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One of the most challenging problems in applied mathematics is the approximate solution of nonlinear partial differential equations (PDEs) in high dimensions.
On the branching process for Brownian particles with an absorbing boundary
Watanabe, S · 1907
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Branching diffusion processes
Skorohod, A. V · 1964
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Application of Brownian motion to the equation of Kolmogorov-Petrovskii-Piskunov
McKean, H. P · 1975
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Partial differential equations
John, F · 1982
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Functional analysis, Sobolev spaces and partial differential equations
Brezis, H · 2010
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Counterparty risk valuation: A marked branching diffusion approach
Henry-Labordere, P · 2012
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A numerical algorithm for a class of BSDEs via the branching process
Henry-Labordère, P., Tan, X., and Touzi, N · 2014
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Multilevel Picard iterations for solving smooth semilinear parabolic heat equations
E, W., Hutzenthaler, M., Jentzen, A., and Kruse, T · 2016
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Machine learning approximation algorithms for high-dimensional fully nonlinear partial differential equations and second-order backward stochastic differential equations
Beck, C., E, W., and Jentzen, A · 2017
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Numerical approximation of BSDEs using local polynomial drivers and branching processes
Bouchard, B., Tan, X., Warin, X., and Zou, Y · 2017
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Deep learning-based numerical methods for high-dimensional parabolic partial differential equations and backward stochastic differential equations
E, W., Han, J., and Jentzen, A · 2017
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The deep Ritz method: A deep learning-based numerical algorithm for solving variational problems
E, W., and Yu, B · 2017
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Deep reinforcement learning for partial differential equation control
Farahmand, A.-m., Nabi, S., and Nikovski, D. N · 2017
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Asymptotic expansion as prior knowledge in deep learning method for high dimensional BSDEs
Fujii, M., Takahashi, A., and Takahashi, M · 2017
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Deep primal-dual algorithm for BSDEs: Applications of machine learning to CVA and IM
Henry-Labordere, P · 2017
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Hutzenthaler, M., and Kruse, T · 2017
Cited alongside, same era.
PDE-Net: Learning PDEs from Data
Long, Z., Lu, Y., Ma, X., and Dong, B · 2017
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Solving stochastic differential equations and Kolmogorov equations by means of deep learning
Deep hidden physics models: Deep learning of nonlinear partial differential equations
Raissi, M · 2018
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DGM: A deep learning algorithm for solving partial differential equations
Sirignano, J., and Spiliopoulos, K · 2018
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Nesting Monte Carlo for high-dimensional non-linear PDEs
Warin, X · 2018
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Deep splitting method for parabolic PDEs
Andersson, A., Beck, C., Becker, S., Cheridito, P., Jentzen, A., and Neufeld, A · 2019
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On multilevel Picard numerical approximations for high-dimensional nonlinear parabolic partial differential equations and high-dimensional nonlinear backward stochastic differential equations
E, W., Hutzenthaler, M., Jentzen, A., and Kruse, T · 2019
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Beck, C., Becker, S., Grohs, P., Jaafari, N., and Jentzen, A · 2018
Cited alongside, same era.
Becker, S., Cheridito, P., and Jentzen, A · 2018
Cited alongside, same era.
A unified deep artificial neural network approach to partial differential equations in complex geometries
Berg, J., and Nyström, K · 2018
Cited alongside, same era.
Machine learning for semi linear PDEs
Chan-Wai-Nam, Q., Mikael, J., and Warin, X · 2018
Cited alongside, same era.
Solving high-dimensional partial differential equations using deep learning
Han, J., Jentzen, A., and E, W · 2018
Cited alongside, same era.
Convergence of the deep BSDE method for coupled FBSDEs
Han, J., and Long, J · 2018
Cited alongside, same era.
Hutzenthaler, M., Jentzen, A., Kruse, T., Nguyen, T. A., and von Wurstemberger, P · 2018
Cited alongside, same era.
Neural networks trained to solve differential equations learn general representations
Magill, M., Qureshi, F., and de Haan, H · 2018
Cited alongside, same era.
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Machine learning for pricing american options in high dimension
Goudenege, L., Molent, A., and Zanette, A · 2019
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Branching diffusion representation of semilinear PDEs and Monte Carlo approximation
Henry-Labordère, P., Oudjane, N., Tan, X., Touzi, N., and Warin, X · 2019
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Some machine learning schemes for high-dimensional nonlinear PDEs
Huré, C., Pham, H., and Warin, X · 2019
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Hutzenthaler, M., Jentzen, A., Kruse, T., and Nguyen, T. A · 2019
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Hutzenthaler, M., Jentzen, A., and von Wurstemberger, P · 2019
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Deep PPDEs for rough local stochastic volatility
Jacquier, A., and Oumgari, M · 2019
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Deep learning observables in computational fluid dynamics
Lye, K. O., Mishra, S., and Ray, D · 2019
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