SM-Net: Learning a Continuous Spectral Manifold from Multiple Stellar Libraries

Omar Anwar; Aaron S. G. Robotham; Luca Cortese; Kevin Vinsen

astro-ph.IMMar 25, 2026

SM-Net: Learning a Continuous Spectral Manifold from Multiple Stellar Libraries

Authors: Omar Anwar, Aaron S. G. Robotham, Luca Cortese, Kevin Vinsen

Organizations: International Centre for Radio Astronomy Research (ICRAR) The University of Western Australia (UWA), 35 Stirling Hwy, Crawley WA 6009, Australia

Abstract

We present SM-Net, a machine-learning model that learns a continuous spectral manifold from multiple high-resolution stellar libraries. SM-Net generates stellar spectra directly from the fundamental stellar parameters effective temperature (Teff), surface gravity (log g), and metallicity (log Z). It is trained on a combined grid derived from the PHOENIX-Husser, C3K-Conroy, OB-PoWR, and TMAP-Werner libraries. By combining their parameter spaces, we construct a composite dataset that spans a broader and more continuous region of stellar parameter space than any individual library. The unified grid covers Teff = 2,000-190,000 K, log g = -1 to 9, and log Z = -4 to 1, with spectra spanning 3,000-100,000 Angstrom. Within this domain, SM-Net provides smooth interpolation across heterogeneous library boundaries. Outside the sampled region, it can produce numerically smooth exploratory predictions, although these extrapolations are not directly validated against reference models. Zero or masked flux values are treated as unknowns rather than physical zeros, allowing the network to infer missing regions using correlations learned from neighbouring grid points. Across 3,538 training and 11,530 test spectra, SM-Net achieves mean squared errors of 1.47 x 10^-5 on the training set and 2.34 x 10^-5 on the test set in the transformed log1p-scaled flux representation. Inference throughput exceeds 14,000 spectra per second on a single GPU. We also release the model together with an interactive web dashboard for real-time spectral generation and visualisation. SM-Net provides a fast, robust, and flexible data-driven complement to traditional stellar population synthesis libraries.

Figures & tables

Figure 1: Top-level schematic of the SM-Net model architecture. The four stellar spectral libraries PHOENIX–Husser, C3K–Conroy, OB–PoWR, and TMAP–Werner are first combined into a unified multi-library dataset spanning a broad region of stellar parameter space. SM-Net is then trained on this dataset to generate spectra in two stages: a global parameter-to-coarse-spectrum prediction, followed by a convolutional refinement to produce the final high-fidelity output. The resulting model is accessed through an interactive dashboard that enables real-time spectral generation and exploration.

Library	Type	$T_{\mathrm{eff}}$ ( $\mathrm{K}$ )	$\log g$	$\log Z$	$\lambda$ (Å)	N
PHOENIX (Husser)	Base	2300–12000	0–6	$-4$ –1	500–55000	7559
C3K (Conroy)	Base	2000–50000	$-1$ –5.5	$-2.1$ –0.5	100– $10^{8}$	8602
OB (PoWR)	Hot	15000–56000	2–4.2	NA	100– $10^{6}$	243
TMAP (Werner)	White	20000–190000	5–9	NA	3–400000	124
SM-Net (combined)	ML Model	2000–190000	$-1$ –9	$-4$ –1	3000–100000	$\infty$

Table 1: Parameter ranges of the stellar spectrum libraries used in this work. N is the number of unique spectra in each library. SM-Net is trained on the combined dataset.

Figure 2: A 3D plot representing the coverage of each of the four libraries PHOENIX-Husser , C3K , OB-PoWR , and TMAP in $(\log_{10}T_{\mathrm{eff}},\log g,\log Z)$ space. The overlapping region between C3K and Husser spans $3.36\leq\log T_{\mathrm{eff}}(K)\leq 4.08$ , $0\leq\log g\leq 5.5$ , and $-2.1\leq\log Z\leq 0.5$ . The overlapping region between C3K and TMAP covers $4.30\leq\log T_{\mathrm{eff}}(K)\leq 4.70$ , $5\leq\log g\leq 5.5$ , and $-2.1\leq\log Z\leq 0.5$ . The overlapping region between C3K and OB-PoWR covers $4.18\leq\log T_{\mathrm{eff}}(K)\leq 4.70$ , $2\leq\log g\leq 4.5$ , and $-2.1\leq\log Z\leq 0.5$ .

Figure 3: Library coverage and overlap on $\log T_{\mathrm{eff}}(K)$ – $\log g$ , $\log T_{\mathrm{eff}}(K)$ – $\log Z$ and $\log g$ – $\log Z$ grids.

$T_{\mathrm{eff}}$	$\log g$	$\log Z$	Train	Val	Test
$t_{1}$	$g_{1}$	$z_{1}$	✓	✓
$t_{2}$	$g_{1}$	$z_{2}$	✓	✓
$t_{2}$	$g_{3}$	$z_{3}$	✓
$t_{3}$	$g_{2}$	$z_{5}$			✓
$t_{5}$	$g_{3}$	$z_{1}$			✓
$t_{5}$	$g_{1}$	$z_{3}$			✓

Table 2: Illustrative assignment of spectra to train/validation/test sets based on the 2–2 parameter split pattern. Ticks indicate membership; boundary cases appear in both the training and validation sets.

Figure 4: Distribution of zero/unknown flux values across the dataset of combined grids. Counts are aggregated over logZ values.

Split	Original $N$	Augmented $N$	Increase factor
Train	3,538	5,784	1.63
Validation	2,386	3,845	1.61
Test	11,530	N/A	N/A

Table 3: Number of spectra in each dataset split before and after augmentation based on spectral uniqueness.

