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Main Authors: Gu, Haohao, He, Sensen, Song, Hanlin, Liang, Bo, Lyu, Zhenwei, Hu, Xiaoguang, Du, Minghui, Xu, Peng, Ma, Bo-Qiang
Format: Preprint
Published: 2026
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Online Access:https://arxiv.org/abs/2604.23625
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author Gu, Haohao
He, Sensen
Song, Hanlin
Liang, Bo
Lyu, Zhenwei
Hu, Xiaoguang
Du, Minghui
Xu, Peng
Ma, Bo-Qiang
author_facet Gu, Haohao
He, Sensen
Song, Hanlin
Liang, Bo
Lyu, Zhenwei
Hu, Xiaoguang
Du, Minghui
Xu, Peng
Ma, Bo-Qiang
contents Spectral problems governed by differential operators underpin a wide range of physical systems, yet remain computationally challenging because their spectra depend sensitively on continuous parameters and often demand repeated evaluations across parameter space. Here we present $\texttt{DeepOPiraKAN}$, an open source physics informed neural network architecture for spectral analysis. By combining operator learning with enhanced optimization stability, it captures the underlying parameter-to-spectrum mapping in a single model, avoiding repeated spectral solutions at isolated points in parameter space. As a representative and stringent benchmark, we apply this framework to the computation of quasinormal modes of Kerr black holes. A single trained network accurately resolves modes with $(\ell,m)\in \{(2,0),(2,1)\}$ and overtones up to $n=7$ across the full spin range, achieving relative errors of $\mathcal{O}(10^{-6})$ for the fundamental mode and gradually increasing to $\mathcal{O}(10^{-4})$ for higher overtones, benchmarked against the Leaver's method. This level of accuracy is already significant for black hole spectroscopy and practical ringdown modelling for current and future observatories. More broadly, these results highlight the potential of $\texttt{DeepOPiraKAN}$ as a general and scalable framework for parameter dependent spectral problems across complex physical systems.
format Preprint
id arxiv_https___arxiv_org_abs_2604_23625
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle Physics informed operator learning of parameter dependent spectra
Gu, Haohao
He, Sensen
Song, Hanlin
Liang, Bo
Lyu, Zhenwei
Hu, Xiaoguang
Du, Minghui
Xu, Peng
Ma, Bo-Qiang
General Relativity and Quantum Cosmology
Instrumentation and Methods for Astrophysics
Computational Physics
Spectral problems governed by differential operators underpin a wide range of physical systems, yet remain computationally challenging because their spectra depend sensitively on continuous parameters and often demand repeated evaluations across parameter space. Here we present $\texttt{DeepOPiraKAN}$, an open source physics informed neural network architecture for spectral analysis. By combining operator learning with enhanced optimization stability, it captures the underlying parameter-to-spectrum mapping in a single model, avoiding repeated spectral solutions at isolated points in parameter space. As a representative and stringent benchmark, we apply this framework to the computation of quasinormal modes of Kerr black holes. A single trained network accurately resolves modes with $(\ell,m)\in \{(2,0),(2,1)\}$ and overtones up to $n=7$ across the full spin range, achieving relative errors of $\mathcal{O}(10^{-6})$ for the fundamental mode and gradually increasing to $\mathcal{O}(10^{-4})$ for higher overtones, benchmarked against the Leaver's method. This level of accuracy is already significant for black hole spectroscopy and practical ringdown modelling for current and future observatories. More broadly, these results highlight the potential of $\texttt{DeepOPiraKAN}$ as a general and scalable framework for parameter dependent spectral problems across complex physical systems.
title Physics informed operator learning of parameter dependent spectra
topic General Relativity and Quantum Cosmology
Instrumentation and Methods for Astrophysics
Computational Physics
url https://arxiv.org/abs/2604.23625