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arXiv 2605.02453gr-qcastro-ph.HEcs.LGphysics.data-anstat.ML
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通过引力波分类测试广义相对论：一种卷积神经网络框架

Testing General Relativity Through Gravitational Wave Classification: A Convolutional Neural Network Framework

Institute for Theoretical Physics, Heidelberg University（海德堡大学理论物理研究所）

Lavinia Heisenberg, Shayan Hemmatyar, Hector Villarrubia-Rojo

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36 pages, 20 figures, 4 tables. Comments welcome!
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AI总结：

本文提出利用卷积神经网络框架测试广义相对论，通过模拟引力波信号和相位变形，改进分类灵敏度，并在大规模引力波数据中检测到广义相对论的偏离。

摘要：

我们提出一个机器学习框架，用于通过二进制黑洞合并的引力波信号测试广义相对论（GR）。使用GWTC目录中的173个BBH事件源参数作为现实的天体物理种群，生成模拟的GR波形，并通过受控的相位变形构造超越GR（BGR）波形。我们引入了一个响应函数形式化，提供了一个系统框架，用于量化任何可观测性对GR修改的响应。我们训练卷积神经网络（CNNs）在两种输入表示上：白化波形和从波形不匹配导出的响应函数类型可观测性，后者隔离了相位偏差对总体信号的影响。使用响应函数作为CNN输入将分类灵敏度提高了约33倍，证明了可观测性表示的选择与分类器架构同样重要。我们通过贝叶斯最优误差分析研究了此分类的基本限制，平均方法揭示了噪声中的相干模式，以及CNN准确度与单特征分类器的比较作为人类性能的代理。在所有变形尺度上，CNN均优于最佳的单特征方法。我们扩展了该框架以应用于物理动机的理论，使用参数化后爱因斯坦（ppE）形式化，并应用于重力理论，其中分类器在aLIGO设计灵敏度下检测到引力子质量约为$ m_g \sim 10^{-23}\;\mathrm{eV}/c^2 $的偏离。

英文摘要：

We present a machine learning framework for testing general relativity (GR) with gravitational wave signals from binary black hole mergers. Using the source parameters of 173 BBH events from the GWTC catalog as a realistic astrophysical population, we generate simulated GR waveforms and construct beyond GR (BGR) waveforms by applying controlled phase deformations. We introduce a response function formalism that provides a systematic framework for quantifying how any observable responds to modifications of GR. We train convolutional neural networks (CNNs) on two input representations: whitened waveforms and a response function type observable derived from the waveform mismatch, which isolates the effect of phase deviations from the bulk signal. Using response functions as the CNN input improves the classification sensitivity by a factor of approximately 33 compared to whitened waveforms, demonstrating that the choice of observable representation is as important as the classifier architecture. We study the fundamental limits of this classification through Bayes optimal error analysis, averaging methods that reveal coherent patterns hidden in noise, and a comparison between CNN accuracy and a single feature classifier as a proxy for human performance. At all deformation scales, the CNN outperforms the best single feature approach. We extend the framework to physically motivated theories using the parameterized post Einsteinian (ppE) formalism and apply it to massive gravity, where the classifier detects deviations for graviton masses of order $m_g \sim 10^{-23}\;\mathrm{eV}/c^2$ with aLIGO design sensitivity.

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