A brief review of the Deep BSDE method for solving high-dimensional partial differential equations

7 May 2025

Papers citing "A brief review of the Deep BSDE method for solving high-dimensional partial differential equations"

39 / 39 papers shown

Title
Deep neural networks with ReLU, leaky ReLU, and softplus activation provably overcome the curse of dimensionality for space-time solutions of semilinear partial differential equations Julia Ackermann Arnulf Jentzen Benno Kuckuck J. Padgett AI4CE 48 3 0 16 Jun 2024
Hutchinson Trace Estimation for High-Dimensional and High-Order Physics-Informed Neural Networks Zheyuan Hu Zekun Shi George Karniadakis Kenji Kawaguchi AI4CE PINN 148 27 0 22 Dec 2023
Stochastic Optimal Control Matching Carles Domingo-Enrich Jiequn Han Brandon Amos Joan Bruna Ricky T. Q. Chen DiffM 124 10 0 04 Dec 2023
Deep learning probability flows and entropy production rates in active matter Nicholas M. Boffi Eric Vanden-Eijnden DiffM 58 20 0 22 Sep 2023
Drift Control of High-Dimensional RBM: A Computational Method Based on Neural Networks B. Ata J. M. Harrison Nian Si 47 3 0 20 Sep 2023
Approximation Results for Gradient Descent trained Neural Networks G. Welper 70 1 0 09 Sep 2023
Approximation results for Gradient Descent trained Shallow Neural Networks in $1d$ R. Gentile G. Welper ODL 112 7 0 17 Sep 2022
From Monte Carlo to neural networks approximations of boundary value problems L. Beznea Iulian Cîmpean Oana Lupascu-Stamate Ionel Popescu A. Zarnescu 48 3 0 03 Sep 2022
Learning High-Dimensional McKean-Vlasov Forward-Backward Stochastic Differential Equations with General Distribution Dependence Jiequn Han Ruimeng Hu Jihao Long AI4CE OOD 60 23 0 25 Apr 2022
Scientific Machine Learning through Physics-Informed Neural Networks: Where we are and What's next S. Cuomo Vincenzo Schiano Di Cola F. Giampaolo G. Rozza Maizar Raissi F. Piccialli PINN 156 1,306 0 14 Jan 2022
Interpolating between BSDEs and PINNs: deep learning for elliptic and parabolic boundary value problems Nikolas Nusken Lorenz Richter PINN DiffM 103 30 0 07 Dec 2021
On the Representation of Solutions to Elliptic PDEs in Barron Spaces Ziang Chen Jianfeng Lu Yulong Lu 83 29 0 14 Jun 2021
Random feature neural networks learn Black-Scholes type PDEs without curse of dimensionality Lukas Gonon 86 37 0 14 Jun 2021
Machine learning moment closure models for the radiative transfer equation I: directly learning a gradient based closure Juntao Huang Yingda Cheng Andrew J. Christlieb L. Roberts AI4CE 60 31 0 12 May 2021
An overview on deep learning-based approximation methods for partial differential equations C. Beck Martin Hutzenthaler Arnulf Jentzen Benno Kuckuck 121 153 0 22 Dec 2020
Friedrichs Learning: Weak Solutions of Partial Differential Equations via Deep Learning Fan Chen J. Huang Chunmei Wang Haizhao Yang 110 33 0 15 Dec 2020
Score-Based Generative Modeling through Stochastic Differential Equations Yang Song Jascha Narain Sohl-Dickstein Diederik P. Kingma Abhishek Kumar Stefano Ermon Ben Poole DiffM SyDa 597 6,609 0 26 Nov 2020
Numerically Solving Parametric Families of High-Dimensional Kolmogorov Partial Differential Equations via Deep Learning Julius Berner Markus Dablander Philipp Grohs 72 47 0 09 Nov 2020
Deep neural network approximation for high-dimensional elliptic PDEs with boundary conditions Philipp Grohs L. Herrmann 92 53 0 10 Jul 2020
