Extraction of Physical Parameters of RRab Variables Using Neural Network Based Interpolator

Abstract

Determining the physical parameters of pulsating variable stars such as RR Lyrae is essential for understanding their internal structure, pulsation mechanisms, and evolutionary state. In this study, we present a machine learning framework that uses feedforward artificial neural networks (ANNs) to infer stellar parameters—mass (M), luminosity (log($L/L_{\odot }$)), effective temperature (log($T_{\mathrm{eff}}$)), and metallicity (Z)—directly from Transiting Exoplanet Survey Satellite (TESS) light curves. The network is trained on a synthetic grid of RRab light curves generated from hydrodynamical pulsation models spanning a broad range of physical parameters. We validate the model using synthetic self-inversion tests and demonstrate that the ANN accurately recovers the input parameters with minimal bias. We then apply the trained model to RRab stars observed by the TESS. The observed light curves are phase-folded, corrected for extinction, and passed through the ANN to derive physical parameters. Based on these results, we construct an empirical period–luminosity–metallicity (PLZ) relation: log($L/L_{\odot }$) = (1.458 ± 0.028) log(P/days) + (–0.068 ± 0.007) [Fe/H] + (2.040 ± 0.007). This work shows that ANN-based light-curve inversion offers an alternative method for extracting stellar parameters from single-band photometry. The approach can be extended to other classes of pulsators such as Cepheids and Miras.

1. Introduction

RR Lyrae stars are low-mass (0.5 ≲ M/${\mathrm{M}}_{\odot }\lesssim$ 0.8), evolved stellar objects (age ≳ 10 Gyr [1]) that occupy the intersection of the horizontal branch and the classical instability strip in the Hertzsprung–Russell diagram. These stars are undergoing a core helium-burning phase, which is similar to the evolutionary stage of intermediate-mass classical Cepheids (3 ≲ M/${\mathrm{M}}_{\odot }\lesssim$ 13). Owing to their well-established period–luminosity relations (PLRs) in the infrared regime—originally identified by Longmore et al. [2] and subsequently refined by several studies (e.g., [3,4,5,6,7])—RR Lyrae variables serve as reliable distance indicators and are critical to calibrating the cosmic distance ladder [8,9]. Furthermore, these stars offer important insights into stellar evolution and pulsation physics [10], and they are effective tracers of ancient stellar populations in various galactic environments [11].

The physical parameters of RR Lyrae stars are traditionally estimated using empirical relations that connect various light curve characteristics—such as Fourier decomposition parameters and color indices—with the pulsation period [12,13,14]. However, advances in the theoretical modeling of stellar pulsation have enabled the construction of extensive model grids to investigate the intrinsic properties of RR Lyrae and other variable stars [15,16,17]. Notably, the radial stellar pulsation (RSP) module developed by Smolec and Moskalik [18], implemented within the Modules for Experiments in Stellar Astrophysics framework (MESA; [19,20,21,22,23]), offers a powerful tool for generating theoretical pulsation models. These models facilitate the derivation of fundamental stellar parameters—such as mass, luminosity, and effective temperature—thereby providing deeper insights into the structure and evolution of RR Lyrae stars.

The motivation for inferring fundamental physical parameters—such as mass, luminosity, effective temperature, and metallicity—from light curves comes from the proliferation of time-domain photometric data from large-scale surveys. While double-lined eclipsing binaries and resolved spectroscopic binaries provide the most precise parameter estimates, such systems are rare with only a few hundred thoroughly characterized examples [24,25]. In contrast, wide-field photometric surveys like EROS [26], MACHO [27], OGLE [28], ASAS [29], TrES [30], HAT [31], CoRoT [32], and Kepler [33] have yielded millions of high-quality light curves for pulsating variables, including RR Lyrae stars. This unprecedented data volume makes light curve-based inference methods increasingly attractive for characterizing stellar populations on a large scale, particularly where spectroscopic data are lacking.

An alternative method for inferring the physical parameters of RR Lyrae stars involves directly comparing observed light curves with a reference library of theoretical models. For instance, Das et al. [34] applied this approach to a sample of RRab stars in the Large Magellanic Cloud (LMC), estimating their physical parameters by matching observed light curves with those from the model grid of Marconi et al. [15]. However, this technique is constrained by the limited coverage of the model grid, as only a small subset of observed LMC light curves closely matched the available theoretical templates. A similar technique is used by Kumar et al. [35] for deriving physical parameters of stars in a globular cluster using medium resolution spectra.

A more sophisticated strategy involves constructing a denser and smoother model grid and employing non-linear optimization techniques for parameter estimation [36]. Nevertheless, generating such a comprehensive model grid is computationally demanding, posing practical limitations. To overcome this challenge, Kumar et al. [37] developed an artificial neural network (ANN) trained on the model grid of Marconi et al. [15] for RRab stars in the V and I photometric bands. The resulting ANN1 serves as an efficient interpolator that is capable of producing high-resolution, smooth model light curves in approximately 55 ms per sample, thereby significantly accelerating the parameter inference process. Hence, we can increase the density of the models using this RRab interpolator. However, the RRab interpolator reliably generates the light curves within the parameter space on which it was trained (see Kumar et al. [37]).

