Fetching the paper…
Reading the bibliography…
It is one of the most challenging problems in applied mathematics to approximatively solve high-dimensional partial differential equations (PDEs).
Martin Hutzenthaler, Arnulf Jentzen, Thomas Kruse and Tuan Nguyen · 1901
Earlier work this paper cites.
“Some machine learning schemes for high-dimensional nonlinear PDEs”
C. Huré, H. Pham and X. Warin · 1902
Earlier work this paper cites.
“Machine Learning for Pricing American Options in High Dimension”
Ludovic Goudenège, Andrea Molent and Antonino Zanette · 1903
Earlier work this paper cites.
Martin Hutzenthaler, Arnulf Jentzen and Philippe von Wurstemberger · 1903
Earlier work this paper cites.
“Deep learning observables in computational fluid dynamics”
Kjetil. Lye, Siddhartha Mishra and Deep Ray · 1903
Earlier work this paper cites.
Christoph Reisinger and Yufei Zhang · 1903
Earlier work this paper cites.
“A Discussion on Solving Partial Differential Equations using Neural Networks”
Tim Dockhorn · 1904
Earlier work this paper cites.
“A Theoretical Analysis of Deep Neural Networks and Parametric PDEs”
Gitta Kutyniok, Philipp Petersen, Mones Raslan and Reinhold Schneider · 1904
Earlier work this paper cites.
“Deep PPDEs for rough local stochastic volatility”
Antoine Jacquier and Mugad Oumgari · 1906
Earlier work this paper cites.
“Deep splitting method for parabolic PDEs”
Christian Beck et al · 1907
Earlier work this paper cites.
Christian Beck et al · 1907
Earlier work this paper cites.
“On existence and uniqueness properties for solutions of stochastic fixed point equations”
Christian Beck, Lukas Gonon, Martin Hutzenthaler and Arnulf Jentzen · 1908
Earlier work this paper cites.
“Solving high-dimensional optimal stopping problems using deep learning”
Sebastian Becker, Patrick Cheridito, Arnulf Jentzen and Timo Welti · 1908
Earlier work this paper cites.
“Space-time error estimates for deep neural network approximations for differential equations”
Philipp Grohs, Fabian Hornung, Arnulf Jentzen and Philipp Zimmermann · 1908
Earlier work this paper cites.
“Deep neural network approximations for Monte Carlo algorithms”
Philipp Grohs, Arnulf Jentzen and Diyora Salimova · 1908
Earlier work this paper cites.
“Neural networks-based backward scheme for fully nonlinear PDEs”
H. Pham and X. Warin · 1908
Earlier work this paper cites.
Yangang Chen and Justin.. Wan · 1909
Earlier work this paper cites.
“Dynamic programming”
Richard Bellman · 1957
Earlier work this paper cites.
“Branching diffusion processes”
A.. Skorohod · 1964
Earlier work this paper cites.
“On the branching process for Brownian particles with an absorbing boundary”
Shinzo Watanabe · 1965
Earlier work this paper cites.
“Application of Brownian motion to the equation of Kolmogorov-Petrovskii-Piskunov”
H.. McKean · 1975
Earlier work this paper cites.
“A course in functional analysis” 96
John. Conway · 1990
Earlier work this paper cites.
“Stochastic equations in infinite dimensions” 44
Giuseppe Da and Jerzy Zabczyk · 1992
Earlier work this paper cites.
“Solving forward-backward stochastic differential equations explicitly—a four step scheme”
Jin Ma, Philip Protter and Jiongmin Yong · 1994
Earlier work this paper cites.
“Numerical methods for forward-backward stochastic differential equations”
Jim Douglas., Jin Ma and Philip Protter · 1996
Earlier work this paper cites.
“Forward-backward stochastic differential equations and their applications” 1702
Jin Ma and Jiongmin Yong · 1999
Earlier work this paper cites.
“Difference equations and inequalities” Theory, methods, and applications 228
Ravi. Agarwal · 2000
Earlier work this paper cites.
“Numerical method for backward stochastic differential equations”
Jin Ma, Philip Protter, Jaime Sanín and Soledad Torres · 2002
Earlier work this paper cites.
