Exploring Machine Learning, Feature Engineering, and Explainability to Constrain Spica’s Apsidal Constant through MESA Simulations

Spica (α-Virginis) is a notable binary star system located in the constellation of Virgo and offers valuable insights into stellar interiors and dynamics. Within binary systems, gravitational forces between the two stars cause minor distortions that alter their orbital motion. The steady rate of this alteration is known as the apsidal constant, which provides key information about a star’s internal structure and its evolutionary state. Traditionally, stellar environments like Spica are studied using simulations, such as MESA (Modules for Experiments in Stellar Astrophysics). These simulations allow researchers to explore various aspects of stellar behavior through the entire evolution of the star. However, determining the apsidal constant through these simulations presents significant challenges, as it requires extensive computational power and prolonged processing times, with repeated evolutionary modeling needed to achieve accurate predictions of the constant. This research aims to incorporate machine learning techniques to effectively constrain Spica’s apsidal constant, focusing on three main objectives. First, it seeks to apply a range of machine learning (ML) and deep learning (DL) models, from basic to more complex architectures, to analyze the output from MESA. The second objective is to assess the efficiency of each ML and DL method and determine which features most influence the apsidal constant through feature engineering and explainability methods. Lastly, the research seeks to develop a weighted fusion approach, leveraging an ensemble voting regressor capable of predicting the apsidal constant with unseen data, ultimately enhancing prediction accuracy, robustness, and generalization. The findings demonstrate significant potential for both ML and DL methods in estimating Spica’s apsidal constant. Based on the evaluation of a range of models, from simple to deep architectures, Random Forest emerged as the top-performing ML model, while the Recursive Neural Network (RNN) stood out among other DL approaches. The study uncovered significant relationships within the dataset, with luminosity, age, and effective temperature emerging as the most impactful features in determining the apsidal constant. These influential features were identified through both model-based and model-agnostic feature engineering techniques. By leveraging these methods, the research highlighted the importance of these variables, offering deeper insights into their roles in shaping the apsidal constant, and ultimately advancing the understanding of Spica’s stellar evolution. Additionally, the implementation of an ensemble voting regressor, integrating two ML and two DL methods, led to improved accuracy in predicting the apsidal constant with unseen data, achieving performance metrics that rivaled individual models in the ensemble. The resulting estimates closely align with prior observations made by Tkachenko in 2016 and Claret in 2019. This integration holds the promise of unveiling new solutions and advancing our understanding of Spica and the evolutionof massive stars further.