Scalable Learning for Spatiotemporal Mean Field Games Using Physics-Informed Neural Operator

Shuo Liu, Xu Chen and Xuan Di ()
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Shuo Liu: Department of Computer Science, Columbia University, New York, NY 10027, USA
Xu Chen: Department of Civil Engineering and Engineering Mechanics, Columbia University, New York, NY 10027, USA
Xuan Di: Department of Civil Engineering and Engineering Mechanics, Columbia University, New York, NY 10027, USA

Mathematics, 2024, vol. 12, issue 6, 1-11

Abstract: This paper proposes a scalable learning framework to solve a system of coupled forward–backward partial differential equations (PDEs) arising from mean field games (MFGs). The MFG system incorporates a forward PDE to model the propagation of population dynamics and a backward PDE for a representative agent’s optimal control. Existing work mainly focus on solving the mean field game equilibrium (MFE) of the MFG system when given fixed boundary conditions, including the initial population state and terminal cost. To obtain MFE efficiently, particularly when the initial population density and terminal cost vary, we utilize a physics-informed neural operator (PINO) to tackle the forward–backward PDEs. A learning algorithm is devised and its performance is evaluated on one application domain, which is the autonomous driving velocity control. Numerical experiments show that our method can obtain the MFE accurately when given different initial distributions of vehicles. The PINO exhibits both memory efficiency and generalization capabilities compared to physics-informed neural networks (PINNs).

Keywords: mean field game; scalable learning; physics-informed neural operator (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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