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Machine learning methods for solving nonlinear partial differential equations (PDEs) are hot topical issues, and different algorithms proposed in the literature show efficient numerical approximation in high dimension.
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“Deep learning-based numerical methods for high-dimensional parabolic partial differential equations and backward stochastic differential equations”
W. E, J. Han and A. Jentzen · 2017
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“Limit theory for controlled McKean-Vlasov dynamics”
D. Lacker · 2017
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“Dynamic programming for optimal control of stochastic McKean-Vlasov dynamics”
H. Pham and X. Wei · 2017
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C. R., H. Su, K. Mo and L. J · 2017
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M. Zaheer, S. Kottur, S. Ravanbakhsh, B. Poczos, R. Salakhutdinov and A. Smola · 2017
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“Probabilistic Theory of Mean Field Games: vol. I, Mean Field FBSDEs, Control, and Games,”
R. Carmona and F. Delarue · 2018
“On the Limitations of Representing Functions on Sets”
E. Wagstaff, F. Fuchs, M. Engelcke, I. Posner and M.. Osborne · 2019
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“An overview on deep learning-based approximation methods for partial differential equations”
C. Beck, M. Hutzenthaler, A. Jentzen and B. Kuckuck · 2020
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B. Bloem-Reddy and Y.W. Teh · 2020
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F Djete · 2020
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J.-P. Fouque and Z. Zhang · 2020
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“Probabilistic Theory of Mean Field Games: vol. II, Mean Field FBSDEs, Control, and Games,”
R. Carmona and F. Delarue · 2018
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“Solving high-dimensional partial differential equations using deep learning”
J. Han, A. Jentzen and E Weinan · 2018
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“A weak martingale approach to linear-quadratic McKean-Vlasov stochastic control problem”
M. Basei and H. Pham · 2019
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R. Carmona and M. Lauri“‘ere · 2019
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“Machine Learning for Semi Linear PDEs”
Q. Chan-Wai-Nam, J. Mikael and X. Warin · 2019
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“Numerical resolution of McKean-Vlasov FBSDEs using neural networks”
M. Germain, J. Mikael and X. Warin · 2019
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C. Hur“’e, H. Pham and X. Warin · 2020
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“A proof that rectified deep neural networks overcome the curse of dimensionality in the numerical approximation of semilinear heat equation”
M. Hutzenthaler, A. Jentzen, T. Kruse and T.A. Nguyen · 2020
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“A machine learning framework for solving high-dimensional mean field game and mean field control problems”
L. Ruthotto, S.. Osher, W. Li, L. Nurbekyan and S.. Fung · 2020
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“Finite Dimensional Approximations of Hamilton–Jacobi–Bellman Equations in Spaces of Probability Measures”
W. Gangbo, S. Mayorga and A. Swiech · 2021
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“Neural networks-based backward scheme for fully nonlinear PDEs.”
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