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We propose a deep learning approach to compute mean field control problems with individual noises.
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Carmona, R., Delarue, F.: Forward–-backward stochastic differential equations and controlled mckean–-vlasov dynamics. The Annals of Probability 43
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Carmona, R.A., Fouque, J.P., Sun, L.H.: Mean field games and systemic risk. Communications in Mathematical Sciences 13
2015
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Bauso, D., Tembine, H., Basar, T.: Opinion dynamics in social networks through mean-field games. SIAM Journal on Control and Optimization 54
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Carmona, R., Delarue, F., et al
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Elamvazhuthi, K., Berman, S.: Mean-field models in swarm robotics: A survey. Bioinspiration Biomimetics 15
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Beck, C., E, W., Jentzen, A.: Machine learning approximation algorithms for high-dimensional fully nonlinear partial differential equations and second-order backward stochastic differential equations. Journal of Nonlinear Science 29
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Cardaliaguet, P., Delarue, F., Lasry, J.-M., Lions, P.-L.: The Master Equation and the Convergence Problem in Mean Field Games:(ams-201). Princeton University Press (2019)
2019
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2020
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Ruthotto, L., Osher, S.J., Li, W., Nurbekyan, L., Fung, S.W.: A machine learning framework for solving high-dimensional mean field game and mean field control problems. Proceedings of the National Academy of Sciences 117
2020
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Ji, S., Peng, S., Peng, Y., Zhang, X.: Three algorithms for solving high-dimensional fully coupled fbsdes through deep learning. IEEE Intelligent Systems 35
2020
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Song, Y., Sohl-Dickstein, J., Kingma, D.P., Kumar, A., Ermon, S., Poole, B.: Score-based generative modeling through stochastic differential equations. In: International Conference on Learning Representations (2020)
2020
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2022
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Li, W., Liu, S., Osher, S.: Controlling conservation laws ii: Compressible navier–stokes equations. Journal of Computational Physics 463
2022
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Li, W., Lee, W., Osher, S.: Computational mean-field information dynamics associated with reaction-diffusion equations. Journal of Computational Physics 466
2022
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Angiuli, A., Fouque, J.-P., Laurière, M.: Unified reinforcement q-learning for mean field game and control problems. Mathematics of Control, Signals, and Systems 34
2022
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Han, J., Lu, J., Zhou, M.: Solving high-dimensional eigenvalue problems using deep neural networks: A diffusion monte carlo like approach. Journal of Computational Physics 423
2020
Cited alongside, same era.
Raynal, P.-E.C., Frikha, N.: From the backward kolmogorov pde on the wasserstein space to propagation of chaos for mckean-vlasov sdes. Journal de Mathématiques Pures et Appliquées 156
2021
Cited alongside, same era.
Zhou, M., Han, J., Lu, J.: Actor-critic method for high dimensional static hamilton–jacobi–bellman partial differential equations based on neural networks. SIAM Journal on Scientific Computing 43
2021
Cited alongside, same era.
Carmona, R., Laurière, M.: Convergence analysis of machine learning algorithms for the numerical solution of mean field control and games i: The ergodic case. SIAM Journal on Numerical Analysis 59
2021
Cited alongside, same era.
Villani, C.: Topics in Optimal Transportation vol. 58. American Mathematical Soc. (2021)
2021
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2021
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Germain, M., Mikael, J., Warin, X.: Numerical resolution of mckean-vlasov fbsdes using neural networks. Methodology and Computing in Applied Probability 24
2022
Cited alongside, same era.
2022
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Carmonaa, R., Laurièrea, M.: Deep learning for mean field games and mean field control with applications to finance. Machine Learning and Data Sciences for Financial Markets: A Guide to Contemporary Practices, 369 (2023)
2023
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Boffi, N.M., Vanden-Eijnden, E.: Probability flow solution of the fokker–planck equation. Machine Learning: Science and Technology 4
2023
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Li, W., Liu, S., Osher, S.: Controlling conservation laws i: Entropy–entropy flux. Journal of Computational Physics 480
2023
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2023
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