本文提出由神经网络插值器和选择函数学习网络组成的快速框架，用于估计 LISA 对 EMRI 的探测选择效应，并在天体物理族群模型中校正偏差、量化关键参数测量精度。
摘要：
对恒星质量致密天体旋近大质量黑洞（MBH）的引力波观测，即极端质量比旋近（EMRI），使我们能够精确测量 MBH 质量和自旋等参数。激光干涉空间天线（Laser Interferometer Space Antenna，LISA）预计将探测到足够多的 EMRI，从而探究其背后的源族群，检验关于 MBH 形成、演化及其环境的理论。族群研究会受到在 EMRI 参数空间中变化的选择效应影响；若不加考虑，这些效应会使推断结果产生偏差。这种偏差可以被校正，但评估大量 EMRI 信号的可探测性在计算上非常昂贵。我们通过以下方式降低这一成本：（i）构建一个快速且准确的神经网络插值器，能够根据 EMRI 的参数预测其信噪比；（ii）利用一个学习选择函数的神经网络进一步加速可探测性估计，并借助第一个神经网络生成数据。由此得到的框架可快速估计选择函数，从而在族群推断分析中完整处理 EMRI 的可探测性。我们将该方法应用于一个具有天体物理动机的 EMRI 族群模型，展示了潜在的选择偏差并随后对其进行校正。在考虑选择效应后，我们预测，利用红移 z=6 以下的 EMRI，LISA 将以 8.8% 的精度测量 MBH 质量函数斜率，以 4.6% 的精度测量致密天体（CO）质量函数斜率，以 10% 的精度测量 MBH 自旋大小分布的宽度，并以 12% 的精度测量事件率。
英文摘要：
Gravitational wave observations of the inspiral of stellar-mass compact objects into massive black holes (MBHs), extreme mass ratio inspirals (EMRIs), enable precision measurements of parameters such as the MBH mass and spin. The Laser Interferometer Space Antenna is expected to detect sufficient EMRIs to probe the underlying source population, testing theories of the formation and evolution of MBHs and their environments. Population studies are subject to selection effects that vary across the EMRI parameter space, which bias inference results if unaccounted for. This bias can be corrected, but evaluating the detectability of many EMRI signals is computationally expensive. We mitigate this cost by (i) constructing a rapid and accurate neural network interpolator capable of predicting the signal-to-noise ratio of an EMRI from its parameters, and (ii) further accelerating detectability estimation with a neural network that learns the selection function, leveraging our first neural network for data generation. The resulting framework rapidly estimates the selection function, enabling a full treatment of EMRI detectability in population inference analyses. We apply our method to an astrophysically motivated EMRI population model, demonstrating the potential selection biases and subsequently correcting for them. Accounting for selection effects, we predict that LISA will measure the MBH mass function slope to a precision of 8.8%, the CO mass function slope to a precision of 4.6%, the width of the MBH spin magnitude distribution to a precision of 10% and the event rate to a precision of 12% with EMRIs at redshifts below z=6.
What Fraction of Extreme Mass Ratio Inspirals That Merge After the LISA Mission Ends Are Detectable?
Oregon State University（俄勒冈州立大学）；Universities Space Research Association（大学空间研究协会）；NASA Marshall Space Flight Center（美国国家航空航天局马歇尔太空飞行中心）；California Institute of Technology（加州理工学院）；University of Southampton（南安普顿大学）
Revealing massive black hole astrophysics: The potential of hierarchical inference with extreme mass-ratio inspiral observations
Institute for Gravitational Research, University of Glasgow（格拉斯哥大学引力研究所）；Institute for Gravitational Wave Astronomy & School of Physics and Astronomy, University of Birmingham（伯明翰大学引力波天文学所与物理天文学院）
Multimessenger prospects of quasi-periodic eruptions
Institute of Theoretical Physics, Faculty of Mathematics and Physics（数学物理学院理论物理研究所）；Dipartimento di Fisica “A. Pontremoli”, Università degli Studi di Milano（米兰大学A. Pontremoli物理系）；Dipartimento di Fisica “G. Occhialini”, Università degli Studi di Milano-Bicocca（米兰比可卡大学G. Occhialini物理系）
From S2 to LISA: Astrometric Bounds on Extreme-Mass-Ratio Inspirals and Bursts
CERN（欧洲核子研究中心）；Dipartimento di Fisica, “Sapienza” Università di Roma & Sezione INFN Roma1（罗马第一大学物理系与INFN罗马第一分部）；Weizmann Institute of Science（魏茨曼科学研究所）
Extreme Mass Ratio Inspirals in Light of Quasi-periodic Eruptions: Milli-Hertz Gravitational Wave Background
Tsung-Dao Lee Institute, Shanghai Jiao-Tong University（上海交大李政道研究所）；School of Physics & Astronomy, Shanghai Jiao-Tong University（上海交通大学物理与天文学院）；Department of Astronomy, School of Physics, Peking University（北京大学物理学院天文学系）；Kavli Institute for Astronomy and Astrophysics at Peking University（北京大学科维理天文与天体物理研究所）
Chaotic migration of LISA Extreme Mass Ratio Inspirals in a turbulent accretion disk: effect on waveform de-phasing
Center for Cosmology and Particle Physics, Physics Department, New York University（纽约大学物理系宇宙学与粒子物理中心）；Department of Astrophysics, University of Zurich（苏黎世大学天体物理学系）；Shanghai Astronomical Observatory, Chinese Academy of Sciences（中国科学院上海天文台）；National Astronomical Observatory of Japan（日本国立天文台）；Department of Astronomy & Astrophysics, University of California, Santa Cruz（加州大学圣克鲁兹分校天文与天体物理学系）；Institute for Advanced Studies, Tsinghua University（清华大学高等研究院）
Extreme Love in the SPA: constraining the tidal deformability of supermassive objects with extreme mass ratio inspirals and semi-analytical, frequency-domain waveforms
Extreme mass ratio inspirals from the Hills mechanism, The eccentricity distribution of Hills EMRIs in LISA
Leiden University（莱顿大学）；Università degli Studi di Trento（特伦托大学）；Università degli Studi di Milano-Bicocca（米兰比可卡大学）；INFN - Sezione di Milano-Bicocca（意大利国家核物理研究所米兰比可卡分部）；Institute of Science and Technology Austria (ISTA)（奥地利科学技术研究院）
Ab uno disce omnes: Single-harmonic search for extreme mass-ratio inspirals
European Space Agency (ESA), European Space Research and Technology Centre (ESTEC)（欧洲空间局（ESA），欧洲空间研究与技术中心（ESTEC））；Universitá degli Studi di Milano-Bicocca（米兰比可卡大学）；INFN, Sezione di Milano-Bicocca（意大利国家核物理研究所，米兰比可卡分校）；University of Birmingham（伯明翰大学）