Artificial neural networks (ANNs) offer several advantages in the modeling and inference of pulsating variable star light curves. Once trained, ANNs can perform parameter inference on observed light curves within milliseconds, which is significantly faster than traditional methods such as grid-based forward modeling or interpolation using physical templates [37,38,39]. Furthermore, ANNs allow the generation of a denser and smoother model grid across the parameter space, improving the fidelity and resolution of the inferred parameters. In our case, the ANN-based interpolator enables efficient mapping from physical parameters to light curves, and vice versa, over a finely sampled synthetic grid. While the current work focuses on the I band, which closely resembles the TESS passband, the approach is generalizable to other photometric bands provided suitable training data are available. These benefits make ANNs a powerful alternative to classical interpolation schemes in the context of variable star analysis.

In this study, we generated a smooth grid of model light curves in the I band over a given parameter space and then trained a reverse interpolator as discussed in Kumar et al. [39] to obtain the physical parameters of non-Blazhko fundamental mode RR Lyrae stars observed in the Transiting Exoplanet Survey Satellite (TESS) field. The I band model light curves were preferred over the V band for training the reverse interpolator, as the TESS light curves exhibit greater similarity to the I band, thereby enabling more accurate parameter estimation from TESS observations.

2. Data and Theoretical Grid

2.1. Synthetic Grid Construction

To accurately determine the physical parameters of pulsating variable stars, it is necessary to compare observed light curves with a grid of model light curves. However, pre-computed grids of hydrodynamical models are typically coarse and unevenly distributed across parameter space, owing to the high computational cost and time required to solve the time-dependent equations governing stellar pulsations. Furthermore, constraints on parameters such as mass, surface gravity, and metallicity often rely on spectroscopic measurements, which are not always available for photometric datasets. Consequently, constructing a fine, dense grid of models becomes essential for reliably inferring stellar properties.

In this work, we generated a fine synthetic grid of RRab light-curve templates in the I band using the RRab interpolator trained by Kumar et al. [37]. We adopted a finer and more uniform sampling where mass (M) varies from 0.5 to 0.8 $M_{\odot }$ with a constant step size of 0.05 $M_{\odot }$, luminosity ($log(L/L_{\odot })$) spans from 1.50 to 2.00 dex with a step size of 0.0555 dex, and effective temperature ($T_{\mathrm{eff}}$) ranges from 5000 K to 8000 K with a step size of approximately 88.23 K. The metallicity (Z) covers the range from ${10}^{-4}$ to ${10}^{-2}$ in seven logarithmic steps. The adopted parameter boundaries correspond to the limits of the original training parameter space of the interpolator, and the step sizes were selected to ensure uniform coverage across each parameter dimension. For each value of metallicity, the hydrogen abundance (X) is computed using the relation $X=1-Y-Z$, assuming a fixed helium fraction $Y=0.245$. The parameter space of the synthetic grid is shown in

Table 1. The synthetic model light curves are generated in the I band using the RRab interpolator for the given combination of the physical parameters.

Parameter	Range	Step Size
Mass ($M/M_{\odot }$)	0.5–0.8	0.05
$log(L/L_{\odot })$	1.50–2.00	0.0555
$T_{\mathrm{eff}}$ (K)	5000–8000	88.23
Metallicity (Z)	${10}^{-4}$–${10}^{-2}$	logarithmic steps
Hydrogen fraction (X)	0.755–0.745	computed as $1-Y-Z$

. Using the trained interpolator, we generate synthetic template light curves in the I band for a grid comprising 17,150 distinct combinations of stellar parameters.

The pulsation period (P) of an RR Lyrae star is closely linked to its mass, luminosity, and effective temperature, as originally described by the van Albada–Baker (vAB) relation [40]. We employ a modern version of the vAB relation, incorporating the dependence on metallicity, as formulated by Marconi et al. [15], to compute the periods for our synthetic models. This relation is specifically calibrated for fundamental-mode (RRab) pulsators.

2.2. Observational TESS Sample

The Transiting Exoplanet Survey Satellite (TESS) is a NASA Astrophysics Explorer mission employing four wide-field CCD cameras to perform a nearly all-sky photometric survey, providing a pre-selected 2-minute cadence and 30-minute full-frame images (FFIs) covering approximately 2300 deg² per sector [41]. The continuous, high-precision optical time-series photometry provided by TESS has revolutionized the study of pulsating variables by offering uniformly sampled, multi-sector light curves free from diurnal gaps [41]. Among its many variable-star discoveries, TESS has observed over a thousand RR Lyrae variables, including hundreds of fundamental-mode RRab pulsators, allowing detailed analyses of their pulsation modes, the incidence and characteristics of the Blazhko effect, and low-amplitude secondary oscillations [42]. Differential-image photometry techniques applied to TESS FFIs have cleanly extracted RRab light curves, which, when combined with Gaia parallaxes, have been used to refine empirical period–luminosity–metallicity relationships and to classify RR Lyrae populations across the sky [42].

We compiled a sample of RRab stars by cross-matching known RRab variables from the SIMBAD database with the TESS Input Catalog version 8.2 [43,44,45]. The selection criteria required that each star had been observed in at least one TESS sector and had available measurements for at least one of the following parameters: effective temperature ($T_{\mathrm{eff}}$), surface gravity ($logg$), or metallicity ([Fe/H]). This process resulted in a final sample of 71 RRab stars. The spatial distribution of these stars is shown in Figure 1. The light curves of these stars were taken from the TESS archive using lightkurve2 [46] tool in Python. We converted the raw Pre-search Data Conditioning Simple Aperture Photometry (PDCSAP) flux to TESS magnitude using a zero point magnitude equal to $20.44$ from TESS data release notes3. We converted the TESS magnitude to I band magnitude by deriving a relation between the TESS magnitude and I band magnitude using the spectra of a typical RRab star.

