PhysicsInformed Graph Neural Operator for Mean Field Games on Graph: A Scalable Learning Approach
Abstract
:1. Introduction
Related Work
2. Background
2.1. MeanField Games on Graphs ($\mathcal{G}$MFG)
2.2. Graph Neural Operator (GNO)
3. Scalable Learning Framework
3.1. PIGNO for Population Behaviors
3.2. PIGNO for Optimal Control
4. Solution Approach
Algorithm 1 PIGNOMFG 

5. Numerical Experiments
6. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
Appendix A
Appendix A.1. Mean Field Games on Graph
Appendix A.2. Toy Example
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Chen, X.; Liu, S.; Di, X. PhysicsInformed Graph Neural Operator for Mean Field Games on Graph: A Scalable Learning Approach. Games 2024, 15, 12. https://doi.org/10.3390/g15020012
Chen X, Liu S, Di X. PhysicsInformed Graph Neural Operator for Mean Field Games on Graph: A Scalable Learning Approach. Games. 2024; 15(2):12. https://doi.org/10.3390/g15020012
Chicago/Turabian StyleChen, Xu, Shuo Liu, and Xuan Di. 2024. "PhysicsInformed Graph Neural Operator for Mean Field Games on Graph: A Scalable Learning Approach" Games 15, no. 2: 12. https://doi.org/10.3390/g15020012