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

Abstract

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.

Figures (16)

• Figure 1: Schematic diagram of the PhDLspec method. The transformer-based spectral model employs an embedding layer that combines wavelength encoding and parameter embedding, followed by multiple encoder blocks with multi-head attention, layer normalization, and feed-forward layers. The output spectra are generated through a fully connected output layer. The model training is regularized with physical gradient spectra from ab initio computation. Observed spectra are fitted by simultaneously optimizing stellar parameters in a $\sim$30-dimensional parameter space.
• Figure 2: Distribution of the Kurucz spectra training set in the $T_{\rm eff}$-$\log g$ diagram, color-coded by their [Fe/H].
• Figure 3: Comparison between the Kurucz spectrum (black squares) and the PhDLspec prediction (red line) for a test star with $T_{\rm eff}=5930$ K, $\log g=4.48$, and [Fe/H]=0.00 (left panel). The top subpanel shows the flux, and the bottom subpanel shows the residual ($\Delta f(\lambda) = f_{\rm PhDLspec} - f_{\rm Kurucz}$). The right panel displays histograms of the overall residuals for a test set of 623 spectra, each with 3800 pixels in wavelength. The standard deviation ($\sigma$) of the residuals is marked.
• Figure 4: The partial derivatives of the normalized fluxes to elemental abundance ratios [Co/Fe] and [La/Fe] for a representative set of stars with different stellar atmospheric parameters ($T_{\rm eff}$, $\log g$, [Fe/H]). For each case, the upper subpanel shows the reference gradients from the Kurucz model (black) alongside the predictions from PhDLspec (red) and the Transformer model (green). The lower subpanel shows the residuals relative to the Kurucz spectra. Results for only wavelength window 3750--4400Å are shown.
• Figure 5: Comparison between the stellar labels derived with PhDLspec and the true labels for the test spectra set. Each panel shows one parameter ratio, with the one-to-one black dashed line indicating perfect agreement. The color represents the [Fe/H] value of the test spectra. The standard deviation of the residuals is presented both for the entire test set ($\sigma_{\mathrm{a}}$) and for metal-rich stars (${\rm [Fe/H]}>-1$) with $4500~\text{K}<T_{\rm eff}<7000~\text{K}$ ($\sigma_{\mathrm{p}}$). Overall, the PhDLspec measurements are consistent with the true labels, especially for metal-rich stars, with dispersion from $0.05$ to $0.3$ dex in the abundance differences, dependent on elements.