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
Machine Learning and Computational Mathematics Weinan E PINN AI4CE 32 61 0 23 Sep 2020
Deep Learning for Constrained Utility Maximisation Ashley Davey Harry Zheng 20 7 0 26 Aug 2020
Iterative Surrogate Model Optimization (ISMO): An active learning algorithm for PDE constrained optimization with deep neural networks K. Lye Siddhartha Mishra Deep Ray P. Chandrasekhar 18 75 0 13 Aug 2020
Convergence of Deep Fictitious Play for Stochastic Differential Games Jiequn Han Ruimeng Hu Jihao Long 19 19 0 12 Aug 2020
Adaptive Physics-Informed Neural Networks for Markov-Chain Monte Carlo M. A. Nabian Hadi Meidani 14 6 0 03 Aug 2020
Expressivity of Deep Neural Networks Ingo Gühring Mones Raslan Gitta Kutyniok 16 51 0 09 Jul 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
Weak error analysis for stochastic gradient descent optimization algorithms A. Bercher Lukas Gonon Arnulf Jentzen Diyora Salimova 26 4 0 03 Jul 2020
Estimates on the generalization error of Physics Informed Neural Networks (PINNs) for approximating a class of inverse problems for PDEs Siddhartha Mishra Roberto Molinaro PINN 16 262 0 29 Jun 2020
Estimates on the generalization error of Physics Informed Neural Networks (PINNs) for approximating PDEs Siddhartha Mishra Roberto Molinaro PINN 25 171 0 29 Jun 2020
Two-Layer Neural Networks for Partial Differential Equations: Optimization and Generalization Theory Tao Luo Haizhao Yang 32 74 0 28 Jun 2020
Learning a functional control for high-frequency finance Laura Leal Mathieu Laurière Charles-Albert Lehalle AIFin 13 20 0 17 Jun 2020
Space-time deep neural network approximations for high-dimensional partial differential equations F. Hornung Arnulf Jentzen Diyora Salimova AI4CE 29 19 0 03 Jun 2020
Semi-supervised deep learning for high-dimensional uncertainty quantification Zequn Wang Mingyang Li UQCV BDL 15 0 0 01 Jun 2020
Enhancing accuracy of deep learning algorithms by training with low-discrepancy sequences Siddhartha Mishra T. Konstantin Rusch 27 49 0 26 May 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 24 104 0 11 May 2020
Neural Network Solutions to Differential Equations in Non-Convex Domains: Solving the Electric Field in the Slit-Well Microfluidic Device M. Magill Andrew M. Nagel H. D. de Haan 6 7 0 25 Apr 2020
Numerical Solution of the Parametric Diffusion Equation by Deep Neural Networks Moritz Geist P. Petersen Mones Raslan R. Schneider Gitta Kutyniok 35 83 0 25 Apr 2020
PFNN: A Penalty-Free Neural Network Method for Solving a Class of Second-Order Boundary-Value Problems on Complex Geometries H. Sheng Chao Yang 22 115 0 14 Apr 2020
Reinforcement Learning in Economics and Finance Arthur Charpentier Romuald Elie Carl Remlinger OffRL 27 150 0 22 Mar 2020
PDGM: a Neural Network Approach to Solve Path-Dependent Partial Differential Equations Yuri F. Saporito Zhao-qin Zhang 31 9 0 04 Mar 2020
Overall error analysis for the training of deep neural networks via stochastic gradient descent with random initialisation Arnulf Jentzen Timo Welti 22 15 0 03 Mar 2020
Learning Stochastic Behaviour from Aggregate Data Shaojun Ma Shu Liu H. Zha Haomin Zhou 15 15 0 10 Feb 2020
Solving high-dimensional eigenvalue problems using deep neural networks: A diffusion Monte Carlo like approach Jiequn Han Jianfeng Lu Mo Zhou DiffM 12 83 0 07 Feb 2020
A Derivative-Free Method for Solving Elliptic Partial Differential Equations with Deep Neural Networks Jihun Han Mihai Nica A. Stinchcombe 30 49 0 17 Jan 2020
The gap between theory and practice in function approximation with deep neural networks Ben Adcock N. Dexter 20 93 0 16 Jan 2020
Universal Differential Equations for Scientific Machine Learning Christopher Rackauckas Yingbo Ma Julius Martensen Collin Warner K. Zubov R. Supekar Dominic J. Skinner Ali Ramadhan Alan Edelman AI4CE 41 569 0 13 Jan 2020
Machine Learning from a Continuous Viewpoint E. Weinan Chao Ma Lei Wu 33 102 0 30 Dec 2019
Polynomial Neural Networks and Taylor maps for Dynamical Systems Simulation and Learning A. Ivanov Anna Golovkina U. Iben PINN 15 8 0 19 Dec 2019
Deep Ritz revisited Johannes Müller Marius Zeinhofer 16 26 0 09 Dec 2019
A Machine Learning Framework for Solving High-Dimensional Mean Field Game and Mean Field Control Problems Lars Ruthotto Stanley Osher Wuchen Li L. Nurbekyan Samy Wu Fung AI4CE 28 214 0 04 Dec 2019
Deep Fictitious Play for Finding Markovian Nash Equilibrium in Multi-Agent Games Jiequn Han Ruimeng Hu 25 43 0 04 Dec 2019
Stationary Points of Shallow Neural Networks with Quadratic Activation Function D. Gamarnik Eren C. Kizildag Ilias Zadik 19 13 0 03 Dec 2019
Extensions of the Deep Galerkin Method A. Al-Aradi Adolfo Correia D. Naiff G. Jardim Yuri F. Saporito 8 27 0 30 Nov 2019
Enabling real-time multi-messenger astrophysics discoveries with deep learning Eliu A. Huerta Gabrielle Allen I. Andreoni J. Antelis E. Bachelet ... Wei Wei J. Wells T. Williams Jinjun Xiong Zhizhen Zhao AI4CE 25 71 0 26 Nov 2019
Uniform error estimates for artificial neural network approximations for heat equations Lukas Gonon Philipp Grohs Arnulf Jentzen David Kofler David Siska 29 34 0 20 Nov 2019
Neural networks for option pricing and hedging: a literature review Johannes Ruf Weiguan Wang 20 121 0 13 Nov 2019
Review: Ordinary Differential Equations For Deep Learning Xinshi Chen AI4TS AI4CE 20 5 0 01 Nov 2019
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
Multi-scale Deep Neural Networks for Solving High Dimensional PDEs Wei Cai Zhi-Qin John Xu AI4CE 19 38 0 25 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
On the space-time expressivity of ResNets J. Muller AI4TS 9 4 0 21 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
Deep Neural Network Framework Based on Backward Stochastic Differential Equations for Pricing and Hedging American Options in High Dimensions Yangang Chen J. Wan 14 59 0 25 Sep 2019
A Neural Network Based Method to Solve Boundary Value Problems Sethu Hareesh Kolluru 11 0 0 24 Sep 2019
A Multi-level procedure for enhancing accuracy of machine learning algorithms K. Lye Siddhartha Mishra Roberto Molinaro 17 32 0 20 Sep 2019
Deep neural network approximations for Monte Carlo algorithms Philipp Grohs Arnulf Jentzen Diyora Salimova 9 34 0 28 Aug 2019
Matrix Lie Maps and Neural Networks for Solving Differential Equations A. Ivanov S. Andrianov 22 3 0 16 Aug 2019
Space-time error estimates for deep neural network approximations for differential equations Philipp Grohs F. Hornung Arnulf Jentzen Philipp Zimmermann 29 33 0 11 Aug 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 11 94 0 05 Aug 2019