The award will support Dr. Ganguly's research on the interface of stochastic analysis and statistical learning theory. Stochastic differential equations (SDEs) are powerful tools for modeling systems that exhibit randomness. Such systems arise from a wide variety of disciplines including biology, environmental science, engineering, physics, medicine, and financial markets. Understanding behaviors of these systems requires not just building mathematical models but integrating them with the available data. The dynamics of these stochastic systems are however intricate with convoluted correlation structures, and there is a critical lack of mathematical results in the literature investigating learning methods for such complex data. This initiative will fill some of this gap by crafting innovative learning algorithms for these problems and will employ asymptotic analysis to assess the efficacy of these learning strategies. The project will develop a probabilistic framework for estimation of the driving functions of SDEs, uncertainty quantification and testing of various hypotheses. Building such data-driven stochastic models backed by rigorous mathematics will enhance our understanding of complex systems across multiple domains and empower informed decision-making in the presence of randomness. The endeavor will engage both undergraduate and graduate students, imparting them with invaluable skills through a blend of theoretical understanding, hands-on application, and practical experience in coding.