双黑洞初始数据的可微参数化模型：I. 共形平坦Bowen-York punctures
A Differentiable Parametric Model of Binary-Black-Hole Initial Data: I. Conformally flat Bowen-York punctures
- KU Leuven（荷语鲁汶大学）
- Institute for Theoretical Physics, KU Leuven（荷语鲁汶大学理论物理研究所）
- Leuven Gravity Institute, KU Leuven（荷语鲁汶大学列日引力研究所）
- STADIUS Center for Dynamical Systems, Signal Processing and Data Analytics, KU Leuven（荷语鲁汶大学STADIUS动力学系统、信号处理与数据分析中心）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
提出一种结合稀疏网格谱插值与Newton细化的可微参数化模型，用于快速生成满足约束的双黑洞初始数据，并实现梯度优化与偏心降低。
AI中文摘要：
满足约束条件的双黑洞初始数据需要在物理参数空间中反复求解非线性椭圆边值问题。我们提出了一种参数化、可微的初始数据模型，该模型将稀疏网格谱插值与Newton细化相结合，应用于一系列双黑洞构型。插值仅用于为底层椭圆求解器提供热启动，而非替代求解器。少量Newton迭代即可将每个插值解细化到离散的、行均衡的约束残差$\\|R\\|_\infty\le10^{-10}$，该残差与插值误差无关，因此每个返回的初始数据集都满足该容差下的离散化约束。我们的JAX实现提供了关于物理参数的解析导数，支持基于梯度的参数定位、优化和敏感性分析。我们使用共形平坦Bowen-York punctures，通过构建四维对齐自旋和八维一般自旋模型，演示了该方法在准圆双黑洞初始数据中的应用。所得初始数据与TwoPunctures进行了验证，并将该方法应用于物理Arnowitt-Deser-Misner质量和角动量的认证目标定位，以及使用专用分离-切向动量模型进行有效势偏心率降低。
英文摘要：
Constraint-satisfying initial data for binary black holes require the repeated solution of a nonlinear elliptic boundary-value problem throughout the physical parameter space. We present a para\-metric, differentiable initial-data model that combines sparse-grid spectral interpolation with Newton refinement over a family of binary configurations. Interpolation is used only to provide warm starts for the underlying elliptic solver, rather than to replace it. A small number of Newton iterations refines each interpolated solution to a discrete, row-equilibrated constraint residual $\|R\|_\infty\le10^{-10}$, independent of the interpolation error, so that every returned initial-data set satisfies the discretized constraint to that tolerance. Our JAX implementation provides analytic derivatives with respect to the physical parameters, enabling gradient-based parameter targeting, optimization, and sensitivity analysis. We demonstrate the method for quasi-circular binary-black-hole initial data using conformally flat Bowen--York punctures by constructing four-dimensional aligned-spin and eight-dimensional general-spin models. The resulting initial data are validated against TwoPunctures, and the method is applied to certified targeting of the physical Arnowitt--Deser--Misner mass and angular momentum and to effective-potential eccentricity reduction using a dedicated separation--tangential-momentum model.
