The study of deep geodynamic processes and their surface expressions—such as earthquakes and volcanic activity——is critical for both scientific advancement and societal safety. While traditional geodynamic models focus on fundamental Earth dynamics with limited direct ties to observations, the emergence of data-driven computational models now enables the integration of real-world data into physics-based simulations. By leveraging techniques such as data assimilation and artificial intelligence,these advanced models can invert observations to constrain model parameters and initial conditions, turning vast and diverse datasets into predictive insights. This talk will explore how such computational approaches are transforming our ability to reconstruct past events,analyze present conditions,and forecast future scenarios in geodynamics. Case studies willinclude mantle-lithosphere dynamics, earthquake mechanics, and lava flow behavior. Each example demonstrates how combining numerical simulation with geological, geophysical, and geodetic data enhances our understanding of planetary dynamics while providing practicalsolutions to challenges in geohazard assessment and georesource management. Through these applications, computationalgeodynamics is proving essential for building a more resilient and resource-aware society.