Deep learning-based numerical methods for high-dimensional parabolic partial differential equations and backward stochastic differential equations

15 June 2017

Papers citing "Deep learning-based numerical methods for high-dimensional parabolic partial differential equations and backward stochastic differential equations"

48 / 248 papers shown

Title
Solving high-dimensional optimal stopping problems using deep learning S. Becker Patrick Cheridito Arnulf Jentzen Timo Welti 11 79 0 05 Aug 2019
Neural networks-based backward scheme for fully nonlinear PDEs H. Pham X. Warin Maximilien Germain 14 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 13 52 0 11 Jul 2019
Deep splitting method for parabolic PDEs C. Beck S. Becker Patrick Cheridito Arnulf Jentzen Ariel Neufeld 23 125 0 08 Jul 2019
Theory of the Frequency Principle for General Deep Neural Networks Tao Luo Zheng Ma Zhi-Qin John Xu Yaoyu Zhang 26 78 0 21 Jun 2019
Meta-learning Pseudo-differential Operators with Deep Neural Networks Jordi Feliu-Fabà Yuwei Fan Lexing Ying 22 39 0 16 Jun 2019
Deep Network Approximation Characterized by Number of Neurons Zuowei Shen Haizhao Yang Shijun Zhang 23 182 0 13 Jun 2019
A neural network based policy iteration algorithm with global $H^2$ -superlinear convergence for stochastic games on domains Kazufumi Ito C. Reisinger Yufei Zhang 14 27 0 05 Jun 2019
Mean-Field Langevin Dynamics and Energy Landscape of Neural Networks Kaitong Hu Zhenjie Ren David Siska Lukasz Szpruch MLT 30 104 0 19 May 2019
Towards a regularity theory for ReLU networks -- chain rule and global error estimates Julius Berner Dennis Elbrächter Philipp Grohs Arnulf Jentzen AI4CE 14 16 0 13 May 2019
A Selective Overview of Deep Learning Jianqing Fan Cong Ma Yiqiao Zhong BDL VLM 38 136 0 10 Apr 2019
A Theoretical Analysis of Deep Neural Networks and Parametric PDEs Gitta Kutyniok P. Petersen Mones Raslan R. Schneider 23 197 0 31 Mar 2019
Deep Fictitious Play for Stochastic Differential Games Ruimeng Hu 25 29 0 22 Mar 2019
Deep learning observables in computational fluid dynamics K. Lye Siddhartha Mishra Deep Ray OOD AI4CE 18 158 0 07 Mar 2019
$Error bounds for approximations with deep ReLU neural networks in $W^{s,p}$ norms$ Error bounds for approximations with deep ReLU neural networks in $W^{s,p}$ norms Ingo Gühring Gitta Kutyniok P. Petersen 28 199 0 21 Feb 2019
Deep backward schemes for high-dimensional nonlinear PDEs Côme Huré H. Pham X. Warin AI4CE 11 98 0 05 Feb 2019
Pricing options and computing implied volatilities using neural networks Shuaiqiang Liu C. Oosterlee S. Bohté 19 119 0 25 Jan 2019
Frequency Principle: Fourier Analysis Sheds Light on Deep Neural Networks Zhi-Qin John Xu Yaoyu Zhang Tao Luo Yan Xiao Zheng Ma 17 503 0 19 Jan 2019
Deep neural networks algorithms for stochastic control problems on finite horizon: numerical applications Achref Bachouch Côme Huré N. Langrené H. Pham 16 84 0 13 Dec 2018
Deep neural networks algorithms for stochastic control problems on finite horizon: convergence analysis Côme Huré H. Pham Achref Bachouch N. Langrené 13 64 0 11 Dec 2018
Wireless Network Intelligence at the Edge Jihong Park S. Samarakoon M. Bennis Mérouane Debbah 21 518 0 07 Dec 2018
Networks for Nonlinear Diffusion Problems in Imaging Simon Arridge A. Hauptmann DiffM MedIm 19 18 0 29 Nov 2018
Frequency Principle in Deep Learning with General Loss Functions and Its Potential Application Z. Xu 14 15 0 26 Nov 2018
Physics-Informed Generative Adversarial Networks for Stochastic Differential Equations Siyu Dai Shawn Schaffert Andreas G. Hofmann 12 355 0 05 Nov 2018
Convergence of the Deep BSDE Method for Coupled FBSDEs Jiequn Han Jihao Long 20 156 0 03 Nov 2018
Physics-Driven Regularization of Deep Neural Networks for Enhanced Engineering Design and Analysis M. A. Nabian Hadi Meidani PINN AI4CE 21 57 0 11 Oct 2018
Unbiased deep solvers for linear parametric PDEs Marc Sabate Vidales David Siska Lukasz Szpruch OOD 32 7 0 11 Oct 2018
Quantifying total uncertainty in physics-informed neural networks for solving forward and inverse stochastic problems Dongkun Zhang Lu Lu Ling Guo George Karniadakis UQCV 27 399 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 18 116 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 14 181 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 16 167 0 07 Sep 2018
Deeply Learning Derivatives Ryan Ferguson Andrew Green 32 43 0 06 Sep 2018
Reinforcement Learning with Function-Valued Action Spaces for Partial Differential Equation Control Yangchen Pan Amir-massoud Farahmand Martha White S. Nabi P. Grover D. Nikovski 48 18 0 13 Jun 2018
A Deep Neural Network Surrogate for High-Dimensional Random Partial Differential Equations M. A. Nabian Hadi Meidani AI4CE 9 100 0 08 Jun 2018
Solving the Kolmogorov PDE by means of deep learning C. Beck S. Becker Philipp Grohs Nor Jaafari Arnulf Jentzen 19 91 0 01 Jun 2018
LMKL-Net: A Fast Localized Multiple Kernel Learning Solver via Deep Neural Networks Ziming Zhang ODL 16 1 0 22 May 2018
Butterfly-Net: Optimal Function Representation Based on Convolutional Neural Networks Yingzhou Li Xiuyuan Cheng Jianfeng Lu 21 23 0 18 May 2018
General solutions for nonlinear differential equations: a rule-based self-learning approach using deep reinforcement learning Shiyin Wei Xiaowei Jin Hui Li AI4CE 39 39 0 13 May 2018
Trainability and Accuracy of Neural Networks: An Interacting Particle System Approach Grant M. Rotskoff Eric Vanden-Eijnden 63 118 0 02 May 2018
Optimal Neural Network Feature Selection for Spatial-Temporal Forecasting E. Covas Emmanouil Benetos AI4TS 6 8 0 30 Apr 2018
Forward-Backward Stochastic Neural Networks: Deep Learning of High-dimensional Partial Differential Equations M. Raissi 25 183 0 19 Apr 2018
Solving for high dimensional committor functions using artificial neural networks Y. Khoo Jianfeng Lu Lexing Ying 26 137 0 28 Feb 2018
Computation of optimal transport and related hedging problems via penalization and neural networks Stephan Eckstein Michael Kupper OT 41 49 0 23 Feb 2018
A unified deep artificial neural network approach to partial differential equations in complex geometries Jens Berg K. Nystrom AI4CE 29 578 0 17 Nov 2017
The Deep Ritz method: A deep learning-based numerical algorithm for solving variational problems E. Weinan Ting Yu 19 1,363 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 6 325 0 18 Sep 2017
DGM: A deep learning algorithm for solving partial differential equations Justin A. Sirignano K. Spiliopoulos AI4CE 14 2,025 0 24 Aug 2017