Collaborative Research: RTG: Building a robust mathematical foundation for AI and integrated data science at Auburn and Tuskegee University

Artificial intelligence (AI) and data science are revolutionizing the way complex systems are modeled, data is analyzed, and decisions are made across science, technology, and industry. There is a growing need to train researchers with a rigorous mathematical foundation to ensure that AI and data-driven methods are reliable, efficient, and adaptable to real-world challenges. This Research Training Group (RTG) project will train undergraduate students, graduate students, and postdoctoral researchers to conduct advanced research at the intersection of mathematics, AI, and data science. Through a structured program of interdisciplinary research, AI and Data Science summer school, seminars, and industry-partnered projects, participants will acquire the mathematical, computational, and analytical tools necessary to contribute to the future of AI and data science, both in theory and in practice. The project centers on three integrated research modules: (1) diffusion modeling for generative AI, (2) topological data analysis (TDA) for complex datasets, and (3) partial differential equation-based machine learning for anomaly detection. These modules pair fundamental mathematics with application areas including wireless communications, medical imaging, and cybersecurity. By rotating through all three modules, trainees will develop a comprehensive skill set on stochastic modeling, algebraic topology, inverse problems, and algorithmic implementation. The program emphasizes both conceptual understanding and hands-on experience through research, capstone projects, and collaboration with industry. Trainees of this project will be prepared to lead in the development and application of mathematically grounded methods in AI and data science. 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.