Machine learning approximation algorithms for high-dimensional fully nonlinear partial differential equations and second-order backward stochastic differential equations

18 September 2017

Papers citing "Machine learning approximation algorithms for high-dimensional fully nonlinear partial differential equations and second-order backward stochastic differential equations"

50 / 52 papers shown

Title
Integration Matters for Learning PDEs with Backwards SDEs Sungje Park Stephen Tu PINN 79 0 0 02 May 2025
Gaussian Process Policy Iteration with Additive Schwarz Acceleration for Forward and Inverse HJB and Mean Field Game Problems Xianjin Yang Jingguo Zhang 29 0 0 01 May 2025
Solving Poisson Equations using Neural Walk-on-Spheres Hong Chul Nam Julius Berner Anima Anandkumar 58 3 0 05 Jun 2024
Full error analysis of the random deep splitting method for nonlinear parabolic PDEs and PIDEs Ariel Neufeld Philipp Schmocker Sizhou Wu 50 7 0 08 May 2024
Approximation of Solution Operators for High-dimensional PDEs Nathan Gaby Xiaojing Ye 40 0 0 18 Jan 2024
Accelerated primal-dual methods with enlarged step sizes and operator learning for nonsmooth optimal control problems Yongcun Song Xiaoming Yuan Hangrui Yue AI4CE 30 2 0 01 Jul 2023
Error Analysis of Physics-Informed Neural Networks for Approximating Dynamic PDEs of Second Order in Time Y. Qian Yongchao Zhang Yuanfei Huang S. Dong PINN 31 1 0 22 Mar 2023
Quantum-Inspired Tensor Neural Networks for Option Pricing Raj G. Patel Chia-Wei Hsing Serkan Şahi̇n Samuel Palmer S. Jahromi ... Mustafa Abid Stephane Aubert Pierre Castellani Samuel Mugel Roman Orus 38 4 0 28 Dec 2022
A deep learning approach to the probabilistic numerical solution of path-dependent partial differential equations Jiang Yu Nguwi Nicolas Privault 54 5 0 28 Sep 2022
Multi-fidelity surrogate modeling using long short-term memory networks Paolo Conti Mengwu Guo Andrea Manzoni J. Hesthaven AI4CE 36 48 0 05 Aug 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 34 15 0 03 Aug 2022
Informed Learning by Wide Neural Networks: Convergence, Generalization and Sampling Complexity Jianyi Yang Shaolei Ren 40 3 0 02 Jul 2022
Robust SDE-Based Variational Formulations for Solving Linear PDEs via Deep Learning Lorenz Richter Julius Berner 37 19 0 21 Jun 2022
A deep branching solver for fully nonlinear partial differential equations Jiang Yu Nguwi Guillaume Penent Nicolas Privault 32 14 0 07 Mar 2022
Convergence of a robust deep FBSDE method for stochastic control Kristoffer Andersson Adam Andersson C. Oosterlee 42 19 0 18 Jan 2022
Exponential Convergence of Deep Operator Networks for Elliptic Partial Differential Equations C. Marcati Christoph Schwab 48 38 0 15 Dec 2021
Interpolating between BSDEs and PINNs: deep learning for elliptic and parabolic boundary value problems Nikolas Nusken Lorenz Richter PINN DiffM 41 28 0 07 Dec 2021
Deep Learning for Principal-Agent Mean Field Games S. Campbell Yichao Chen Arvind Shrivats S. Jaimungal 34 16 0 03 Oct 2021
Exploration noise for learning linear-quadratic mean field games François Delarue A. Vasileiadis MLT 39 11 0 02 Jul 2021
Cell-average based neural network method for hyperbolic and parabolic partial differential equations Changxin Qiu Jue Yan 26 10 0 02 Jul 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 24 22 0 07 May 2021
dNNsolve: an efficient NN-based PDE solver V. Guidetti F. Muia Y. Welling A. Westphal 27 6 0 15 Mar 2021
A Deep Collocation Method for the Bending Analysis of Kirchhoff Plate Hongwei Guo X. Zhuang Timon Rabczuk AI4CE 32 433 0 04 Feb 2021
