Solving the Teukolsky equation with physics-informed neural networks
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arXiv
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| Auteurs principaux: | , , , , |
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| Format: | Preprint |
| Publié: |
2022
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| _version_ | 1866929304277876736 |
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| author | Luna, Raimon Bustillo, Juan Calderón Martínez, Juan José Seoane Torres-Forné, Alejandro Font, José A. |
| author_facet | Luna, Raimon Bustillo, Juan Calderón Martínez, Juan José Seoane Torres-Forné, Alejandro Font, José A. |
| contents | We use physics-informed neural networks (PINNs) to compute the first quasi-normal modes of the Kerr geometry via the Teukolsky equation. This technique allows us to extract the complex frequencies and separation constants of the equation without the need for sophisticated numerical techniques, and with an almost immediate implementation under the \texttt{PyTorch} framework. We are able to compute the oscillation frequencies and damping times for arbitrary black hole spins and masses, with accuracy typically below the percentual level as compared to the accepted values in the literature. We find that PINN-computed quasi-normal modes are indistinguishable from those obtained through existing methods at signal-to-noise ratios (SNRs) larger than 100, making the former reliable for gravitational-wave data analysis in the mid term, before the arrival of third-generation detectors like LISA or the Einstein Telescope, where SNRs of ${\cal O}(1000)$ might be achieved. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2212_06103 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Solving the Teukolsky equation with physics-informed neural networks Luna, Raimon Bustillo, Juan Calderón Martínez, Juan José Seoane Torres-Forné, Alejandro Font, José A. General Relativity and Quantum Cosmology High Energy Astrophysical Phenomena Computational Physics We use physics-informed neural networks (PINNs) to compute the first quasi-normal modes of the Kerr geometry via the Teukolsky equation. This technique allows us to extract the complex frequencies and separation constants of the equation without the need for sophisticated numerical techniques, and with an almost immediate implementation under the \texttt{PyTorch} framework. We are able to compute the oscillation frequencies and damping times for arbitrary black hole spins and masses, with accuracy typically below the percentual level as compared to the accepted values in the literature. We find that PINN-computed quasi-normal modes are indistinguishable from those obtained through existing methods at signal-to-noise ratios (SNRs) larger than 100, making the former reliable for gravitational-wave data analysis in the mid term, before the arrival of third-generation detectors like LISA or the Einstein Telescope, where SNRs of ${\cal O}(1000)$ might be achieved. |
| title | Solving the Teukolsky equation with physics-informed neural networks |
| topic | General Relativity and Quantum Cosmology High Energy Astrophysical Phenomena Computational Physics |
| url | https://arxiv.org/abs/2212.06103 |