Forward-Backward Stochastic Neural Networks: Deep Learning of High-dimensional Partial Differential Equations

19 April 2018

Papers citing "Forward-Backward Stochastic Neural Networks: Deep Learning of High-dimensional Partial Differential Equations"

43 / 43 papers shown

Title
Anant-Net: Breaking the Curse of Dimensionality with Scalable and Interpretable Neural Surrogate for High-Dimensional PDEs Sidharth S. Menon Ameya D. Jagtap PINN 160 0 0 06 May 2025
Integration Matters for Learning PDEs with Backwards SDEs Sungje Park Stephen Tu PINN 60 0 0 02 May 2025
Stochastic Taylor Derivative Estimator: Efficient amortization for arbitrary differential operators Zekun Shi Zheyuan Hu Min-Bin Lin Kenji Kawaguchi 157 5 0 27 Nov 2024
Full error analysis of the random deep splitting method for nonlinear parabolic PDEs and PIDEs Ariel Neufeld Philipp Schmocker Sizhou Wu 45 7 0 08 May 2024
A backward differential deep learning-based algorithm for solving high-dimensional nonlinear backward stochastic differential equations Lorenc Kapllani Long Teng 31 2 0 12 Apr 2024
Temporal Difference Learning for High-Dimensional PIDEs with Jumps Liwei Lu Hailong Guo Xueqing Yang Yi Zhu AI4CE 23 6 0 06 Jul 2023
A Survey on Solving and Discovering Differential Equations Using Deep Neural Networks Hyeonjung Jung Jung Jayant Gupta B. Jayaprakash Matthew J. Eagon Harish Selvam Carl Molnar W. Northrop Shashi Shekhar AI4CE 35 5 0 26 Apr 2023
Neural Partial Differential Equations with Functional Convolution Z. Wu Xingzhe He Yijun Li Cheng Yang Rui Liu S. Xiong Bo Zhu 23 1 0 10 Mar 2023
Simultaneous upper and lower bounds of American option prices with hedging via neural networks Ivan Guo Nicolas Langrené Jiahao Wu 22 0 0 24 Feb 2023
Error-Aware B-PINNs: Improving Uncertainty Quantification in Bayesian Physics-Informed Neural Networks Olga Graf P. Flores P. Protopapas K. Pichara PINN 37 6 0 14 Dec 2022
Transfer Learning with Physics-Informed Neural Networks for Efficient Simulation of Branched Flows Raphael Pellegrin Blake Bullwinkel M. Mattheakis P. Protopapas PINN AI4CE 26 9 0 01 Nov 2022
Deep learning for gradient flows using the Brezis-Ekeland principle Laura Carini Max Jensen R. Nürnberg 21 0 0 28 Sep 2022
DEQGAN: Learning the Loss Function for PINNs with Generative Adversarial Networks Blake Bullwinkel Dylan Randle P. Protopapas David Sondak 24 3 0 15 Sep 2022
Quantum-Inspired Tensor Neural Networks for Partial Differential Equations Raj G. Patel Chia-Wei Hsing Serkan Şahi̇n S. Jahromi Samuel Palmer ... Stephane Aubert Pierre Castellani Chi-Guhn Lee Samuel Mugel Roman Orus 18 14 0 03 Aug 2022
Convergence of a robust deep FBSDE method for stochastic control Kristoffer Andersson Adam Andersson C. Oosterlee 34 19 0 18 Jan 2022
Interpolating between BSDEs and PINNs: deep learning for elliptic and parabolic boundary value problems Nikolas Nusken Lorenz Richter PINN DiffM 31 27 0 07 Dec 2021
Uncertainty Quantification in Neural Differential Equations Olga Graf P. Flores P. Protopapas K. Pichara UQCV AI4CE 34 7 0 08 Nov 2021
A novel control method for solving high-dimensional Hamiltonian systems through deep neural networks Shaolin Ji S. Peng Ying Peng Xichuan Zhang 19 1 0 04 Nov 2021
Neural network architectures using min-plus algebra for solving certain high dimensional optimal control problems and Hamilton-Jacobi PDEs Jérome Darbon P. Dower Tingwei Meng 8 22 0 07 May 2021
Adversarial Multi-task Learning Enhanced Physics-informed Neural Networks for Solving Partial Differential Equations Pongpisit Thanasutives M. Numao Ken-ichi Fukui AI4CE 24 24 0 29 Apr 2021
