Machine learning for understanding pulsating stars I: the non-linear phenomenon in {\delta} Scuti stars

$\delta$ Scuti stars are pulsating variable stars that exhibit both radial and non-radial pulsations, making them key objects for understanding stellar evolution and internal structures. The current classification of $\delta$ Scuti stars into High-Amplitude $\delta$ Scuti (HADS) and Low-Amplitude $\delta$ Scuti (LADS) stars is based on the peak-to-peak amplitude of their light curves (>0.3 mag). Nevertheless, this classification may not fully capture the complexity of their pulsation mechanisms and non-linear effects, leading to possible misclassifications. This investigation aims to challenge the existing classification of $\delta$ Scuti stars according to amplitude, employing the exploration of frequency domain features and non-linear mechanisms in order to identify intrinsic subgroups. The objective is to get a deeper understanding of the properties of $\delta$ Scuti stars. We use machine learning clustering techniques, specifically hierarchical clustering (HC) with Ward's linkage, to analyze a sample of 142 $\delta$ Scuti stars observed by space telescopes such as CoRoT, Kepler, and TESS. We focus on frequency-domain features, including fundamental and overtone modes, as well as non-linear features such as harmonic, sums, and subtraction frequencies, to uncover intrinsic subgroups within $\delta$ Scuti stars. The results of the clustering process indicate that the present amplitude-based classification (HADS/LADS) exhibits partial alignment with the clusters identified by using features from the frequency-domain. However, the study identified additional sub-groups, suggesting a greater variety of nonlinear effects that are not captured by the amplitude alone. It highlights the importance of non-linear features, such as the number of subtraction combinations, which may be indicative of resonance effects or other internal physical mechanisms.