3. Parameter Estimator ANN Model

To derive the physical parameters of RRab stars observed by TESS, we first constructed a fine synthetic grid of model light curves covering a broad range of stellar masses, luminosities, effective temperatures, and metallicities. The template light curves were generated in the I band, matching the photometric bandpass most closely related to the TESS instrumental response. The synthetic grid comprised 17,150 distinct parameter combinations, each corresponding to a unique model light curve generated using the trained RRab interpolator. The uniform and dense coverage of the grid enables robust interpolation across the relevant regions of parameter space and circumvents the limitations imposed by the sparsity of traditional hydrodynamical models. The TESS light curves, corrected for interstellar extinction and folded on their best periods, serve as the observational inputs for the extraction of physical parameters.

The relationship between the observed light curve (y) and the corresponding set of physical parameters (x) can be expressed as a forward mapping function f such that $y\equiv f\left(x\right)$. Inverting this mapping—recovering x given y—requires the construction of an inverse function g such that $x\equiv g\left(y\right)=f^{-1}\left(y\right)$. Artificial neural networks (ANNs) provide a powerful and flexible framework for approximating such inverse mappings, particularly when the underlying functions are continuous and differentiable [47,48,49]. By training an ANN on the synthetic grid of light curves and associated stellar parameters, we enable the efficient and accurate retrieval of mass, luminosity, effective temperature, and metallicity for observed RRab stars directly from their light-curve morphology.

We trained a reverse interpolator using a synthetic grid of light curves and corresponding physical parameters. In this setup, the reverse interpolator is a feedforward ANN, where the input is the absolute I band light curve, sampled at 500 equally spaced phase points between 0 and 1, and the output consists of the physical parameters—mass ($M/M_{\odot }$), luminosity ($log(L/L_{\odot })$), effective temperature ($log\left(T_{\mathrm{eff}}\right)$), and metallicity (Z).

The input layer consists of 500 absolute I band magnitude values, each corresponding to one of the sampled phase points. Since the physical parameters exhibit vastly different numerical ranges, we employed the Robust Scaler method to scale the output values. This approach scales the data using the interquartile range (IQR), making the network less sensitive to outliers and leading to more stable and efficient training. By transforming the physical parameter outputs into a more uniform scale, we ensured that the ANN training could converge more quickly and avoid issues stemming from disparities in the different parameters.

The most crucial part in training any ANN is the choice of hyperparameters of the network, like the number of hidden layers, number of neurons in each hidden layer, activation function, optimization algorithm and learning rate. The training time and the convergence of the ANN depend on these choices of hyperparameters. We used RandomSearch tuner from the KerasTuner library for conducting a systematic hyperparameter tuning.

We defined the model architecture in such a way that allows the number of hidden layers to vary between one and six. For each hidden layer, the number of units and activation function were treated as tunable parameters, and the output layer was kept without any activation to predict the physical parameters. We chose the adam [50] optimizer with the learning rate sampled logarithmically between ${10}^{-4}$ and ${10}^{-2}$. All layers were initialized with the Glorot uniform initializer. We trained each model for 50 epochs with a batch size of 128, using the mean squared error (MSE) as both the loss function and tuning objective.

The hyperparameter search explored 100 different configurations in total.

Table 2. Hyperparameter grid for ANN model tuning.

Hyperparameter	Values
Number of layers	1 to 6
Units per layer	16, 32, 64, 128, 256, 512
Activation function	ReLU, tanh
Learning rate	${10}^{-4}$ to ${10}^{-2}$ (log-uniform sampling)
Batch size	32 (fixed)
Optimizer	adam [50]
Kernel initializer	Glorot Uniform (fixed seed)
Loss function	Mean Squared Error (MSE)

summarizes the hyperparameter grid. The dataset was divided into three parts: 80% for training, 10% for validation, and the remaining 10% for testing. The final model selection was based on the configuration achieving the minimum validation MSE.

We achieved the lowest validation loss with an ANN model comprising $four$ hidden layers containing 256, 128, 32, and 8 neurons, respectively. Each hidden layer has the ReLU activation function and includes L2 regularization with a strength of ${10}^{-6}$ to mitigate overfitting. The output layer consists of four neurons and no activation function, corresponding to the four scaled predicted physical parameters. A schematic diagram of the final ANN architecture is shown in Figure 2.

The final ANN model was trained using the adam optimizer with an initial learning rate of $0.001$ and MSE as the loss function with 80% of the original models used for training, 10% for validation, and the remaining 10% reserved for testing. To facilitate efficient convergence, we implemented a piecewise constant learning rate schedule: the learning rate was decreased by a factor of 5 at batch sizes of 10 and 100, respectively. Training was performed over 1200 epochs with a batch size of 32. The model weights were updated using shuffling at each epoch, and training was parallelized across eight CPU workers with multiprocessing. The total training time was ~$27.35$ min, utilizing a system equipped with 64 CPU cores operating at a maximum frequency of $3.5$ GHz.

The training and validation loss curve for the ANN model, along with the learning rate, is shown in Figure 3. The curve shows the training and validation loss (MSE) during the training over the course of 1200 epochs while also showing the variation in the learning rate. This figure provides insight into both the convergence behavior of the model and the effect of the learning rate.

4. Results

4.1. Self Inversion

To assess the performance of the trained parameter estimator ANN model, we performed a self-inversion test. In this test, the synthetic model I band light curves from the test grid were passed through the trained ANN, and the recovered physical parameters were compared with their original values.

The comparison between the ANN-predicted and true values of mass, luminosity, effective temperature, and metal abundance for the test set is shown in Figure 4. The strong correlation between the predicted and true values demonstrates that the network accurately recovers stellar parameters across the entire grid. The predicted points closely match the original values with negligible scatter or systematic bias, as presented in

Table 3. Performance of the trained parameter estimator model on the test set based on MSE and relative root-mean-square error (Relative RMSE). The Relative RMSE is computed as the RMSE normalized by the mean absolute value of the true parameter values.

Parameter	MSE	Relative RMSE (%)
Mass (M)	$5.6\times {10}^{-5}$	1.15
Luminosity (L)	$1.6\times {10}^{-5}$	0.23
$log\left(T_{\mathrm{eff}}\right)$	$3.1\times {10}^{-6}$	0.04
Metallicity (Z)	$1.1\times {10}^{-7}$	12.81

.

The relative root-mean-square error (Relative RMSE) provides an intuitive measure of a model’s predictive performance across parameters with different numerical scales. It is defined as the root-mean-square error normalized by the mean absolute value of the true parameter values and is expressed as a percentage:

$$\mathrm{Relative}\mathrm{RMSE}=\left({\displaystyle \frac{\sqrt{\frac{1}{n}{\sum }_{i=1}^n{(x_i-{\widehat{x}}_i)}^2}}{\frac{1}{n}{\sum }_{i=1}^n\left|x_i\right|}}\right)\times 100\%$$

where $x_i$ and ${\widehat{x}}_i$ are the true and predicted values of the parameter, respectively.

The synthetic self-inversion tests confirm that the trained parameter estimator model is capable of recovering the physical parameters of RRab stars from their light curves with high accuracy and minimal bias. For example, the model achieves relative RMSE values of only 1.15% for mass, 0.23% for luminosity, and 0.04% for $log\left(T_{\mathrm{eff}}\right)$, indicating excellent agreement between predicted and true values. This test validates the internal consistency and predictive reliability of the trained parameter estimator model, although a relatively higher relative RMSE of 12.81% is observed for metallicity.

4.2. Application to TESS RRab Stars

4.2.1. Light-Curve Processing and Folding

To apply the trained parameter estimator model to real data, we selected a sample of RRab stars observed by the TESS for which literature estimates of fundamental stellar parameters are available in Stassun et al. [45]. The TESS light curves were downloaded in the form of short-cadence (2-min) simple aperture photometry (SAP) flux from SPOC Jenkins et al. [51] pipeline FITS files. The fluxes were converted into apparent magnitudes using the standard TESS zero point (adopted from TESS data release notes4):

$$m_{\mathrm{TESS}}=-2.5{log}_{10}\left(\mathrm{flux}\right)+20.44.$$

(1)

The period for each light curve was derived using the Lomb–Scargle [52,53] method and then phase-folded using this derived period. Only positive flux points were retained to avoid contamination. To suppress observational noise and fill missing data segments, we fitted a Fourier series to the folded light curve with 10 Fourier components (see Equation (6) of Kumar et al. [39]). The smoothed light curve was sampled at 1000 phase points and then rebinned to 500 evenly spaced bins between phases 0 and 1. This format matches the structure of the input layer used during ANN training.

4.2.2. Photometric Corrections and Calibration

To convert apparent TESS band magnitudes into absolute I band magnitudes, several corrections were applied. Gaia DR3 parallaxes were used to compute distances, from which the distance modulus $\mu$ was derived as

$$\mu =5{log}_{10}\left(d\left[\mathrm{pc}\right]\right)-5.$$

(2)

Extinction values were obtained from the IRSA Galactic Dust Reddening Tool, which returns extinction in V band magnitudes ($A_V$) based on the star’s equatorial coordinates using the reddening maps of the Schlafly and Finkbeiner [54]. The I band extinction $A_I$ was estimated using standard extinction ratios and applied to the apparent TESS magnitudes after converting them to the I band. As TESS does not operate in the standard I band, we employed the empirical transformation:

$$I=m_{\mathrm{TESS}}-0.0695.$$

(3)

Thus, the absolute I band magnitude for each star becomes

$$M_I=I-\mu -A_I.$$

(4)

4.2.3. ANN-Based Parameter Inference

The preprocessed and rebinned absolute I band light curves were then passed through the trained ANN to predict the underlying stellar parameters. The ANN output includes the stellar mass $M/M_{\odot }$, logarithmic luminosity $log(L/L_{\odot })$, effective temperature $log\left(T_{\mathrm{eff}}\right)$, and metallicity Z:

$$\left(M,logL,log{T}_{\mathrm{eff}},Z\right)=\mathrm{ANN}\left(y_{\mathrm{TESS}}\right).$$

(5)

The effective temperature can be recovered via inverse logarithmic transformation: $T_{\mathrm{eff}}={10}^{log{T}_{\mathrm{eff}}}$. To derive the iron abundance, we converted Z to [Fe/H] using the relation provided by [55]

$$[\mathrm{Fe}/\mathrm{H}]={log}_{10}\left({\displaystyle \frac{Z/X}{Z_{\odot }/X_{\odot }}}\right),$$

(6)

where $Z_{\odot }=0.0122$ and $X_{\odot }=0.7392$ [56]. The hydrogen abundance X is calculated from $X=1-Y-Z$, assuming a fixed helium mass fraction $Y=0.245$. This value corresponds to the primordial helium abundance, which is suitable for RR Lyrae stars given their old evolutionary status. Helium enrichment in such populations is expected to be minimal. Observational support for this assumption is provided by Marconi and Minniti [57], who found little evidence of helium enhancement among RR Lyrae stars in the Galactic bulge.

