Project Grant 2513336

This Project Grant award, funded by the National Science Foundation (NSF) under the Mathematical and Physical Sciences program (CFDA 47.049), supports the development of efficient and scalable computational methods for solving complex kinetic equations. The key products and services to be delivered include:

1. Developing learning-enhanced, structure-preserving particle methods for nonlinear partial differential equations, with a focus on plasma models. These methods are intended to complement existing particle-in-cell approaches and offer improvements in scalability and stability for collisional plasma simulations.

2. Designing reduced-order methods for optimization problems constrained by kinetic equations, leveraging the multiscale nature of the equations or employing intelligent use of randomness. The proposed methods aim to meet the need for efficient inverse solvers, given the growing applications of kinetic theory to real-world problems.

This $220,000 award, with a performance period from July 1, 2025, to June 30, 2028, will be executed by the Regents of the University of Minnesota, a prominent land-grant research institution. The project also includes the training of graduate students, contributing to the development of the next generation of computational mathematicians.