Project Grant 2608776

Federal Grant Award Summary

The National Science Foundation's Division of Mathematical Sciences awarded a $350,000 Project Grant to the University of Pennsylvania (award date: June 15, 2026; completion date: May 31, 2029) under the Mathematical and Physical Sciences program (CFDA 47.049). This collaborative research initiative develops physics-preserving machine learning architectures designed to learn reduced Partial Differential Equation (PDE) models that incorporate constrained tensors used in complex physical systems. The research delivers structure-preserving Scientific Machine Learning (SciML) models that embed geometric and physical constraints directly into artificial intelligence architectures, enabling simulators to operate thousands of times faster than traditional computational methods while maintaining accuracy and physical reliability.

The project produces computational tools and methodologies applicable to aerospace, materials science, and energy sectors by creating digital twins for complex systems governed by PDEs with tensorial constraints—such as stress and strain tensors in linear elasticity, deviatoric stress, and internal stress configurations. Beyond core research deliverables, the award supports workforce development by training scientists across high school, undergraduate, and graduate levels at the intersection of computational mathematics and machine learning, directly advancing federal strategic interests in artificial intelligence and advanced manufacturing while strengthening the nation's scientific enterprise in mathematical and physical sciences.