Mean-Field Games: From Partial Differential Equations to Numerical Methods
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Organizer(s): |
Name:
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Affiliation:
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Country:
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Diogo Gomes
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King Abdullah University of Science and Technology
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Saudi Arabia
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Alpar Meszaros
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Durham University
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England
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Marco Cirant
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University of Padova
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Italy
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Introduction:
| | This special session focuses on the interplay between the mathematical analysis and the numerical approximation of Mean-Field Games (MFG). The session will cover a broad spectrum of recent advances, ranging from the fundamental theory of MFG systems, including the well-posedness of Master equations, regularity results for Hamilton-Jacobi-Bellman and Fokker-Planck systems, and weak solution concepts based on monotone operator theory, to the rigorous development of computational schemes.
Particular attention will be devoted to the interface between PDEs and numerics, with talks on finite element methods, splitting algorithms, and optimization-based approaches for stationary and time-dependent problems, including those with non-smooth Hamiltonians. The session will also explore asymptotic regimes, such as the mean-field limit of interacting particle systems, flocking models, and convergence analysis in the Wasserstein space. By convening experts in partial differential equations, control theory, and numerical analysis, this session aims to address open challenges in designing novel algorithms that preserve the theoretical properties of the underlying mean-field models.
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