Federal Grant Award Summary

The University of Delaware received a $158,270 Project Grant from the National Science Foundation's Directorate for Mathematical and Physical Sciences (CFDA 47.049) awarded February 15, 2026, with completion targeted for July 31, 2026. This award supports research into Structure-Preserving Machine Learning Moment Closures for Kinetic Equations, which aims to develop reduced-order models that approximate kinetic equations through machine learning (ML) techniques while preserving critical mathematical structures. The primary deliverable is the development of robust, accurate, and efficient ML moment models with provable mathematical structures—specifically focusing on preserving the hyperbolicity of kinetic models to ensure well-posedness of partial differential equations and enable robust numerical simulations.

The research methodologies to be investigated include: (1) symmetrizer-based and eigenvalue-based approaches that preserve hyperbolicity in multidimensional cases; (2) ML approaches for learning boundary conditions that satisfy well-posedness requirements for initial boundary value problems; and (3) generalized data-driven ML models with enforced hyperbolicity. Beyond the technical research products, the award provides educational benefits through research opportunities for graduate and undergraduate students in computational mathematics and curriculum development support for the University of Delaware's department. These deliverables address long-standing computational challenges in kinetic theory applications spanning supersonic flows, microelectromechanical systems, unconventional gas reservoirs, space vehicle re-entry, and nuclear fusion.