NSF-DMS-2510856 ($270,000 - Starting 09/01/2025, 36 months)
This project concerns the integration of first-principles physics into statistical modeling procedures. Our approach is based on the development and analysis of new challenge problems paired with the derivation of probabilistic high performance computing methods to resolve crucial statistical quantities (means, correlations, confidence bands). This work confronts numerous exciting challenges in modeling, computation, and rigorous analysis which will lead to impactful new applications in a variety of areas such as medical imaging, weather and climate modeling, robotics, geology, and geophysics. As such our work will develop improved methods to better formulate and quantify uncertainties for demanding real world problems in the above domains. This program will incorporate the comprehensive training and the promotion of excellence in applied mathematics and statistics for a new generation of scholars which the PI will mentor supported by this grant and its research activities.
