发表机构
Kyoto University; Asia Pacific Center for Theoretical Physics; Pohang University of Science and Technology; Gwangju Institute of Science and Technology（京都大学; 亚太理论物理中心; 浦项科技大学; 光州科学技术院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
提出基于神经常微分方程的物理信息机器学习框架，从边界费米子谱函数重建极值RN-AdS时空，并揭示近视界等谱简并性，验证红外CFT普适性。
AI 中文摘要
我们提出了一种基于神经常微分方程的物理信息机器学习框架，用于解决全息逆问题：直接从边界费米子谱函数重建带电AdS黑洞的体时空和规范场。通过将紫外渐近性、视界正则性和零温度极值性作为硬约束编码到神经网络架构中，我们的框架在由$U(1)$探针电荷设定的三个量子临界区域——非费米液体、边际费米液体（奇异金属）和类费米液体态——中可靠地重建了极值Reissner-Nordström AdS几何，并能联合推断探针电荷本身，精度达到亚百分比。放宽近AdS边界约束揭示了一种几何简并性：在径向方向上不同但在近视界$AdS_2 \times \mathbb{R}^2$数据上共享相同数据的体轮廓，在费米面附近再现了相同的谱函数。这种等谱非唯一性正是零温度下一般全息原理所预期的体简并性，并且它在独立训练运行中的自发出现表明，网络隔离了红外CFT普适性，而不是过度拟合单个紫外完备化。
英文摘要
We present a physics-informed machine learning framework based on Neural Ordinary Differential Equations that solves the holographic inverse problem: reconstructing the bulk spacetime and gauge field of a charged AdS black hole directly from boundary fermionic spectral functions. Encoding the UV asymptotics, horizon regularity, and zero temperature extremality as hard constraints in the neural network architecture, our framework reliably reconstructs the extremal Reissner-Nordström AdS geometry across three quantum critical regimes set by the $U(1)$ probe charge---non-Fermi liquid, marginal Fermi liquid (strange metal), and Fermi-liquid-like states---and can jointly infer the probe charge itself to sub-percent accuracy. Relaxing the near-AdS boundary constraint uncovers a geometrical degeneracy: bulk profiles that differ throughout the radial direction but share the same near-horizon $AdS_2 \times \mathbb{R}^2$ data reproduce identical spectral functions near the Fermi surface. This isospectral non-uniqueness is precisely the bulk degeneracy expected on general holographic grounds at zero temperature, and its spontaneous emergence across independent training runs shows that the network isolates the IR CFT universality rather than overfitting a single UV completion.
Comments15 pages, 9 figures