Table 4. Physical parameters of RR Lyrae stars derived from TESS light curves using ANN method compared with literature values.

ID	TESS ID	Plxlit	Period	Period LS	$T_{{\mathrm{eff}}_{\mathrm{lit}}}$	$T_{{\mathrm{eff}}_{\mathrm{ANN}}}$	Mlit	MANN	Lumlit	LumANN	[Fe/H]lit	[Fe/H]ANN	logglit
		(”)	(d)	(d)	(K)	(K)	(M⊙)	(M⊙)	(LM⊙)	(LM⊙)	(dex)	(dex)	(dex)
XZ Dra	229913521	1.30 ± 0.02	0.476475	0.476574	6447 ± 224	6824	1.31 ± 0.22	0.67	34.76 ± 1.98	40.91	–	−0.56	3.21 ± 0.12
V1195 Her	232570970	0.53 ± 0.02	0.609729	0.608373	5889 ± 167	6420	–	0.67	–	56.91	−1.60 ± 0.01	−0.19	–
TW Lyn	241174387	0.62 ± 0.04	0.481854	0.481025	6008 ± 162	6659	–	0.62	–	39.10	−0.64 ± 0.01	−0.47	–
TT Lyn	29172806	1.22 ± 0.04	0.597443	0.597684	6191 ± 193	6635	–	0.65	–	52.51	−1.65 ± 0.02	−0.45	–
TW Boo	68076619	0.72 ± 0.02	0.532264	0.531162	6247 ± 42	6645	–	0.70	–	45.32	−1.46 ± 0.07	–	–
SV Eri	9843991	1.22 ± 0.06	0.713900	0.713374	6200 ± 249	6360	–	0.81	–	60.43	−2.06 ± 0.06	−0.56	–
SS Tau	311091712	0.67 ± 0.05	0.369910	0.369768	6724 ± 108	6903	1.43 ± 0.26	0.64	21.14 ± 3.31	25.00	0.17 ± 0.03	−0.33	3.53 ± 0.11
RX Eri	114923989	1.62 ± 0.03	0.587252	0.586150	6443 ± 205	6629	–	0.63	–	49.70	–	−0.56	–
U Lep	146324929	0.93 ± 0.03	0.581458	0.580807	6541 ± 229	6689	–	0.74	–	58.66	–	–	–
TZ Aur	328588068	0.66 ± 0.04	0.391673	0.391437	7128 ± 145	6867	1.59 ± 0.28	0.64	26.79 ± 3.39	31.72	−0.15 ± 0.02	−0.64	3.58 ± 0.10
SZ Gem	63172763	0.59 ± 0.04	0.501165	0.501342	6050 ± 101	6856	–	0.71	–	42.36	−1.65 ± 0.13	–	–
EZ Cnc	197217727	0.50 ± 0.05	0.545777	0.546779	6625 ± 100	6662	1.39 ± 0.23	0.61	31.60 ± 6.34	35.19	−0.00 ± 0.03	−0.32	3.32 ± 0.13
SS Gru	129710422	0.14 ± 0.04	0.959791	0.956326	6942 ± 379	6252	–	0.95	–	291.22	–	−0.56	–
VW Scl	41833926	0.85 ± 0.07	0.510917	0.511665	6672 ± 111	6816	1.41 ± 0.23	0.70	31.06 ± 5.55	41.71	−1.27 ± 0.05	–	3.35 ± 0.11
Z Mic	89358641	0.81 ± 0.07	0.586928	0.585981	6398 ± 200	6480	1.28 ± 0.21	0.60	34.01 ± 5.69	40.01	–	−0.18	3.19 ± 0.13
VX Scl	32282599	0.43 ± 0.03	0.637078	0.635441	6716 ± 208	6597	–	0.76	–	59.59	–	−0.95	–
RZ Cet	1129237	0.68 ± 0.04	0.510600	0.511475	6248 ± 182	6729	1.21 ± 0.18	0.67	25.68 ± 3.12	53.38	−1.90 ± 0.02	−0.96	3.25 ± 0.12
BN Aqr	39999072	0.38 ± 0.06	0.469600	0.468717	6955 ± 760	6849	1.52 ± 0.40	0.69	46.69 ± 14.23	60.60	–	–	3.27 ± 0.31
CP Aqr	248483300	0.78 ± 0.09	0.463400	0.463006	7148 ± 522	6806	1.59 ± 0.32	0.64	26.65 ± 6.66	34.45	–	−0.74	3.59 ± 0.22
SW Aqr	387498678	0.76 ± 0.23	0.459305	0.459871	–	6824	–	0.72	–	43.47	–	–	–
RR Cet	344299442	1.52 ± 0.08	0.553041	0.552368	6650 ± 139	6589	1.40 ± 0.24	0.66	42.32 ± 4.75	48.09	−1.35 ± 0.10	−1.84	3.20 ± 0.10
SX Aqr	353029655	0.62 ± 0.07	0.535708	0.536120	6325 ± 194	6838	1.25 ± 0.19	0.71	31.85 ± 7.46	61.80	–	−1.84	3.19 ± 0.14
AO Peg	283289876	0.35 ± 0.04	0.547245	0.546917	6342 ± 71	6554	–	0.67	–	51.16	−1.25 ± 0.07	−2.81	–
SW And	437761208	1.78 ± 0.16	0.442261	0.441881	6735 ± 138	6613	1.44 ± 0.24	0.59	30.35 ± 6.28	29.13	−0.07 ± 0.10	−0.25	3.38 ± 0.13
DM Cyg	117638854	0.97 ± 0.05	0.419868	0.419951	6415 ± 151	6748	1.29 ± 0.19	0.61	20.62 ± 2.50	32.85	0.03 ± 0.10	−0.38	3.42 ± 0.10
XX And	186452465	0.69 ± 0.05	0.722772	0.721256	6097 ± 9	6613	–	0.70	–	67.68	−1.67 ± 0.01	−0.46	–
DH Hya	47291018	0.47 ± 0.04	0.488996	0.488922	6259 ± 54	6856	–	0.71	–	59.94	−1.52 ± 0.09	–	–
RR Leo	3941985	1.00 ± 0.09	0.452403	0.451699	6593 ± 291	6863	1.37 ± 0.25	0.72	33.79 ± 6.00	41.59	–	–	3.28 ± 0.16
WY Ant	168276785	0.91 ± 0.06	0.574350	0.575440	6765 ± 277	6583	1.45 ± 0.27	0.69	46.47 ± 6.23	50.15	–	–	3.21 ± 0.15
V595 Cen	152231997	0.44 ± 0.03	0.690994	0.691325	6430 ± 191	6569	–	0.65	–	53.30	–	−0.25	–
TU UMa	144376546	1.56 ± 0.06	0.557658	0.556678	6200 ± 65	6643	–	0.65	–	44.82	−1.31 ± 0.14	−1.39	–
SS Leo	49417864	1.13 ± 0.72	0.626351	0.626993	–	6676	–	0.70	–	58.65	–	−1.80	–
W Crt	219249305	0.75 ± 0.04	0.412012	0.412036	6740 ± 305	6845	1.44 ± 0.27	0.64	29.59 ± 3.80	32.68	–	−0.70	3.39 ± 0.15
UV Vir	377172421	0.56 ± 0.05	0.587065	0.586541	7550 ± 130	6714	1.75 ± 0.28	0.66	38.59 ± 6.88	49.96	−1.10 ± 0.10	−0.41	3.56 ± 0.11
