符号回归管线用于 NV 色心系综光谱校准
From Single Spins to Ensembles: A Calibrated Symbolic Regression Pipeline for NV Spectroscopy
物理和机器学习交叉的好工作，符号回归把单颗 NV 色心的光谱推到系综级别，误差降了一半多，还保留了可解释的哈密顿量。
研究团队构建了一套符号回归管线，将单中心自旋结构扩展到氮空位（NV）色心系综的校准模型。该管线从单中心 ODMR 光谱中筛选厄米算符项并拟合系数，再结合权重组合成系综光谱。在公开数据上，零场系综的保持频率 RMSE 从 0.008835 降至 0.003872，提升 56.2%。在 128 个位点、4 种 NV 取向的 QuTiP 仿真系综中，用 0 和 3 mT 校准的模型预测 5.17 mT 光谱，误差 0.000207-0.000228，接近噪声标准差 0.000200。
From Single Spins to Ensembles: A Calibrated Symbolic Regression Pipeline for NV Spectroscopy
Characterizing nitrogen-vacancy (NV) ensembles requires connecting their collective spectra to individual centers that experience different local environments. We develop a symbolic-regression pipeline that carries single-center spin structure into a calibrated ensemble model by generating individual spectral responses and combining them with explicit weights. A constrained search selects Hermitian operator terms from single-center optically detected magnetic resonance spectra, fits their coefficients, and retains the selected expressions as source models for the ensemble. Ensemble calibration then accounts for resonance shifts, local disorder, orientation, and optical response while keeping the individual spectral contributions accessible. On public single-center and ensemble data, the zero-field ensemble held-frequency root-mean-square error decreases from 0.008835 to 0.003872 in normalized photoluminescence, a 56.2% improvement over matched uncorrected composition. In controlled QuTiP ensembles of 128 sites spanning four NV orientations, models calibrated at 0 and 3 mT predict an independently held-out 5.17 mT spectrum with errors of 0.000207-0.000228 across three random seeds, comparable to the 0.000200 noise standard deviation. Resolving the simulated response into its individual-center contributions shows how local spectral diversity combines into the ensemble line shape. By retaining the source Hamiltonians while calibrating sample-dependent spectral differences, the pipeline connects local spin physics to collective optical readout and makes the contributions to an ensemble line shape available for physical interpretation.