Efficient training of physics-informed neural networks via importance sampling M. A. Nabian R. J. Gladstone Hadi Meidani DiffM PINN 71 223 0 26 Apr 2021
A Deep Collocation Method for the Bending Analysis of Kirchhoff Plate Hongwei Guo X. Zhuang Timon Rabczuk AI4CE 19 433 0 04 Feb 2021
An overview on deep learning-based approximation methods for partial differential equations C. Beck Martin Hutzenthaler Arnulf Jentzen Benno Kuckuck 30 146 0 22 Dec 2020
On the eigenvector bias of Fourier feature networks: From regression to solving multi-scale PDEs with physics-informed neural networks Sizhuang He Hanwen Wang P. Perdikaris 131 439 0 18 Dec 2020
Solving non-linear Kolmogorov equations in large dimensions by using deep learning: a numerical comparison of discretization schemes Raffaele Marino N. Macris 19 16 0 09 Dec 2020
Stochastic analysis of heterogeneous porous material with modified neural architecture search (NAS) based physics-informed neural networks using transfer learning Hongwei Guo X. Zhuang Timon Rabczuk 20 82 0 03 Oct 2020
Self-Adaptive Physics-Informed Neural Networks using a Soft Attention Mechanism L. McClenny U. Braga-Neto PINN 28 444 0 07 Sep 2020
Solving stochastic optimal control problem via stochastic maximum principle with deep learning method Shaolin Ji S. Peng Ying Peng Xichuan Zhang 24 13 0 05 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 12 103 0 11 May 2020
A Derivative-Free Method for Solving Elliptic Partial Differential Equations with Deep Neural Networks Jihun Han Mihai Nica A. Stinchcombe 22 49 0 17 Jan 2020
Highly-scalable, physics-informed GANs for learning solutions of stochastic PDEs Liu Yang Sean Treichler Thorsten Kurth Keno Fischer D. Barajas-Solano ... Valentin Churavy A. Tartakovsky Michael Houston P. Prabhat George Karniadakis AI4CE 47 38 0 29 Oct 2019
Towards Robust and Stable Deep Learning Algorithms for Forward Backward Stochastic Differential Equations Batuhan Güler Alexis Laignelet P. Parpas OOD 21 16 0 25 Oct 2019
A deep surrogate approach to efficient Bayesian inversion in PDE and integral equation models Teo Deveney Amelia Gosse Peter Du 23 9 0 03 Oct 2019
Adaptive Deep Learning for High-Dimensional Hamilton-Jacobi-Bellman Equations Tenavi Nakamura-Zimmerer Q. Gong W. Kang 13 132 0 11 Jul 2019
EM-like Learning Chaotic Dynamics from Noisy and Partial Observations Duong Nguyen Said Ouala Lucas Drumetz Ronan Fablet 13 29 0 25 Mar 2019
Physics-Constrained Deep Learning for High-dimensional Surrogate Modeling and Uncertainty Quantification without Labeled Data Yinhao Zhu N. Zabaras P. Koutsourelakis P. Perdikaris PINN AI4CE 46 854 0 18 Jan 2019
Quantifying total uncertainty in physics-informed neural networks for solving forward and inverse stochastic problems Dongkun Zhang Lu Lu Ling Guo George Karniadakis UQCV 24 397 0 21 Sep 2018
Machine Learning for semi linear PDEs Quentin Chan-Wai-Nam Joseph Mikael X. Warin ODL 21 111 0 20 Sep 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 16 116 0 19 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 11 167 0 07 Sep 2018
Hidden Fluid Mechanics: A Navier-Stokes Informed Deep Learning Framework for Assimilating Flow Visualization Data M. Raissi A. Yazdani George Karniadakis AI4CE PINN 19 158 0 13 Aug 2018
Solving the Kolmogorov PDE by means of deep learning C. Beck S. Becker Philipp Grohs Nor Jaafari Arnulf Jentzen 11 91 0 01 Jun 2018
Deep Hidden Physics Models: Deep Learning of Nonlinear Partial Differential Equations M. Raissi PINN AI4CE 17 745 0 20 Jan 2018