Time: 3-4 pm Eastern Time, April 4 (Friday), 2025

Location: MSEE 112

Zoom Link: https://purdue-edu.zoom.us/j/98798335169

Coffee and snacks will be provide.

Computational Forward and Inverse Mean-Field Games: From Conventional Methods to Deep Generative Models

Abstract: 

Mean field game (MFG) problems study how a large number of similar rational agents make strategic movements to minimize their costs. They have recently gained great attention due to their connection to various problems, including optimal transport, gradient flow, path planning, deep generative models, and reinforcement learning. In this talk, I will discuss our recent computational efforts on MFGs and their inverse problems. I will begin with a low-dimensional setting,  employing conventional discretization and optimization methods. I will then extend the discussion to high-dimensional problems by bridging the trajectory representation of MFG with a special type of deep generative model—normalizing flows. This connection not only helps solve high-dimensional MFGs but also provides a way to improve the robustness of normalizing flows. Furthermore, I will extend the discussion to our recent work on supervised solution operator learning for MFG using transformers, enabling near real time inference for new tasks. I will further address its extension to its associated inverse problems for learning dynamics, where the cost function of MFGs may not be available, rendering the associated agent dynamics unavailable. To tackle this, we propose a bilevel optimization formulation for learning dynamics guided by MFGs with unknown obstacles and metrics. Our numerical experiments demonstrate the efficacy of the proposed methods.

Speaker:

Dr. Rongjie Lai received his Ph.D. in Applied Mathematics from UCLA. He was previously an associate professor at Rensselaer Polytechnic Institute before joining the Department of Mathematics at Purdue University as a full professor in 2023. His research spans computational mathematics, focusing on imaging, data science, and manifoldstructured data analysis through variational PDEs, computational differential geometry, and machine learning. He develops efficient numerical algorithms for solving variational PDEs and optimization problems. Recently, his work has expanded to the mathematical foundations of deep learning, emphasizing representation and generalization analysis, as well as mean-field control perspectives for deep generative models. Dr. Lai received the NSF CAREER Award in 2018.

Organizers: Ziran Wang (ziran@purdue.edu), Nak-seung Patrick Hyun (nhyun@purdue.edu), & Yan Gu (yangu@purdue.edu)