Solving high-dimensional Hamilton-Jacobi-Bellman PDEs using neural networks: perspectives from the theory of controlled diffusions and measures on path space Nikolas Nusken Lorenz Richter AI4CE 103 112 0 11 May 2020
Solving high-dimensional eigenvalue problems using deep neural networks: A diffusion Monte Carlo like approach Jiequn Han Jianfeng Lu Mo Zhou DiffM 86 87 0 07 Feb 2020
A Derivative-Free Method for Solving Elliptic Partial Differential Equations with Deep Neural Networks Jihun Han Mihai Nica A. Stinchcombe 77 50 0 17 Jan 2020
Deep Fictitious Play for Finding Markovian Nash Equilibrium in Multi-Agent Games Jiequn Han Ruimeng Hu 63 45 0 04 Dec 2019
Ab-Initio Solution of the Many-Electron Schrödinger Equation with Deep Neural Networks David Pfau J. Spencer A. G. Matthews W. Foulkes 127 467 0 05 Sep 2019
Convergence Analysis of Machine Learning Algorithms for the Numerical Solution of Mean Field Control and Games: II -- The Finite Horizon Case René Carmona Mathieu Laurière 76 99 0 05 Aug 2019
Neural networks-based backward scheme for fully nonlinear PDEs H. Pham X. Warin Maximilien Germain 88 85 0 31 Jul 2019
Three algorithms for solving high-dimensional fully-coupled FBSDEs through deep learning Shaolin Ji S. Peng Ying Peng Xichuan Zhang AI4CE 56 55 0 11 Jul 2019
Adaptive Deep Learning for High-Dimensional Hamilton-Jacobi-Bellman Equations Tenavi Nakamura-Zimmerer Q. Gong W. Kang 134 134 0 11 Jul 2019
Deep splitting method for parabolic PDEs C. Beck S. Becker Patrick Cheridito Arnulf Jentzen Ariel Neufeld 110 126 0 08 Jul 2019
Convergence of the Deep BSDE Method for Coupled FBSDEs Jiequn Han Jihao Long 90 160 0 03 Nov 2018
A proof that deep artificial neural networks overcome the curse of dimensionality in the numerical approximation of Kolmogorov partial differential equations with constant diffusion and nonlinear drift coefficients Arnulf Jentzen Diyora Salimova Timo Welti AI4CE 76 119 0 19 Sep 2018
Analysis of the Generalization Error: Empirical Risk Minimization over Deep Artificial Neural Networks Overcomes the Curse of Dimensionality in the Numerical Approximation of Black-Scholes Partial Differential Equations Julius Berner Philipp Grohs Arnulf Jentzen 129 183 0 09 Sep 2018
A proof that artificial neural networks overcome the curse of dimensionality in the numerical approximation of Black-Scholes partial differential equations Philipp Grohs F. Hornung Arnulf Jentzen Philippe von Wurstemberger 89 171 0 07 Sep 2018
Solving the Kolmogorov PDE by means of deep learning C. Beck S. Becker Philipp Grohs Nor Jaafari Arnulf Jentzen 92 96 0 01 Jun 2018
The Deep Ritz method: A deep learning-based numerical algorithm for solving variational problems E. Weinan Ting Yu 143 1,400 0 30 Sep 2017
Machine learning approximation algorithms for high-dimensional fully nonlinear partial differential equations and second-order backward stochastic differential equations C. Beck Weinan E Arnulf Jentzen 87 333 0 18 Sep 2017
DGM: A deep learning algorithm for solving partial differential equations Justin A. Sirignano K. Spiliopoulos AI4CE 120 2,073 0 24 Aug 2017
Deep Learning Approximation for Stochastic Control Problems Jiequn Han E. Weinan BDL 67 197 0 02 Nov 2016
Deep Residual Learning for Image Recognition Kaiming He Xinming Zhang Shaoqing Ren Jian Sun MedIm 2.8K 195,310 0 10 Dec 2015