An overview on deep learning-based approximation methods for partial differential equations C. Beck Martin Hutzenthaler Arnulf Jentzen Benno Kuckuck 48 148 0 22 Dec 2020
Solving non-linear Kolmogorov equations in large dimensions by using deep learning: a numerical comparison of discretization schemes Raffaele Marino N. Macris 34 16 0 09 Dec 2020
State-Dependent Temperature Control for Langevin Diffusions Xuefeng Gao Z. Xu X. Zhou 48 27 0 15 Nov 2020
Analysis of three dimensional potential problems in non-homogeneous media with physics-informed deep collocation method using material transfer learning and sensitivity analysis Hongwei Guo X. Zhuang Pengwan Chen N. Alajlan Timon Rabczuk 32 58 0 03 Oct 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 25 82 0 03 Oct 2020
A fast and accurate physics-informed neural network reduced order model with shallow masked autoencoder Youngkyu Kim Youngsoo Choi David Widemann T. Zohdi AI4CE 16 191 0 25 Sep 2020
Convergence of Deep Fictitious Play for Stochastic Differential Games Jiequn Han Ruimeng Hu Jihao Long 34 19 0 12 Aug 2020
Weak error analysis for stochastic gradient descent optimization algorithms A. Bercher Lukas Gonon Arnulf Jentzen Diyora Salimova 41 4 0 03 Jul 2020
Space-time deep neural network approximations for high-dimensional partial differential equations F. Hornung Arnulf Jentzen Diyora Salimova AI4CE 39 19 0 03 Jun 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 43 107 0 11 May 2020
Numerical Solution of the Parametric Diffusion Equation by Deep Neural Networks Moritz Geist P. Petersen Mones Raslan R. Schneider Gitta Kutyniok 45 83 0 25 Apr 2020
Overall error analysis for the training of deep neural networks via stochastic gradient descent with random initialisation Arnulf Jentzen Timo Welti 34 15 0 03 Mar 2020
Uniform error estimates for artificial neural network approximations for heat equations Lukas Gonon Philipp Grohs Arnulf Jentzen David Kofler David Siska 42 34 0 20 Nov 2019
Full error analysis for the training of deep neural networks C. Beck Arnulf Jentzen Benno Kuckuck 27 47 0 30 Sep 2019
Deep Neural Network Framework Based on Backward Stochastic Differential Equations for Pricing and Hedging American Options in High Dimensions Yangang Chen J. Wan 30 60 0 25 Sep 2019
Space-time error estimates for deep neural network approximations for differential equations Philipp Grohs F. Hornung Arnulf Jentzen Philipp Zimmermann 42 33 0 11 Aug 2019
DeepXDE: A deep learning library for solving differential equations Lu Lu Xuhui Meng Zhiping Mao George Karniadakis PINN AI4CE 52 1,498 0 10 Jul 2019
Deep splitting method for parabolic PDEs C. Beck S. Becker Patrick Cheridito Arnulf Jentzen Ariel Neufeld 45 127 0 08 Jul 2019
Learning to Discretize: Solving 1D Scalar Conservation Laws via Deep Reinforcement Learning Yufei Wang Ziju Shen Zichao Long Bin Dong AI4CE PINN 24 40 0 27 May 2019
Mean-Field Langevin Dynamics and Energy Landscape of Neural Networks Kaitong Hu Zhenjie Ren David Siska Lukasz Szpruch MLT 35 104 0 19 May 2019
Pricing options and computing implied volatilities using neural networks Shuaiqiang Liu C. Oosterlee S. Bohté 27 120 0 25 Jan 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 51 857 0 18 Jan 2019
Machine Learning for semi linear PDEs Quentin Chan-Wai-Nam Joseph Mikael X. Warin ODL 24 111 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 29 119 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 19 182 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 26 168 0 07 Sep 2018
Solving the Kolmogorov PDE by means of deep learning C. Beck S. Becker Philipp Grohs Nor Jaafari Arnulf Jentzen 31 92 0 01 Jun 2018