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"

50 / 248 papers shown

Title
$PINNs error estimates for nonlinear equations in $\mathbb{R}$-smooth Banach spaces$ PINNs error estimates for nonlinear equations in $\mathbb{R}$ -smooth Banach spaces Jiexing Gao Yurii Zakharian 28 1 0 18 May 2023
Nearly Optimal VC-Dimension and Pseudo-Dimension Bounds for Deep Neural Network Derivatives Yahong Yang Haizhao Yang Yang Xiang 31 19 0 15 May 2023
Error Analysis of Kernel/GP Methods for Nonlinear and Parametric PDEs Pau Batlle Yifan Chen Bamdad Hosseini H. Owhadi Andrew M. Stuart 34 17 0 08 May 2023
A Stable and Scalable Method for Solving Initial Value PDEs with Neural Networks Marc Finzi Andres Potapczynski M. Choptuik A. Wilson 26 12 0 28 Apr 2023
Pseudo-Hamiltonian neural networks for learning partial differential equations Sølve Eidnes K. Lye 26 10 0 27 Apr 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
Score-based Generative Modeling Through Backward Stochastic Differential Equations: Inversion and Generation Zihao Wang DiffM 38 4 0 26 Apr 2023
On forward-backward SDE approaches to continuous-time minimum variance estimation J. W. Kim Sebastian Reich 9 1 0 25 Apr 2023
Application of Tensor Neural Networks to Pricing Bermudan Swaptions Raj G. Patel Tomas Dominguez M. Dib Samuel Palmer Andrea Cadarso ... Eva Andrés J. Luis-Hita Escolástico Sánchez-Martínez Samuel Mugel Roman Orus 32 1 0 18 Apr 2023
In-Context Operator Learning with Data Prompts for Differential Equation Problems Liu Yang Siting Liu Tingwei Meng Stanley J. Osher 40 60 0 17 Apr 2023
Deep Generative Modeling with Backward Stochastic Differential Equations Xingcheng Xu PINN 27 0 0 08 Apr 2023
Multilevel CNNs for Parametric PDEs Cosmas Heiß Ingo Gühring Martin Eigel AI4CE 25 8 0 01 Apr 2023
GPT-PINN: Generative Pre-Trained Physics-Informed Neural Networks toward non-intrusive Meta-learning of parametric PDEs Yanlai Chen Shawn Koohy PINN AI4CE 37 24 0 27 Mar 2023
Deep Learning for Mean Field Optimal Transport Sebastian Baudelet Brieuc Frénais Mathieu Laurière Amal Machtalay Yuchen Zhu OT 28 2 0 28 Feb 2023
Achieving High Accuracy with PINNs via Energy Natural Gradients Johannes Müller Marius Zeinhofer 13 5 0 25 Feb 2023
Entropy-dissipation Informed Neural Network for McKean-Vlasov Type PDEs Zebang Shen Zhenfu Wang 19 5 0 11 Feb 2023
Algorithmically Designed Artificial Neural Networks (ADANNs): Higher order deep operator learning for parametric partial differential equations Arnulf Jentzen Adrian Riekert Philippe von Wurstemberger 29 1 0 07 Feb 2023
Convergence Analysis of the Deep Galerkin Method for Weak Solutions Yuling Jiao Yanming Lai Yang Wang Haizhao Yang Yunfei Yang 21 3 0 05 Feb 2023
Neural Control of Parametric Solutions for High-dimensional Evolution PDEs Nathan Gaby X. Ye Haomin Zhou 19 6 0 31 Jan 2023
Deep learning numerical methods for high-dimensional fully nonlinear PIDEs and coupled FBSDEs with jumps Wansheng Wang Jie Wang Jinping Li Feifei Gao Yida Fu 17 6 0 30 Jan 2023
Efficient Pricing and Hedging of High Dimensional American Options Using Recurrent Networks Andrews Na J. Wan 31 9 0 19 Jan 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 25 3 0 28 Dec 2022
Mean-field neural networks-based algorithms for McKean-Vlasov control problems * Huyen Pham X. Warin 14 9 0 22 Dec 2022
Separable PINN: Mitigating the Curse of Dimensionality in Physics-Informed Neural Networks Junwoo Cho Seungtae Nam Hyunmo Yang S. Yun Youngjoon Hong Eunbyung Park PINN AI4CE 28 8 0 16 Nov 2022
Mean-field neural networks: learning mappings on Wasserstein space H. Pham X. Warin 21 13 0 27 Oct 2022
