Energy-Stable Neural Basis Methods for Multiscale Porous Media Flow

Many important physical systems involve complex processes spanning multiple physical scales, including those arising in carbon storage, hydrogen containment, and groundwater management. Accurate prediction of these systems is essential for sustainable energy technologies, environmental protection, and national economic competitiveness. Over the past decade, physics-informed artificial intelligence methods have shown strong potential for accelerating scientific discovery and enabling rapid simulation of complex physical processes. However, existing approaches often lose accuracy and stability when applied to realistic multiscale systems. This project develops a new class of scientifically grounded artificial intelligence methods for reliable modeling of complex fluid flow and transport phenomena. The work advances foundational research at the intersection of computational mathematics, artificial intelligence, and scientific computing, supporting national priorities in AI-enabled scientific discovery and high-performance computing. The project will also train graduate and undergraduate students through research, mentoring, outreach, and open-source software development, strengthening the nation’s technical workforce in artificial intelligence and computational science. The project develops an energy-stable neural basis framework for multiscale partial differential equations arising in porous media flow and transport. The research addresses fundamental limitations in physics-informed machine learning approaches by identifying how inappropriate residual metrics degrade approximation quality and stability in multiscale settings. Building on Petrov-Galerkin theory and classical numerical analysis, the project develops operator-aware, energy-consistent residual formulations with expressive neural basis representations. Fractional Sobolev boundary treatments are further incorporated to achieve physically faithful and efficient approximations with reduced mesh dependence and computational complexity. The research further extends to parametric systems through enhanced learning of mappings between physical parameters and neural solution coefficients, enabling stable, accurate, and fast predictions. Additional investigations will address coupled flow-transport dynamics and applications beyond porous media flow. The resulting framework aims to establish a mathematically grounded and scalable paradigm for AI-enabled simulation of multiscale physical systems. 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: 2608740 | Program: 01002627DB NSF RESEARCH & RELATED ACTIVIT | Principal Investigator: Min Wang | Institution: University of Houston, HOUSTON, TX | Award Amount: $300,000 View on NSF Award Search: https://www.nsf.gov/awardsearch/show-award/?AWD_ID=2608740 View on Research.gov: https://www.research.gov/awardapi-service/v1/awards/2608740.html