Dissecting stellar populations with manifold learning: I. Validation of the method on a synthetic Milky Way-like galaxy

Context. Different stellar populations may be identified through differences in chemical, kinematic, and chronological properties, suggesting the interplay of various physical mechanisms that led to their origin and subsequent evolution. As such, the identification of stellar populations is key for gaining an insight into the evolutionary history of the Milky Way. This task is complicated by the fact that stellar populations share a significant overlap in their chrono-chemo-kinematic properties, hindering efforts to identify and define stellar populations. Aims. Our goal is to offer a novel and effective methodology that can provide a deeper insight into the nonlinear and nonparametric properties of the multidimensional physical parameters that define stellar populations. Methods. For this purpose, we explore the ability of manifold learning to differentiate stellar populations with minimal assumptions about their number and nature. Manifold learning is an unsupervised machine learning technique that seeks to intelligently identify and disentangle manifolds hidden within the input data. To test this method, we make use of Gaia DR3-like synthetic stellar samples generated from the FIRE-2 cosmological simulations. These represent red-giant stars constrained by asteroseismic data from TESS. Results. We reduced the 5D input chrono-chemo-kinematic parameter space into 2D latent space embeddings generated by manifold learning. We then study these embeddings to assess how accurately they represent the original data and whether they contain meaningful information that can be used to discern stellar populations. Conclusions. We conclude that manifold learning possesses promising abilities to differentiate stellar populations when considering realistic observational constraints.