UZ CVn	376689735	0.51 ± 0.03	0.697793	0.696838	6329 ± 58	6599	–	0.66	–	56.78	−2.22 ± 0.09	−0.85	–
SV Hya	453469791	1.21 ± 0.05	0.478527	0.478892	6744 ± 324	6850	1.44 ± 0.28	0.71	31.79 ± 3.08	51.43	–	–	3.36 ± 0.15
UY Boo	458457951	0.62 ± 0.05	0.650800	0.651139	6433 ± 292	6581	–	0.77	–	69.01	–	-0.73	–
RS Boo	409373422	1.36 ± 0.04	0.377365	0.377471	6610 ± 132	6719	1.38 ± 0.22	0.61	24.05 ± 1.74	29.52	−0.12 ± 0.10	−0.21	3.43 ± 0.09
V413 CrA	253708643	1.13 ± 0.05	0.589343	0.589858	5945 ± 47	6521	–	0.60	–	50.39	−0.94 ± 0.05	−0.15	–
V4424 Sgr	271404999	1.70 ± 0.04	0.424503	0.424840	6240 ± 181	6511	1.21 ± 0.18	0.55	25.46 ± 1.63	24.36	–	−0.00	3.25 ± 0.10
TV Lib	79403057	0.79 ± 0.04	0.269624	0.269903	6620 ± 132	6897	1.39 ± 0.23	0.64	17.68 ± 1.81	16.29	−0.43 ± 0.10	−0.28	3.57 ± 0.10
BT Aqr	248815852	0.56 ± 0.05	0.406357	0.406222	6700 ± 268	6681	1.42 ± 0.27	0.62	25.69 ± 4.50	37.35	–	−0.55	3.44 ± 0.15
AA Aql	248097218	0.68 ± 0.05	0.361768	0.361829	6550 ± 146	6915	1.35 ± 0.24	0.65	27.71 ± 4.25	30.46	−0.32 ± 0.10	−0.63	3.35 ± 0.12
V456 Ser	46253107	0.22 ± 0.04	0.517558	0.517328	6600 ± 40	6084	–	0.76	–	151.05	−2.64 ± 0.17	−0.66	–
VY Ser	371355048	1.32 ± 0.07	0.714096	0.712959	6055 ± 50	6448	–	0.70	–	64.02	−1.82 ± 0.05	−0.36	–
V341 Aql	375822497	0.84 ± 0.05	0.578042	0.579124	6504 ± 272	6666	–	0.73	–	63.17	–	−1.63	–
AT Ser	264584937	0.58 ± 0.05	0.746609	0.745240	6591 ± 249	6436	–	0.75	–	73.06	–	−0.47	–
DX Del	85211589	1.68 ± 0.03	0.472611	0.472674	6454 ± 118	6534	1.31 ± 0.21	0.60	32.36 ± 1.84	36.11	−0.14 ± 0.06	−0.16	3.24 ± 0.09
VX Her	356085581	0.98 ± 0.06	0.455356	0.456175	6369 ± 135	6786	1.27 ± 0.20	0.74	37.00 ± 4.74	46.23	−1.45 ± 0.07	–	3.14 ± 0.11
BN Vul	111443222	1.40 ± 0.03	0.594132	0.593941	6318 ± 222	6749	–	0.85	–	143.31	–	−0.86	–
TW Her	10581605	0.86 ± 0.02	0.399596	0.400107	7465 ± 147	6836	1.71 ± 0.29	0.66	29.37 ± 1.94	36.89	−0.35 ± 0.10	−1.14	3.65 ± 0.09
CN Lyr	317170031	1.11 ± 0.03	0.411382	0.411798	6355 ± 106	6393	1.26 ± 0.19	0.54	22.33 ± 1.79	24.38	−0.04 ± 0.10	−0.01	3.36 ± 0.09
VZ Her	85516380	0.63 ± 0.02	0.440360	0.440466	5732 ± 153	6870	–	0.71	–	42.43	−1.71 ± 0.01	–	–
FN Lyr	158553034	0.30 ± 0.03	0.527390	0.527304	6745 ± 410	6735	–	0.78	–	77.00	–	−1.09	–
SW For	175492625	0.36 ± 0.02	0.803760	0.803760	6389 ± 176	6426	–	0.67	–	59.24	–	−0.26	–
U Pic	259590223	0.73 ± 0.02	0.440373	0.440466	6642 ± 106	6718	1.40 ± 0.23	0.63	30.57 ± 2.50	35.96	−0.69 ± 0.08	−0.69	3.34 ± 0.09
CD Vel	34069197	0.57 ± 0.03	0.573516	0.572059	7099 ± 261	6558	1.58 ± 0.27	0.80	54.15 ± 6.25	75.49	–	−0.74	3.26 ± 0.12
ST Pic	150166721	2.00 ± 0.02	0.485749	0.486130	6549 ± 182	6422	1.35 ± 0.22	0.56	33.05 ± 1.70	28.96	–	−0.06	3.27 ± 0.10
AE Tuc	234507163	0.63 ± 0.02	0.414528	0.414589	6274 ± 116	6826	1.22 ± 0.17	0.64	20.32 ± 1.79	33.14	−0.45 ± 0.07	−0.78	3.36 ± 0.09
W Tuc	234518883	0.57 ± 0.03	0.642247	0.643122	6042 ± 106	6655	–	0.72	–	66.97	−1.31 ± 0.08	−1.18	–
BI Cen	267930751	0.69 ± 0.03	0.453193	0.452948	7085 ± 341	6765	1.57 ± 0.28	0.86	47.25 ± 5.75	106.42	–	−0.82	3.32 ± 0.14
YY Tuc	220512467	0.43 ± 0.03	0.634857	0.634866	6350 ± 233	6595	–	0.77	–	69.81	–	−1.37	–
RV Phe	425863844	0.52 ± 0.04	0.596419	0.596355	6471 ± 195	6504	–	0.68	–	56.92	–	−0.39	–
TY Aps	258812822	0.62 ± 0.03	0.501720	0.501070	6588 ± 283	6749	–	0.68	–	42.88	–	–	–
EX Aps	294832702	0.58 ± 0.03	0.471799	0.472235	6738 ± 297	6741	1.44 ± 0.27	0.64	29.83 ± 3.51	41.24	–	−0.87	3.39 ± 0.14
V Ind	126910093	1.50 ± 0.04	0.479594	0.479773	6551 ± 105	6742	1.36 ± 0.21	0.73	33.35 ± 2.39	44.11	−1.32 ± 0.03	–	3.27 ± 0.08
MS Ara	337440887	0.55 ± 0.04	0.524988	0.525991	6735 ± 254	6503	1.44 ± 0.25	0.81	45.39 ± 6.95	56.61	–	−0.69	3.21 ± 0.13
CD-45 13628	129081118	1.26 ± 0.04	0.510247	0.510016	6133 ± 115	6305	1.16 ± 0.16	0.56	28.45 ± 2.40	30.13	−0.35 ± 0.08	−0.08	3.15 ± 0.09
CD-42 14707	129112145	0.99 ± 0.27	0.551264	0.551323	–	6649	–	0.61	–	44.16	–	−0.40	–
CD-48 13332	166463208	0.40 ± 0.04	0.579506	0.578464	6651 ± 349	6711	–	0.67	–	45.00	–	−1.79	–
GI Psc	406413012	0.42 ± 0.05	0.734199	0.736294	6487 ± 262	6477	–	0.71	–	59.77	–	−0.34	–

