A Learning-Augmented Framework for Multi-Level Multiscale Modeling

Flow in porous media is a fundamental multiscale problem central to energy and environmental applications such as carbon storage and groundwater management. These processes involve complex interactions across scales, from microscopic pore-scale dynamics to large-scale subsurface transport, making accurate prediction challenging. Existing large-scale models often rely on simplified assumptions that fail to capture important fine-scale physical behavior, limiting predictive reliability. This project seeks to develop mathematical and computational approaches that combine multiscale modeling with machine learning to improve reduced models for complex flow systems. The research will develop data-informed models that remain computationally efficient while preserving physical interpretability. The project will advance AI-enhanced scientific computing while supporting national priorities in sustainable energy and environmental resilience. It will also support workforce development through training in applied mathematics, machine learning, and high-performance computing, while outreach and mentoring activities will broaden participation in computational science and engineering. The project will develop a multi-level multiscale modeling framework that augments reduced models with supplemental equation-variable pairs learned from data. Building on multicontinuum homogenization, the framework will systematically incorporate unresolved fine-scale effects into coarse-scale flow descriptions. The research will investigate algorithms for integrating heterogeneous datasets with varying resolutions and physical meanings, including high-fidelity simulations and observational measurements. It will also analyze the expressive capacity and stability of the resulting models, establishing theoretical foundations for approximating broad classes of partial differential operators. Additional efforts will focus on feature extraction, complexity control, and scalable optimization strategies. The resulting methods are expected to produce accurate, interpretable, and computationally efficient models for multiscale flow and transport problems, together with open-source software tools for broader scientific and engineering applications. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria. NSF Award ID: 2603912 | Program: 01002627DB NSF RESEARCH & RELATED ACTIVIT | Principal Investigator: Min Wang | Institution: University of Houston, HOUSTON, TX | Award Amount: $199,000 View on NSF Award Search: https://www.nsf.gov/awardsearch/show-award/?AWD_ID=2603912 View on Research.gov: https://www.research.gov/awardapi-service/v1/awards/2603912.html