In this study, we explore the application of two pillars of Scientific Machine Learning—Neural Ordinary Differential Equations (Neural ODEs) and Universal Differential Equations (UDEs)—to a cornerstone of astrophysical theory: the Chandrasekhar White Dwarf Equation (CWDE). The CWDE is fundamental for understanding the life cycle of a star and describes the relationship between the density of the white dwarf and its distance from the core.Despite the growing importance of SciML, the systematic exploration of these techniques in astrophysics, particularly in modeling complex ODEs like the CWDE, remains largely unexplored. In this study, we bridge that gap by demonstrating how Neural ODEs and UDEs can be employed for both accurate prediction and reliable long-term forecasting of the CWDE. Furthermore, we introduce the 'forecasting breakdown point'—the time at which forecasting fails for both Neural ODEs and UDEs.Through rigorous hyperparameter optimization testing, we assess neural network architectures, activation functions, and optimizer configurations to determine the best performance. This study offers a new lens to understand the physics of white dwarfs and paves the way for future research on using SciML frameworks for forecasting tasks across a range of scientific domains.