Notes: ID is the variable star identifier. TESS ID is the TESS Input Catalog identifier. Plx is the parallax in arcseconds. Period is the pulsation period in days (from the literature), and Period LS is the period determined from the Lomb–Scargle periodogram applied to TESS light curves. Columns with subscript ‘lit’ show values from the literature with their uncertainties when available. Columns with the subscript ‘ANN’ show values derived from our ANN.

presents the derived physical parameters for a sample of RRab stars based on their TESS light curves, using our trained ANN-based parameter estimator. For each star, the table lists the TESS ID, parallax from the TESS Input Catalog v8.2 [45], the literature period, and the Lomb–Scargle period measured from the TESS data. The effective temperature ($T_{\mathrm{eff}}$), mass (M), luminosity (L), and metallicity (Z) inferred by the ANN are compared against corresponding values from the literature when available. We also report the photometric surface gravity ($logg$).

Figure 5 shows the comparison between the physical parameters of RR Lyrae stars derived from ANN analysis of TESS light curves and those from literature values. The top row displays one-to-one comparisons with literature values on the x-axis and ANN predictions on the y-axis, while the bottom row shows error distributions. The ANN method produces effective temperatures with a mean error of 143 K ($\sigma =352$ K), metallicities with a mean error of $0.27$ dex ($\sigma =0.83$ dex), masses with a mean error of $-0.74M_{\odot }$ ($\sigma =0.13M_{\odot }$), and luminosities with a mean error of $9.63L_{\odot }$ ($\sigma =11.32L_{\odot }$).

