KINGSTON, RI – Oct. 16, 2024 – The mathematics department at the College of Arts and Sciences has received two substantial grants from the National Science Foundation. Both grants are related to the cutting edge research in big data and artificial intelligence. 

“Our Department is very proud of Kelum and Nhu and their grant-supported research on the cutting edge of the ongoing revolution in the computational sciences. We are happy that our young faculty members have found a nurturing environment at URI where they can thrive,” said Dr. Barbara Kaskosz, chair of the math department. 

Hadamard Deep Autoencoders and Alternating Directional Methods of Multipliers for Manifold Learning Enabled Distance Preserving Matrix Completion by Dr. Kelum Gajamannage’s will receive a $250K grant. Gajamannage’s research encompasses Matrix Completion (MC),  a technique of imputing missing entries of a partially observed data matrix . 

MC frameworks have “limited transferability and robustness” when applied in diverse domains as this method does not consider the natural correlation of data. Gajamannage’s research intends to optimize these processes by transitioning the MC framework to be both highly transferable and a system that can harness the natural correlation of data. His approach will include efficient low-rank matrix algebra and high-precision Deep Neural Network (DNN). The proposed frameworks  being validated by theoretical analysis, and both synthetic and real-world benchmark datasets.

“I am thrilled to have received this sole-PI NSF research grant which enhances both the mathematical foundations of my machine learning research and the pedagogy of my data science courses,” said Gajamannage.

This project is jointly funded by the Launching Early-Career Academic Pathways in the Mathematical and Physical Sciences Program and the Established Program to Stimulate Competitive Research. 

Collaborative Research: Stochastic Functional Systems: Analysis, Algorithms and Applications by Dr. Nhu Nguyen will receive a $200K grant. Nguyen’s research aims to systematically investigate modeling systems to establish their critical properties, broaden current applications, and discover new applications in science, machine learning, and data science.

The modeling systems in question include classics like stochastic functional differential equations (SFDE), McKean-Vlasov stochastic functional differential equations (MVSFDE), and an emerging interest in functional stochastic approximation algorithms (FSAA).The future state of these systems is not determined by its present state, but also by the state of the system at prior periods of time. In the past, these systems have been used to measure epidemic and ecological models, multi-agent models in financial systems, neural network models, and other areas in statistics, data science, and engineering.

The project will provide research opportunities for graduate students, engage high school students through math tournaments, and work towards creating a network of academia, students, and industry representatives to enhance career opportunities for students and increase public awareness of the role of mathematics in real-world applications.