This $150,000 Project Grant award from the National Science Foundation's (NSF) Mathematical and Physical Sciences program (CFDA 47.049) supports research at Carnegie Mellon University (CMU) to advance the understanding and performance of sampling algorithms, which are crucial for applications across scientific domains such as molecular dynamics, statistical physics, Bayesian statistics, and machine learning. The research will use mathematical tools from partial and stochastic differential equations, probability theory, and numerical analysis to study the theoretical and algorithmic aspects of sampling dynamics, with a focus on two key objectives: (1) analyzing the long-time convergence properties of sampling dynamics characterized by kinetic equations, and (2) studying sampling dynamics structured as gradient flows, including scenarios where standard gradient flow theory is not directly applicable. This award, which runs from August 1, 2024 to July 31, 2027, aims to provide useful insights for practitioners and also includes a plan for mentoring undergraduate researchers and developing educational courses on sampling for advanced undergraduate and early-stage graduate students.
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