“A quantization algorithm for solving multi-dimensional discrete-time optimal stopping problems”
Vlad Bally and Gilles Pagès · 2003
Earlier work this paper cites.
“Discrete-time approximation and Monte-Carlo simulation of backward stochastic differential equations”
Bruno Bouchard and Nizar Touzi · 2004
Earlier work this paper cites.
“A numerical scheme for BSDEs”
Jianfeng Zhang · 2004
Earlier work this paper cites.
“A regression-based Monte Carlo method to solve backward stochastic differential equations”
E. Gobet, J.-P. Lemor and X. Warin · 2005
Earlier work this paper cites.
“Infinite dimensional analysis” A hitchhiker’s guide
Charalambos. Aliprantis and Kim. Border · 2006
Earlier work this paper cites.
“A forward-backward stochastic algorithm for quasi-linear PDEs”
François Delarue and Stéphane Menozzi · 2006
Earlier work this paper cites.
“Rate of convergence of an empirical regression method for solving generalized backward stochastic differential equations”
Jean-Philippe Lemor, Emmanuel Gobet and Xavier Warin · 2006
Earlier work this paper cites.
“Numerical algorithms for forward-backward stochastic differential equations”
G.. Milstein and M.. Tretyakov · 2006
Cited alongside, same era.
“A forward scheme for backward SDEs”
Christian Bender and Robert Denk · 2007
Cited alongside, same era.
“Discretization of forward-backward stochastic differential equations and related quasi-linear parabolic equations”
G.. Milstein and M.. Tretyakov · 2007
Cited alongside, same era.
“Numerical simulation of BSDEs using empirical regression methods: theory and practice”
E. Gobet and J.-P. Lemor · 2008
Cited alongside, same era.
“Tractability of multivariate problems. Vol. 1: Linear information” 6
Erich Novak and Henryk Woźniakowski · 2008
Cited alongside, same era.
“Monte Carlo solution of Cauchy problem for a nonlinear parabolic equation”
Ankush Agarwal and Julien Claisse · 2017
Later among the works it cites.
“A primal-dual algorithm for BSDEs”
Christian Bender, Nikolaus Schweizer and Jia Zhuo · 2017
Later among the works it cites.
“Hybrid PDE solver for data-driven problems and modern branching”
Francisco Bernal, Gonçalo dos Reis and Greig Smith · 2017
Later among the works it cites.
“Numerical approximation of BSDEs using local polynomial drivers and branching processes”
Bruno Bouchard, Xiaolu Tan, Xavier Warin and Yiyi Zou · 2017
Later among the works it cites.
“Deep learning-based numerical methods for high-dimensional parabolic partial differential equations and backward stochastic differential equations”
Weinan E, Jiequn Han and Arnulf Jentzen · 2017
Later among the works it cites.
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
A. Rasulov, G. Raimova and M. Mascagni · 2009
Cited alongside, same era.
“Probabilistic methods for semilinear partial differential equations. Applications to finance”
D. Crisan and K. Manolarakis · 2010
Cited alongside, same era.
“On the Monte Carlo simulation of BSDEs: an improvement on the Malliavin weights”
D. Crisan, K. Manolarakis and N. Touzi · 2010
Cited alongside, same era.
“Solving BSDE with adaptive control variate”
E. Gobet and C. Labart · 2010
Cited alongside, same era.
“Tractability of multivariate problems. Volume II: Standard information for functionals” 12
Erich Novak and Henryk Woźniakowski · 2010
Cited alongside, same era.
“Solving backward stochastic differential equations using the cubature method: application to nonlinear pricing”
D. Crisan and K. Manolarakis · 2012
Cited alongside, same era.
“Counterparty Risk Valuation: A Marked Branching Diffusion Approach”
Pierre Henry-Labordère · 2012
Cited alongside, same era.
“Deep reinforcement learning for partial differential equation control”
Amir-massoud Farahmand, S. Nabi and D.. Nikovski · 2017
Later among the works it cites.
“Deep Primal-Dual Algorithm for BSDEs: Applications of Machine Learning to CVA and IM”, 2017, pp. 16 pages
Pierre Henry-Labordère · 2017
Later among the works it cites.
Martin Hutzenthaler and Thomas Kruse · 2017
Later among the works it cites.
