Dating Cool Stars with Neural Networks and Spotted Models. Tracing the Star Formation History in the Local Bubble

Accurately determining the fundamental parameters and ages of pre-main sequence (PMS) 
cool stars is a challenge, hampered by the complex interplay of 
extinction, distance, and intense magnetic activity. In this contribution, we demonstrate
how young open clusters can serve as ideal laboratories to calibrate stellar ages by 
explicitly accounting for magnetic activity effects, and how these refined ages can resolve
macroscopic debates in Galactic star formation.

We present a novel Deep Learning framework (Tarantino et al. 2025) designed
to predict robust effective temperatures for cool stars (<7000 K). Trained on high-quality
Gaia-ESO Survey spectroscopy and applied to Gaia DR3 and 2MASS photometry, our Neural 
Network bypasses the limitations of purely photometric color-Teff relations. By combining
these temperatures with state-of-the-art evolutionary models parameterized by the starspot
coverage fraction (β), we derive highly precise isochronal ages for a large sample of 
low-mass stars in young clusters (<100 Myr). We validate our method against 
model-independent age tracers, such as Lithium depletion, demonstrating that the inclusion
of magnetic activity (spots) is strictly required to obtain reliable age estimates and to
correctly interpret the intrinsic age spreads observed in young stellar populations.
Finally, we present the Galactic impact of this calibration by 
tracing the 3D spatio-temporal architecture of the Solar Neighborhood. Leveraging advanced
statistical tests, we map the age distribution of young stars across the Local Bubble (LB)
shell. Our unprecedented age resolution allows us to quantify the chronological gradient
across the expanding shock front, providing a purely empirical, data-driven framework to
test whether the LB expansion triggered the birth of nearby stellar associations or the
LB is superimposed on, and interacts with, a broader pre-existing hierarchy of recent 
star-forming structures  (Tarantino et al. 2026, submitted).