Towards solving General Relativity with Physics-Informed Neural Networks
Abstract
Physics-Informed Neural Networks (PINNs) are a machine-learning framework for approximating solutions to systems of partial differential equations by constraining neural networks to satisfy the underlying physical laws. The resulting continuous representation does not require a predefined computational mesh and can be evaluated at arbitrary points within the training domain. In this work, we investigate the application of PINNs to Einstein's equations of General Relativity. We discuss the mathematical formulation, network architectures, loss functions, and training strategies used to obtain accurate spacetime solutions, and demonstrate the approach through a series of standard benchmarks from Numerical Relativity. We then extend the method to a more astrophysical setting by considering the dynamical evolution of an isolated solitonic boson star. Our simulations show that a PINN operating directly in three-dimensional Cartesian coordinates can reproduce the equilibrium structure of a highly compact boson star and recover its characteristic radial oscillation frequencies. These results establish PINNs as a viable complementary framework for solving coupled matter-Einstein equations and exploring alternative formulations in numerical relativity.
Related
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BibTeX
@misc{carretero2026towards,
title = {{Towards solving General Relativity with Physics-Informed Neural Networks}},
author = {Juan A. Carretero and Jorge F. Urbán and Fernando Abalos and Joan Massó and Oscar A. Reula and Jose A. Pons and Carlos Palenzuela},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.38331},
eprint = {2609.38331},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.38331},
}
RIS
TY - UNPB
TI - Towards solving General Relativity with Physics-Informed Neural Networks
AU - Juan A. Carretero
AU - Jorge F. Urbán
AU - Fernando Abalos
AU - Joan Massó
AU - Oscar A. Reula
AU - Jose A. Pons
AU - Carlos Palenzuela
PY - 2026
DA - 2026/09/29
PB - arXiv
DO - 10.48550/arxiv.2609.38331
UR - https://arxiv.org/abs/2609.38331
AB - Physics-Informed Neural Networks (PINNs) are a machine-learning framework for approximating solutions to systems of partial differential equations by constraining neural networks to satisfy the underlying physical laws. The resulting continuous representation does not require a predefined computational mesh and can be evaluated at arbitrary points within the training domain. In this work, we investigate the application of PINNs to Einstein's equations of General Relativity. We discuss the mathematical formulation, network architectures, loss functions, and training strategies used to obtain accurate spacetime solutions, and demonstrate the approach through a series of standard benchmarks from Numerical Relativity. We then extend the method to a more astrophysical setting by considering the dynamical evolution of an isolated solitonic boson star. Our simulations show that a PINN operating directly in three-dimensional Cartesian coordinates can reproduce the equilibrium structure of a highly compact boson star and recover its characteristic radial oscillation frequencies. These results establish PINNs as a viable complementary framework for solving coupled matter-Einstein equations and exploring alternative formulations in numerical relativity.
ER -