Neural Network Approximations of PDEs Beyond Linearity: A Representational Perspective Tanya Marwah Zachary Chase Lipton Jianfeng Lu Andrej Risteski 52 10 0 21 Oct 2022
Convergence of the Backward Deep BSDE Method with Applications to Optimal Stopping Problems Chengfan Gao Siping Gao Ruimeng Hu Zimu Zhu 31 14 0 08 Oct 2022
Optimization-Informed Neural Networks Da-Lin Wu A. Lisser 27 0 0 05 Oct 2022
CAS4DL: Christoffel Adaptive Sampling for function approximation via Deep Learning Ben Adcock Juan M. Cardenas N. Dexter 33 8 0 25 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 29 14 0 03 Aug 2022
EgPDE-Net: Building Continuous Neural Networks for Time Series Prediction with Exogenous Variables Penglei Gao Xi Yang Rui Zhang Ping Guo John Y. Goulermas Kaizhu Huang AI4TS 24 5 0 03 Aug 2022
wPINNs: Weak Physics informed neural networks for approximating entropy solutions of hyperbolic conservation laws Tim De Ryck Siddhartha Mishra Roberto Molinaro PINN 32 29 0 18 Jul 2022
Error analysis for deep neural network approximations of parametric hyperbolic conservation laws Tim De Ryck Siddhartha Mishra PINN 15 10 0 15 Jul 2022
Robust SDE-Based Variational Formulations for Solving Linear PDEs via Deep Learning Lorenz Richter Julius Berner 27 19 0 21 Jun 2022
Finite Expression Method for Solving High-Dimensional Partial Differential Equations Senwei Liang Haizhao Yang 34 18 0 21 Jun 2022
SAIBench: Benchmarking AI for Science Yatao Li Jianfeng Zhan 21 7 0 11 Jun 2022
Computational Doob's h-transforms for Online Filtering of Discretely Observed Diffusions Nicolas Chopin Andras Fulop J. Heng Alexandre Hoang Thiery 23 1 0 07 Jun 2022
Approximation of Functionals by Neural Network without Curse of Dimensionality Yahong Yang Yang Xiang 29 6 0 28 May 2022
Generic bounds on the approximation error for physics-informed (and) operator learning Tim De Ryck Siddhartha Mishra PINN 63 59 0 23 May 2022
A scalable deep learning approach for solving high-dimensional dynamic optimal transport Wei Wan Yuejin Zhang Chenglong Bao Bin Dong Zuoqiang Shi 19 6 0 16 May 2022
Deep learning approximations for non-local nonlinear PDEs with Neumann boundary conditions V. Boussange S. Becker Arnulf Jentzen Benno Kuckuck Loïc Pellissier 30 12 0 07 May 2022
BI-GreenNet: Learning Green's functions by boundary integral network Guochang Lin Fu-jun Chen Pipi Hu Xiang Chen Junqing Chen Jun Wang Zuoqiang Shi 34 20 0 28 Apr 2022
Learning High-Dimensional McKean-Vlasov Forward-Backward Stochastic Differential Equations with General Distribution Dependence Jiequn Han Ruimeng Hu Jihao Long AI4CE OOD 13 21 0 25 Apr 2022
PI-VAE: Physics-Informed Variational Auto-Encoder for stochastic differential equations Weiheng Zhong Hadi Meidani DRL 30 37 0 21 Mar 2022
Error estimates for physics informed neural networks approximating the Navier-Stokes equations Tim De Ryck Ameya Dilip Jagtap S. Mishra PINN 49 115 0 17 Mar 2022
A deep branching solver for fully nonlinear partial differential equations Jiang Yu Nguwi Guillaume Penent Nicolas Privault 14 14 0 07 Mar 2022
Neural Galerkin Schemes with Active Learning for High-Dimensional Evolution Equations Joan Bruna Benjamin Peherstorfer Eric Vanden-Eijnden 27 61 0 02 Mar 2022
Temporal Difference Learning with Continuous Time and State in the Stochastic Setting Ziad Kobeissi Francis R. Bach OffRL 21 2 0 16 Feb 2022
$A Regularity Theory for Static Schrödinger Equations on $\mathbb{R}^d$ in Spectral Barron Spaces$ A Regularity Theory for Static Schrödinger Equations on $\mathbb{R}^d$ in Spectral Barron Spaces Ziang Chen Jianfeng Lu Yulong Lu Sheng-Wei Zhou 26 0 0 25 Jan 2022
Overview frequency principle/spectral bias in deep learning Z. Xu Yaoyu Zhang Tao Luo FaML 33 66 0 19 Jan 2022