate binary-puncture initial data and complement conventional elliptic solvers in numerical relativity.
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BibTeX
@misc{assumpcao2026binary,
title = {{Binary Black Hole Puncture Initial Data with Physics-Informed Neural Networks}},
author = {Thiago Assumpção and Ignacio Brevis and Irene Pitsiladi and Martin Zinzen and Miguel Bezares},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.27094},
eprint = {2610.27094},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.27094},
}
RIS
TY - UNPB
TI - Binary Black Hole Puncture Initial Data with Physics-Informed Neural Networks
AU - Thiago Assumpção
AU - Ignacio Brevis
AU - Irene Pitsiladi
AU - Martin Zinzen
AU - Miguel Bezares
PY - 2026
DA - 2026/10/19
PB - arXiv
DO - 10.48550/arxiv.2610.27094
UR - https://arxiv.org/abs/2610.27094
AB - We present Pinndorama, a physics-informed neural network (PINN) code for solving the Hamiltonian constraint in the puncture formalism. The networks are trained solely on the governing equation and boundary conditions, without an analytical or perturbative guiding solution, with collocation points sampled in curvilinear coordinates. Training combines two optimization algorithms: an initial stage using adaptive moment estimation (Adam), followed by the self-scaled Broyden quasi-Newton method. We apply this approach to a spherically symmetric test problem with a known exact solution, axisymmetric binary punctures with unequal spins, and a fully three-dimensional GW150914-like configuration with unequal spins and orbital momenta. Comparisons with the NRPyElliptic solver yield relative L^2 errors of order 10^−8 in axisymmetry and 10^−5 in three dimensions. In addition, we reduce the hyperbolic-relaxation time in NRPyElliptic by a factor of approximately $4.6$ by training a parametric network that takes the puncture spin as input and provides a physics-informed initial guess to the solver. These results demonstrate that PINNs can provide accurate binary-puncture initial data and complement conventional elliptic solvers in numerical relativity.
ER -