“A Dual Method For Backward Stochastic Differential Equations with Application to Risk Valuation”
Andrzej Ruszczynski and Jianing Yao · 2017
Later among the works it cites.
“Variations on branching methods for non linear PDEs”
Xavier Warin · 2017
Later among the works it cites.
“Solving stochastic differential equations and Kolmogorov equations by means of deep learning”
Christian Beck et al · 2018
Later among the works it cites.
“A unified deep artificial neural network approach to partial differential equations in complex geometries”
Jens Berg and Kaj Nyström · 2018
Later among the works it cites.
Julius Berner, Philipp Grohs and Arnulf Jentzen · 2018
Later among the works it cites.
“The deep Ritz method: a deep learning-based numerical algorithm for solving variational problems”
Weinan E and Bing Yu · 2018
Later among the works it cites.
“DNN Expression Rate Analysis of High-dimensional PDEs: Application to Option Pricing”
Dennis Elbrächter, Philipp Grohs, Arnulf Jentzen and Christoph Schwab · 2018
Later among the works it cites.
Philipp Grohs, Fabian Hornung, Arnulf Jentzen and Philippe von Wurstemberger · 2018
Later among the works it cites.
“Solving high-dimensional partial differential equations using deep learning”
Jiequn Han, Arnulf Jentzen and Weinan E · 2018
Later among the works it cites.
“Convergence of the Deep BSDE Method for Coupled FBSDEs”
Jiequn Han and Jihao Long · 2018
Later among the works it cites.
“Branching diffusion representation for nonlinear Cauchyproblems and Monte Carlo approximation”
Pierre Henry-Labordère and Nizar Touzi · 2018
Later among the works it cites.
Martin Hutzenthaler et al · 2018
Later among the works it cites.
Arnulf Jentzen, Sara Mazzonetto and Diyora Salimova · 2018
Later among the works it cites.
Arnulf Jentzen, Diyora Salimova and Timo Welti · 2018
Later among the works it cites.
“PDE-Net: Learning PDEs from Data”
Zichao Long, Yiping Lu, Xianzhong Ma and Bin Dong · 2018
Later among the works it cites.
“Neural Networks Trained to Solve Differential Equations Learn General Representations”
Martin Magill, Faisal Qureshi and Hendrick de Haan · 2018
Later among the works it cites.
“Deep Hidden Physics Models: Deep Learning of Nonlinear Partial Differential Equations”
Maziar Raissi · 2018
Later among the works it cites.
“DGM: A deep learning algorithm for solving partial differential equations”
Justin Sirignano and Konstantinos Spiliopoulos · 2018
Later among the works it cites.
“Machine Learning Approximation Algorithms for High-Dimensional Fully Nonlinear Partial Differential Equations and Second-order Backward Stochastic Differential Equations”
Christian Beck, Weinan E and Arnulf Jentzen · 2019
Closest in time.
“Deep optimal stopping”
Sebastian Becker, Patrick Cheridito and Arnulf Jentzen · 2019
Closest in time.
“Probabilistic Representations of Nonlocal Nonlinear PDEs via Branching Diffusions with Jumps”, 2019, pp. 28 pages
Christoph Belak, Daniel Hoffmann and Frank Seifried · 2019
Closest in time.
“Numerical approximation of general Lipschitz BSDEs with branching processes”
Bruno Bouchard, Xiaolu Tan and Xavier Warin · 2019
Closest in time.
“Machine learning for semi linear PDEs”
Quentin Chan-Wai-Nam, Joseph Mikael and Xavier Warin · 2019
Closest in time.
“On multilevel Picard numerical approximations for high-dimensional nonlinear parabolic partial differential equations and high-dimensional nonlinear backward stochastic differential equations”
Weinan E, Martin Hutzenthaler, Arnulf Jentzen and Thomas Kruse · 2019
Closest in time.
“Asymptotic Expansion as Prior Knowledge in Deep Learning Method for High dimensional BSDEs”
Masaaki Fujii, Akihiko Takahashi and Masayuki Takahashi · 2019
Closest in time.
“Branching diffusion representation of semilinear PDEs and Monte Carlo approximation”
Pierre Henry-Labordère et al · 2019
Closest in time.