While the temperature and luminosity predictions show reasonable agreement with literature values, mass estimates from the ANN are systematically lower by approximately $0.74M_{\odot }$. From stellar evolution, RR Lyrae stars are known to have masses in the range $0.5$–$0.8M_{\odot }$. In contrast, many literature values (from the TIC catalogue) report anomalously high masses (1.1–1.7 $M_{\odot }$), which is likely due to the use of isochrone or SED fitting methods that may not have accounted for the evolved, low-mass RR Lyrae stars.

The relatively large spread in metallicity ($\sigma =0.83$ dex) and mean offset of $0.27$ dex likely arises from degeneracies in light curve morphology, where variations in metallicity can mimic the effects of other parameters. Furthermore, literature metallicities are derived from diverse sources and methods, which introduces inconsistencies when used as a reference benchmark.

Overall, the ANN method demonstrates reasonable predictive power for effective temperature and luminosity, while systematic shifts in mass and scatter in metallicity reflect a combination of astrophysical degeneracies and uncertainties in the literature values. This supports our approach of deriving fundamental stellar parameters directly from time-series photometry while also highlighting the need for caution when comparing to literature sources that may not be tailored for RR Lyrae-type variables.

4.3. Period–Luminosity–Metallicity (PLZ) Relation

Using the stellar parameters inferred from the TESS RRab light curves via the trained ANN, we constructed a new empirical period–luminosity–metallicity (PLZ) relation. We fitted the logarithm of the luminosity as a linear function of the pulsation period and metallicity:

$$log(L/L_{\odot })=alog(P/\mathrm{days})+b[\mathrm{Fe}/\mathrm{H}]+c,$$

(7)

where P is the pulsation period in days, and $[\mathrm{Fe}/\mathrm{H}]$ is the derived metallicity from the ANN-inferred Z values. The coefficients a, b, and c were determined using a least-squares fitting.

$$a=1.458\pm 0.028,b=-0.068\pm 0.007,c=2.040\pm 0.007.$$

(8)

Figure 6 presents a plot of the ANN predicted luminosities as a function of period and metallicity, which was overlaid with the fitted PLZ plane. The scatter of individual stars around the plane is shown as a color-coded scatter plot with the color scale representing [Fe/H]. Stars with lower metallicity (bluer colors) lie systematically higher in luminosity at fixed period, which is consistent with theoretical expectations.

5. Conclusions

In this study, we developed and validated an artificial neural network (ANN)-based framework to infer the physical parameters of fundamental-mode RR Lyrae (RRab) stars directly from their light curves. Using a synthetic grid of pulsation models, we trained a feedforward ANN to learn the inverse mapping from I band light-curve morphology to stellar parameters: mass (M), luminosity ($logL$), effective temperature ($log{T}_{\mathrm{eff}}$), and metallicity (Z). The network achieved high accuracy in recovering these parameters in synthetic self-inversion tests, demonstrating strong internal consistency and robustness across a wide parameter space.

The self-inversion test, conducted on a hold-out test set of 1,715 models not seen during training, showed good agreement between predicted and true values, particularly for $log{T}_{\mathrm{eff}}$ and $logL$. However, the performance was comparatively poorer for M and Z, which was likely due to degeneracies in the light-curve morphology, where multiple combinations of parameters can lead to similar pulsation features.

We then applied the trained parameter estimator model to observed RRab stars from the TESS mission. After preprocessing the light curves, including flux-to-magnitude conversion, phase folding, Fourier smoothing, extinction correction, and distance modulus calibration, we extracted stellar parameters from the light curves of individual stars. The values of M, $logL$, $log{T}_{\mathrm{eff}}$, and Z, inferred using the model, were used to compute surface gravity ($logg$) and iron abundance $[\mathrm{Fe}/\mathrm{H}]$, providing a complete physical characterization based solely on photometric data.

We compared the ANN-inferred values with those available in the literature (TIC v8.2 catalog). While the ANN-predicted values for $log{T}_{\mathrm{eff}}$ and $logL$ generally aligned well with the catalog values, the agreement was notably worse for mass and metallicity. A significant fraction of the TIC-inferred masses for RRab stars was found to lie in the range $1.1$–$1.7M_{\odot }$, which is inconsistent with established evolutionary models for RR Lyrae stars that predict a mass range of $0.5$–$0.8M_{\odot }$. These discrepancies suggest that catalog masses—often derived from isochrone or SED fitting—may not be reliable for evolved horizontal-branch stars like RR Lyraes. Consequently, the differences are more likely due to limitations in the literature data rather than overfitting or failure of the ANN model.

Furthermore, a period–luminosity–metallicity (PLZ) relation was derived using the ANN-predicted parameters. While the PLZ relation is physically plausible, its interpretation is naturally constrained by the accuracy of the inferred stellar properties.

This work demonstrates that an ANN-based inversion of RRab light curves offers an alternative to traditional model fitting and spectroscopic analysis. In the future, the method can be extended to include multi-band light curves, overtone RRc stars, and different classes of pulsating variable stars like Cepheids and BL Herculis-type variables. This work is the first step and can provide a fast way to estimate global physical parameters when trained with an extended parameter space of RRab theoretical models. Uncertainty-aware architectures and larger, better-constrained training sets will further improve the robustness and applicability of such data-driven frameworks in time-domain stellar astrophysics.