Comparative Validation of Analytical Physics and Machine Learning Models

The search for habitable exoplanets is one of the most exciting challenges in modern science. As astronomical surveys continue to discover thousands of planets beyond our solar system, it has become increasingly important to develop clear and reliable ways to evaluate which of them might support life. While astrophysics provides strong theoretical foundations for defining habitable conditions, the growing size and complexity of exoplanet datasets require computational methods that can analyze large amounts of data efficiently. Traditionally, scientists assess planetary habitability using physics-based factors such as equilibrium temperature, stellar luminosity, and planetary size. These parameters help define the classical habitable zone and determine whether a planet could potentially maintain liquid water on its surface. However, as exoplanet catalogs expand, analytical calculations alone are no longer sufficient. They need to be supported by scalable, data-driven techniques that can handle thousands of planetary systems. In this study, I develop a framework that connects analytical physics modeling with machine learning. First, I construct a habitability score based on established astrophysical principles, combining key planetary and stellar parameters into an interpretable model. Then, I train a machine learning model to independently learn the same scoring pattern using observational data. By comparing the analytical results with the machine learning predictions, I examine whether data-driven methods can reproduce physically meaningful patterns without being explicitly guided by theory. This comparison serves two main goals. It tests how robust the physics-based formulation is, and it evaluates whether machine learning can generalize theoretical principles across large exoplanet populations. Through statistical validation, ranking comparisons, sensitivity analysis, and interpretability techniques, the results show strong structural agreement between the theoretical and data-driven approaches, while also revealing subtle differences. By combining astrophysical theory with modern computational methods, this study demonstrates how interdisciplinary approaches can strengthen the identification of promising exoplanet candidates and support the broader search for habitable worlds.