CAREER:Taming and exploiting uncertainty in complex systems: mean field games and diffusion generative models

Modern engineering and economic challenges often involve complex systems that push the limits of traditional approaches, driven by uncertainty and the high dimensionality of real-world data. Scientists in a variety of fields have unprecedented access to massive amounts of data which hinge on complex structures. Decision makers often need to optimize strategies involving large populations full of randomness. This project will address these challenges by developing principled approaches for analyzing and solving complex systems. The project will focus on developing innovations in stochastic control theory and artificial intelligence (AI) algorithms which will inform basic science, technology and economic questions arising in a broad range of disciplines. The results will be disseminated broadly across scientific communities and the general public. The project will also provide training opportunities for graduate students and AI literacy programming at the K-12 level. The project will focus on two interconnected research thrusts to address the aforementioned challenges, centered around the theoretical foundations of stochastic control and games. The first thrust involves studying mean field games (MFGs), which are used to model the macroscopic profile of large interacting systems, unraveling high degrees of freedom of these systems and enhancing tractability of large-scale problems. The goal is to build a quantitative theory for first-order MFGs in response to a surge of interest in modeling large systems with strong signals. Both theoretical and numerical challenges will be addressed, and the project will focus on direct applications in statistical physics and decentralized finance. The second thrust involves advancing generative AI to help mitigate uncertainty in the design of large-scale systems, and provide data-driven insights to identify unforeseen challenges in these systems. The goal of this second part of the project is to build a rigorous mathematical paradigm for diffusion generative models in the context of diffusion model alignment from the perspective of control theory, leading to principled algorithms for generating large, goal-specific data. 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: 2538791 | Program: 01003031DB NSF RESEARCH & RELATED ACTIVIT,01002627DB NSF RESEARCH & RELATED ACTIVIT,01002930DB NSF RESEARCH & RELATED ACTIVIT | Principal Investigator: Wenpin Tang | Institution: Columbia University, NEW YORK, NY | Award Amount: $253,570 View on NSF Award Search: https://www.nsf.gov/awardsearch/show-award/?AWD_ID=2538791 View on Research.gov: https://www.research.gov/awardapi-service/v1/awards/2538791.html