发表机构
Nagoya University（名古屋大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究在Kiselev黑洞基准中区分插值精度与物理可识别性，发现环引力与光子几何互补可显著提升参数可识别性，但逆估计器鲁棒性仍受条件限制。
AI 中文摘要
高插值精度并不能确立物理参数的可识别性。我们在一个受控的Kiselev黑洞基准中研究这一区别，该基准采用经过验证的类时发射体和三维零测地线发射计算。精确的$k=0$边界提供了一个解析已知的零控制，因为此时时空变为Schwarzschild且与$w_q$无关。环引力对于形变幅度$k$具有信息量，而光子几何提供了独立的响应方向，可解决$w_q$的大部分简并性。相对于仅使用环引力，环引力加光子几何在最小奇异值上实现了中位逐点$4.54\ imes$的增益，在雅可比条件数上实现了$2.28\ imes$的改进。在分组物理插值中，可识别$w_q$的归一化平均绝对误差从0.309降至0.087。随机分割更为乐观，而方向外推则困难得多，且分割共形覆盖在分布偏移下会退化。一个非学习的最近模型逆方法表明，该增益并不仅限于所测试的学习架构。一个均匀的161相位审计给出了典型的归一化预测偏移为$9.48\ imes10^{-4}$，而一个针对性的321相位审计解决了剩余的向前特征比较。然而，冻结的HGB和随机森林尾部偏移超过了预设的鲁棒性阈值。因此，物理观测互补性得到支持，但逆估计器的鲁棒性仍是有条件的。这是一个理论可识别性基准，而非观测约束。
英文摘要
High interpolation accuracy does not establish that physical parameters are identifiable. We study this distinction in a controlled Kiselev black hole benchmark with a validated timelike-emitter and three-dimensional null-geodesic shooting calculation. The exact $k=0$ boundary provides an analytically known null control because the spacetime becomes Schwarzschild and independent of $w_q$. Ringdown is informative for the deformation amplitude $k$, while photon geometry supplies an independent response direction that resolves much of the $w_q$ degeneracy. Relative to ringdown alone, ringdown plus photon geometry gives a median pointwise $4.54\times$ gain in minimum singular value and a $2.28\times$ improvement in Jacobian condition number. In grouped physical interpolation, identifiable-$w_q$ normalized mean absolute error decreases from 0.309 to 0.087. Random splitting is more optimistic, while directional extrapolation is substantially harder and split-conformal coverage degrades under distribution shift. A non-learned nearest-model inverse shows that the gain is not confined to the tested learned architectures. A uniform 161-phase audit gives a typical normalized prediction shift of $9.48\times10^{-4}$, while a targeted 321-phase audit resolves the remaining forward-feature comparisons. However, frozen HGB and random-forest tail shifts exceed prespecified robustness thresholds. Thus, physical observable complementarity is supported, but inverse-estimator robustness remains conditional. This is a theoretical identifiability benchmark, not an observational constraint.
Comments30 pages, 18 figures, 12 tables. Theoretical black hole identifiability benchmark with validated direct null-geodesic shooting, Jacobian diagnostics, leakage-aware inverse learning, non-learned baselines, and numerical-resolution audits. Code and reproducibility archive: Zenodo, DOI 10.5281/zenodo.23191840