Figure 5: The replication counts for the entire dataset based on spectral dissimilarity, aggregated over $\log Z$ .

Figure 6: Block-level architecture of SM-Net, showing the two-stage mapping from stellar parameters to a high-resolution synthetic spectrum. The Lookup Block takes the input parameters (effective temperature, surface gravity, and metallicity) and produces a coarse, low-frequency spectral estimate through a sequence of embedding, fully connected, and projection layers. This coarse spectrum, together with the physical parameters and positional encodings, is passed to the Refinement Block, where convolutional feature extractors and residual convolutional blocks learn wavelength-dependent corrections. The refinement output is added to the coarse spectrum to produce the final high-resolution stellar spectrum.

Figure 7: Training and validation losses throughout the training process. Red lines indicate the epochs at which the learning rate was reduced and the batch size was reduced, both by a factor of 0.8.

Figure 8: Mean and median residual of spectra between Husser and C3K libraries as a function of $\log_{10}(\lambda)$ , across 783 matched $(T_{\mathrm{eff}},\log g,\log Z)$ points on the grid between two libraries. The shaded region indicates the $\pm 1\sigma$ dispersion of the residuals.

Figure 9: Mean of Mean Square Difference (Teff vs logG) between the common spectra of Husser and C3K libraries. The mean is computed over the logZ axis.

Figure 10: C3K and PHOENIX-Husser spectrum for $T_{\mathrm{eff}}=2,500~\mathrm{K}$ , $\log g=4.0$ , and $\log Z=-1.5$ , and the SM-Net generated spectrum for the same parameters. The residual highlights the underlying differences in the physics between the two libraries.

Split	$N$	mean $\mathrm{MSE}$	$\mathrm{RMS}_{\mathrm{flux}}$ [%]	Median MSE	10th perc. MSE	90th perc. MSE	Min MSE	Max MSE
Train	3,538	$1.47\times 10^{-5}$	$0.38$	$4.20\times 10^{-6}$	$1.13\times 10^{-6}$	$3.17\times 10^{-5}$	$1.78\times 10^{-7}$	$6.34\times 10^{-4}$
Validation	2,386	$2.62\times 10^{-5}$	$0.51$	$5.59\times 10^{-6}$	$1.56\times 10^{-6}$	$5.35\times 10^{-5}$	$2.59\times 10^{-7}$	$9.81\times 10^{-4}$
Test	11,530	$2.34\times 10^{-5}$	$0.48$	$5.09\times 10^{-6}$	$1.39\times 10^{-6}$	$4.23\times 10^{-5}$	$1.86\times 10^{-7}$	$3.73\times 10^{-3}$

Table 4: Summary of SM-Net reconstruction quality across the combined multi-library dataset. For each split,

N

is the number of spectra, mean

\mathrm{MSE}

is the mean per-spectrum mean squared error, and

\mathrm{RMS}_{\mathrm{flux}}

is the corresponding root-mean-square flux deviation. Percentiles and min/max values are computed over the per-spectrum MSE distribution.

Panel of Figure 11 — Figure 11: Distribution of MSE prediction errors across $T_{\mathrm{eff}}$ . High MSE occurs predominantly at low temperatures, with consistent trends across splits, indicating robust generalisation.

Panel of Figure 12 — Figure 12: Distribution of MSE across $\log g$ . Elevated errors appear near the boundaries of PHOENIX–Husser and C3K overlap, indicating inconsistencies between the underlying physics of the two libraries.

Panel of Figure 13 — Figure 13: Distribution of MSE across $\log Z$ . Errors are broadly uniform, with particularly low mean and median MSEs at $\log Z=-4$ and $-3$ , which originate from regions governed by a single library and therefore contain no cross-library inconsistencies.

Panel of Figure 14 — Figure 14: Distribution of MSE across $T_{\mathrm{eff}}$ for the four libraries.

Panel of Figure 15 — Figure 15: Distribution of MSE across $\log g$ for the four libraries.

Panel of Figure 16 — Figure 16: Distribution of MSE across $\log Z$ for the four libraries.

Figure 17: Predicted spectrum for Sun, and the target spectrum from PHOENIX-Husser with the closest Sun-like parameters.

Figure 18: High-fidelity SM-Net reconstruction for $T_{\mathrm{eff}}=6900,\mathrm{K}$ , $\log g=5.0$ , and $\log Z=-4.0$ , shown against the corresponding PHOENIX–Husser reference spectrum.

Figure 19: High-quality SM-Net reconstruction for $T_{\mathrm{eff}}=13{,}000~\mathrm{K}$ , $\log g=4.5$ , and $\log Z=-1.5$ , compared with the corresponding C3K reference spectrum.

Figure 20: Example of a low-quality reconstruction at $T_{\mathrm{eff}}=2,200~\mathrm{K}$ , $\log g=3.0$ , and $\log Z=-2.1$ , shown against the corresponding C3K reference spectrum.

Figure 21: Example of a low-quality reconstruction for $T_{\mathrm{eff}}=18,000~\mathrm{K}$ , $\log g=2.0$ , and $\log Z=-4.0$ , compared against the corresponding OB-PoWR reference spectrum.

Figure 22: Example of SM-Net reconstructing missing high-wavelength flux for $T_{\mathrm{eff}}=60{,}000~\mathrm{K}$ and $\log g=8.0$ , compared with the corresponding TMAP reference spectrum.

Figure 23: The layout of the interactive interface.

Figure 24: Example of a visualisation of a 3D grid via SM-Net interface, based on a CSV uploaded by the user.

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T_{\mathrm{eff}}

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