基于神经微分方程的机器学习框架从费米子谱函数重构黑洞时空
Deep learning emergent spacetime from fermionic spectral functions in holography
物理学家们用机器学习工具，从费米子谱函数里反推出了黑洞的时空结构，这个方法还挺靠谱。
本文提出一种基于神经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构带电AdS黑洞的体时空和规范场。该框架将紫外渐近性、视界正则性和零温极端性作为硬约束嵌入神经网络架构，在三个由U(1)探针电荷决定的量子临界区域（非费米液体、 marginal费米液体（奇异金属）和费米液体态）中可靠地重构了极端Reissner-Nordström AdS几何，并能以亚百分之一的精度联合推断探针电荷。放松近AdS边界约束揭示了拓扑退化：体剖面在整个径向方向不同但共享相同近视界AdS₂×R²数据的剖面会产生相同的费米面附近谱函数。这种等谱非唯一性是零温下全息论预期的体退化，且在独立训练运行中自发出现，表明网络隔离了红外CFT普适性而非过拟合单一紫外完成。
Deep learning emergent spacetime from fermionic spectral functions in holography
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.