Project Grant 2608930

The National Science Foundation Division of Mathematical Sciences awarded the University of Alabama $229,586 on October 1, 2026, under the Mathematical and Physical Sciences program (CFDA 47.049) to develop neural network-enhanced reduced order modeling methods for solving partial differential equations with high dimensionality, randomness, nonlinear behavior, and multiscale features.

The research combines reduced order model stability and efficiency with neural network flexibility to accelerate simulations of physical systems—including heat transfer, gas dispersion, fluid flow through complex materials, and environmental conditions affecting autonomous robots—while maintaining accuracy and consistency with governing physical principles. The work addresses computational bottlenecks that arise when systems include many variables, uncertain inputs, changing conditions, or small-scale details strongly affecting overall behavior.

The project runs through September 30, 2029, with performance at the University of Alabama in Tuscaloosa, Alabama. Beyond research advancement, the award supports education and workforce development through training of graduate and undergraduate students in computational mathematics, numerical methods, machine learning, and data science; incorporation of research outcomes into courses and seminars; summer research experiences; and mathematics outreach to local students. The funding is classified as a Project Grant, an assistance type delivering basic or applied research.