From Single Spins to Ensembles: A Calibrated Symbolic Regression Pipeline for NV Spectroscopy

Evan Zhang, Zhenghang Zhi, Zewei Wang, Zeheng Wang

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…