PhDLspec: physical-prior embedded deep learning method for spectroscopic determination of stellar labels in high-dimensional parameter space

Unlocking the full physical information encoded in low-resolution spectra poses a significant challenge for astronomical survey analysis. Such a task demands modeling spectra and optimizing astrophysical parameters in high-dimensional space, as a consequence of line blending. Here we present PhDLspec -- a deep learning framework embedded with physical priors for stellar spectra modeling and analysis. By imposing differential spectra derived from ab initio stellar atmospheric model calculation on a transformer framework, PhDLspec can rigorously and precisely model stellar spectra by simultaneously taking into account more than 30 physical parameters, at a computational speed hundreds of times faster than ab initio model calculation. With such a flexible stellar modeling approach, PhDLspec can effectively derive ~30 stellar labels from a low-resolution spectrum using affordable optimization techniques. Application to LAMOST spectra (R~1800) yields stellar elemental abundances in good agreement with high-resolution spectroscopic surveys, following essential calibrations to correct systematic biases in elemental abundance estimates using wide binaries and reference high-resolution datasets. We provide a catalog of 25 elemental abundances for 116,611 subgiant stars with precise age estimates. The successful application of PhDLspec to LAMOST spectra for high-dimensional parameter determination sheds light on similar challenges faced by other surveys and disciplines.