Federal Project Grant Award Summary

The University of Houston is developing a learning-augmented mathematical and computational framework for multi-level multiscale modeling of flow in porous media under a $199,000 Project Grant from the National Science Foundation (NSF) Division of Mathematical Sciences (CFDA 47.049). The research integrates machine learning with multiscale modeling techniques to create reduced models that accurately capture complex flow dynamics across multiple scales—from microscopic pore-level interactions to large-scale subsurface transport. The framework augments traditional reduced models with supplemental equation-variable pairs learned from heterogeneous datasets, including high-fidelity simulations and observational measurements, while maintaining computational efficiency and physical interpretability. The project emphasizes developing algorithms for data integration, analyzing model expressiveness and stability, and establishing theoretical foundations for approximating broad classes of partial differential operators.

Beyond research deliverables, the award supports workforce development through training in applied mathematics, machine learning, and high-performance computing. The project includes outreach and mentoring activities designed to broaden participation in computational science and engineering. The award runs from July 1, 2026, through June 30, 2029, and advances NSF's Mathematical and Physical Sciences program objective to promote progress in mathematical research while strengthening the Nation's scientific enterprise and addressing critical national priorities in sustainable energy and environmental resilience, particularly carbon storage and groundwater management applications.