Assistant Professor Yulong Lu earns NSF CAREER award
MINNEAPOLIS / ST. PAUL (7/1/2025) – Assistant Professor Yulong Lu of the School of Mathematics has recently earned the Faculty Early Career Development Program (CAREER) award from the National Science Foundation. CAREER Awards support early-career faculty who have the potential to serve as academic role models in research and education and to lead advances in the mission of their department or organization. Lu is the third School of Mathematics faculty member to receive a CAREER Award in the past two years.
Through his CAREER project, Lu will explore Generative Artificial Intelligence (GenAI). GenAI represents an emerging AI paradigm capable of creating novel content, such as images and text. As demonstrated by models like ChatGPT, GenAI is quickly becoming a transformative force across society, science, and technology. Beyond their initial applications in image and text generation, GenAI models provide versatile tools driving significant breakthroughs across the spectrum of science. However, their rapid advancement has introduced fundamental theoretical challenges that are largely unaddressed.
The primary goal of Lu’s project is to establish the mathematical foundations of two influential models that underpin the cutting-edge GenAI methodologies in a number of scientific contexts: score-based generative models and transformer-based foundation models. The project will utilize and develop mathematical tools for examining the generative capabilities of score-based generative models in high dimensions and understanding the predictive capabilities and limitations of transformers in solving a broad range of scientific problems. These fundamental understandings will be critical for developing scientifically reliable and socially responsible AI systems. The project will also support undergraduate and graduate students through research mentorship and education in the mathematical foundations of GenAI.
Lu joined the University of Minnesota faculty in Fall 2023. Prior to his appointment at UMN, he was an Assistant Professor in the Department of Mathematics and Statistics at the University of Massachusetts, Amherst. His primary research interests lie at the intersection between applied and computational mathematics, statistics, and data science. His recent research is focused on the interplay between deep learning (DL) and partial differential equations (PDEs). While DL has shown impressive success in solving scientific problems modeled by PDEs, its theoretical foundations remain incomplete. One aspect of Lu’s work aims to develop rigorous error analysis for DL solvers in high-dimensional PDEs. In another vein of his research, he explores how PDEs can be used as powerful tools to analyze different machine learning architectures and algorithms.