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Applied Mathematics Colloquium – Rongjie Lai, Purdue University

April 24 @ 4:00 pm - 5:00 pm

Title: Unsupervised Solution Operator Learning for Mean-Field Games

Speaker: Rongjie Lai, Department of Mathematics, Purdue University

Abstract: Recent advances in deep learning have introduced numerous innovative frameworks for solving high-dimensional mean-field games (MFGs). However, these methods are often limited to solving single-instance MFGs and require extensive computational time for each instance, presenting challenges for practical applications.

In this talk, I will present our recent work on a novel framework for learning the MFG solution operator. Our model takes MFG instances as input and directly outputs their solutions in a single forward pass, significantly improving computational efficiency. Our method offers two key advantages: (1) it is discretization-free, making it particularly effective for high-dimensional MFGs, and (2) it can be trained without requiring supervised labels, thereby reducing the computational burden of preparing training datasets common in existing operator learning methods. If time permits, I will also explore connections between this framework and in-context learning, highlighting its broader implications and potential for further advancements.

Details

Date:
April 24
Time:
4:00 pm - 5:00 pm
Event Category: