Federal Grant Award Summary

The University of Illinois received a $349,985 Project Grant from the National Science Foundation's Division of Mathematical Sciences (CFDA 47.049) awarded on June 15, 2026, with completion targeted for May 31, 2029. This collaborative research initiative develops physics-preserving machine learning models that embed geometric and physical constraints directly into artificial intelligence architectures to solve partial differential equations (PDEs) with tensorial constraints. The research focuses on creating structure-preserving scientific machine learning architectures capable of learning reduced PDE models that incorporate constrained tensors—such as stress and strain tensors in linear elasticity, deviatoric stress tensors, and internal stress tensors—using higher-order differential complexes formulated through De Rham complexes and Bernstein-Gelfand-Gelfand techniques.

The project delivers advanced computational simulators that operate thousands of times faster than traditional methods while maintaining accuracy and physical reliability by design. These physics-informed AI models support federal strategic interests in artificial intelligence and advanced manufacturing by enabling the creation of real-time, highly accurate digital twins for complex systems in aerospace, materials science, and energy sectors. Additionally, the research supports workforce development across high school, undergraduate, and graduate education levels at the intersection of computational mathematics and machine learning, positioning the work to strengthen the nation's scientific enterprise in emerging computational disciplines.