# FFNN-TabNet: An Enhanced Stellar Age Determination Method Based on TabNet
## 8 Method Based on Stellar Activity
### Machine-Learning and Deep-Learning Methods  
Machine-learning and deep-learning methods involve using stellar elemental abundance and asteroseismic parameters as features to train models for age determination. [PERSON] et al. [42] used The Cannon [43], a model for generating observed spectra, with features like \(T_{\rm eff}\) (effective temperature), \(\log~{}g\) (surface gravity), [Fe/H] (metallicity, logarithm of the ratio of iron to hydrogen atoms), and elements abundances, predicting the mass and age of 70,000 distant red giants, including red clump stars. [PERSON] et al. [44] trained a random forest regressor, applied to observational data and evolutionary models, to quickly and accurately infer the initial conditions and current age of several stars, including the Sun and 16 Cyg A and B. However, this method has issues with inaccurate parameter weighting. [PERSON] et al. [45] used neural networks (NNs) to determine the fundamental parameters of sun-like stars, demonstrating robustness in a broad parameter space and low computational cost, but the accuracy of their age determinations needs improvement. [PERSON] et al. [46] used linear regression algorithms with [C/Fe] (Individual element abundance of [C/Fe] determined by the Convolutional Neural Network (CNN) [47] method) and [N/Fe] (Individual element abundance of [N/Fe] determined by the CNN method) elemental abundances and asteroseismic parameters as features, determining the masses and ages of 1475 red giants. [PERSON] et al. [48] applied [PERSON] et al. 's method to LAMOST DR2, determining the ages of 230,000 red giants. [PERSON] et al. [49] used KPCA to determine the masses and ages of 6940 red giants, with errors around 7% for mass determination and 25% for age determination. [PERSON] et al. [50] proposed a new method (MADE), centered on ANN, which can learn from and entirely substitute stellar isochrones. By combining asteroseismic parameters, luminosity, and spectroscopic data, they determined the masses, ages, and distances of red giants. [PERSON] et al. [51] continued their 2017 work, selecting 640,986 Milky Way disk Red Giant Branch stars and providing determination of their ages and masses. [PERSON] and [PERSON] [52] adopted a deep neural network (DNN) to enhance the computational efficiency of asteroseismic modeling, focusing on the consistent oscillation modes of medium- to high-mass stars. Although their method revealed significant uncalibrated issues in core superfluidity and envelope mixing, it shows notable differencesfrom other methods in modeling low-mass stars solely based on asteroseismic quantities. [PERSON] et al. [53] utilized a Mixture Density Network (MDN) [54] to combine modal frequency information with other spectroscopic and global seismic parameters to determine the age and mass of subgiant stars. However, with a Mean Absolute Percentage Error (MAPE) of 8.12%, there remains room for improvement. [PERSON] et al. [55] combined KPCA with RF, using labels like \(\Delta v\) (large frequency separation), \(T_{\text{eff}}\) (effective temperature), \(\log~{}g\) (surface gravity), [Ba/Fe] (individual element abundance of [Ba/Fe] determined by the CNN method), [C/Fe], [Ca/Fe] (individual element abundance of [Ca/Fe] determined by the CNN method), and [Fe/H] elemental abundances, determining the masses and ages of 163,105 red clump cluster stars, with masses determination errors around 9% and ages determination errors around 18%. Compared to traditional methods, machine-learning and deep-learning approaches can integrate a variety of input features, such as spectroscopic data and asteroseismic parameters, to capture complex relationships and enhance determination accuracy. While current machine-learning and deep-learning methodologies have garnered notable achievements, they are not without their constraints. For example, techniques like linear regression and KPCA are inadequate in comprehensively capturing intricate nonlinear correlations and latent linkages within the features of high-dimensional data.