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Mean field games (MFG) and mean field control (MFC) are critical classes of multi-agent models for efficient analysis of massive populations of interacting agents.
A fast approach to optimal transport: the back-and-forth method
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Dynamic programming
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Introduction to Matrix Analysis (2Nd Ed.)
R. Bellman · 1997
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Partial differential equations and Monge-Kantorovich mass transfer
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A computational fluid mechanics solution to the Monge-Kantorovich mass transfer problem
J. D. Benamou and Y. Brenier · 2000
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Lecture notes on optimal transport problems
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Topics in Optimal Transportation
C. Villani · 2003
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Controlled Markov processes and viscosity solutions
W. H. Fleming and H. M. Soner · 2006
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Large population stochastic dynamic games: closed-loop McKean-Vlasov systems and the Nash certainty equivalence principle
M. Huang, R. P. Malhamé, and P. E. Caines · 2006
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On a Problem of Monge
L. V. Kantorovich · 2006
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Jeux à champ moyen. I. Le cas stationnaire
J.-M. Lasry and P.-L. Lions · 2006
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Jeux à champ moyen. II. Horizon fini et contrôle optimal
J.-M. Lasry and P.-L. Lions · 2006
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Numerical Optimization
J. Nocedal and S. Wright · 2006
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Large-population cost-coupled LQG problems with nonuniform agents: individual-mass behavior and decentralized ϵ \epsilon -Nash equilibria
M. Huang, P. E. Caines, and R. P. Malhamé · 2007
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Mean field games
J.-M. Lasry and P.-L. Lions · 2007
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Gradient flows in metric spaces and in the space of probability measures
L. Ambrosio, N. Gigli, and G. Savaré · 2008
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Optimal transport: old and new
C. Villani · 2008
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FAIR: flexible algorithms for image registration
J. Modersitzki · 2009
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Robust Stochastic Approximation Approach to Stochastic Programming
A. Nemirovski, A. Juditsky, G. Lan, and A. Shapiro · 2009
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Partial differential equations
L. C. Evans · 2010
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Mean field games and applications
O. Guéant, J.-M. Lasry, and P.-L. Lions · 2011
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On a mean field game approach modeling congestion and aversion in pedestrian crowds
A. Lachapelle and M.-T. Wolfram · 2011
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Finite difference methods for mean field games
Y. Achdou · 2013
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Mean field games and mean field type control theory
A. Bensoussan, J. Frehse, and P. Yam · 2013
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Partial differential equation models in macroeconomics
Y. Achdou, F. J. Buera, J.-M. Lasry, P.-L. Lions, and B. Moll · 2014
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Mean field games with nonlinear mobilities in pedestrian dynamics
M. Burger, M. Di Francesco, P. A. Markowich, and M.-T. Wolfram · 2014
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Adam: A method for stochastic optimization
D. P. Kingma and J. Ba · 2014
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A semi-Lagrangian scheme for a degenerate second order mean field game system
E. Carlini and F. J. Silva · 2015
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Existence of a solution to an equation arising from the theory of mean field games
W. Gangbo and A. Święch · 2015
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Economic models and mean-field games theory
D. A. Gomes, L. Nurbekyan, and E. A. Pimentel · 2015
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A Multilevel Method for the Solution of Time Dependent Optimal Transport
E. Haber and R. Horesh · 2015
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Variational Inference with Normalizing Flows
D. J. Rezende and S. Mohamed · 2015
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Mean field type control with congestion (II): An augmented Lagrangian method
Y. Achdou and M. Laurière · 2016
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First-order, stationary mean-field games with congestion
D. Evangelista, R. Ferreira, D. A. Gomes, L. Nurbekyan, and V. Voskanyan · 2018
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A mean-field game approach to price formation in electricity markets
D. A. Gomes and J. Saúde · 2018
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Solving high-dimensional partial differential equations using deep learning
J. Han, A. Jentzen, and W. E · 2018
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Flux: Elegant machine learning with julia
M. Innes · 2018
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Visualizing the loss landscape of neural nets
H. Li, Z. Xu, G. Taylor, and T. Goldstein · 2018
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Constrained dynamical optimal transport and its lagrangian formulation
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Regularity theory for mean-field game systems
D. A. Gomes, E. A. Pimentel, and V. Voskanyan · 2016
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Deep Learning Approximation for Stochastic Control Problems
J. Han and W. E · 2016
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Deep Residual Learning for Image Recognition
K. He, X. Zhang, S. Ren, and J. Sun · 2016
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Efficiency of the price formation process in presence of high frequency participants: a mean field game analysis
A. Lachapelle, J.-M. Lasry, C.-A. Lehalle, and P.-L. Lions · 2016
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Income and wealth distribution in macroeconomics: A continuous-time approach
Y. Achdou, J. Han, J.-M. Lasry, P.-L. Lions, and B. Moll · 2017
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Two numerical approaches to stationary mean-field games
N. Almulla, R. Ferreira, and D. Gomes · 2017
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W. Li and S. Osher · 2018
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Fourier approximation methods for first-order nonlocal mean-field games
L. Nurbekyan and J. Saúde · 2018
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DGM: A deep learning algorithm for solving partial differential equations
J. Sirignano and K. Spiliopoulos · 2018
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Deep mean field games for learning optimal behavior policy of large populations
J. Yang, X. Ye, R. Trivedi, H. Xu, and H. Zha · 2018
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Monge-Ampère Flow for Generative Modeling
L. Zhang, W. E, and L. Wang · 2018
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Mean field games for modeling crowd motion
Y. Achdou and J.-M. Lasry · 2019
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An entropy minimization approach to second-order variational mean-field games
J.-D. Benamou, G. Carlier, S. Di Marino, and L. Nenna · 2019
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On the implementation of a primal-dual algorithm for second order time-dependent mean field games with local couplings
L. Briceño Arias, D. Kalise, Z. Kobeissi, M. Laurière, A. Mateos González, and F. J. Silva · 2019
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The master equation and the convergence problem in mean field games
P. Cardaliaguet, F. Delarue, J.-M. Lasry, and P.-L. Lions · 2019
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R. Carmona and M. Laurière · 2019
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R. Carmona and M. Laurière · 2019
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Algorithmic trading in competitive markets with mean field games
P. Casgrain and S. Jaimungal · 2019
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Introduction to variational methods for viscous ergodic mean-field games with local coupling
A. Cesaroni and M. Cirant · 2019
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Algorithm for Hamilton–Jacobi equations in density space via a generalized Hopf formula
Y. T. Chow, W. Li, S. Osher, and W. Yin · 2019
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A mean field game approach for distributed control of thermostatic loads acting in simultaneous energy-frequency response markets
A. De Paola, V. Trovato, D. Angeli, and G. Strbac · 2019
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Layer-Parallel Training of Deep Residual Neural Networks
S. Günther, L. Ruthotto, J. B. Schroder, E. C. Cyr, and N. R. Gauger · 2019
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Solving Large-Scale Optimization Problems with a Convergence Rate Independent of Grid Size
M. Jacobs, F. Léger, W. Li, and S. Osher · 2019
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An integral control formulation of mean field game based large scale coordination of loads in smart grids
A. C. Kizilkale, R. Salhab, and R. P. Malhamé · 2019
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Fluid Flow Mass Transport for Generative Networks
J. Lin, K. Lensink, and E. Haber · 2019
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Computational optimal transport
G. Peyré and M. Cuturi · 2019
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Describing nonequilibrium soft matter with mean field game theory
P. M. Welch, K. Ø. Rasmussen, and C. F. Welch · 2019
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Potential Flow Generator with L 2
L. Yang and G. E. Karniadakis · 2019
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