Numerically Solving Parametric Families of High-Dimensional Kolmogorov Partial Differential Equations via Deep Learning

9 November 2020

Papers citing "Numerically Solving Parametric Families of High-Dimensional Kolmogorov Partial Differential Equations via Deep Learning"

14 / 14 papers shown

Title
Multilevel Picard approximations and deep neural networks with ReLU, leaky ReLU, and softplus activation overcome the curse of dimensionality when approximating semilinear parabolic partial differential equations in $L^p$ -sense Ariel Neufeld Tuan Anh Nguyen 42 0 0 30 Sep 2024
Improving PINNs By Algebraic Inclusion of Boundary and Initial Conditions Mohan Ren Zhihao Fang Keren Li Anirbit Mukherjee PINN AI4CE 53 0 0 30 Jul 2024
Base Models for Parabolic Partial Differential Equations Xingzi Xu Ali Hasan Jie Ding Vahid Tarokh 45 1 0 17 Jul 2024
Feynman-Kac Operator Expectation Estimator Jingyuan Li Wei Liu 38 0 0 02 Jul 2024
Solving Poisson Equations using Neural Walk-on-Spheres Hong Chul Nam Julius Berner Anima Anandkumar 39 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 45 7 0 08 May 2024
Generative Modelling with Tensor Train approximations of Hamilton--Jacobi--Bellman equations David Sommer Robert Gruhlke Max Kirstein Martin Eigel Claudia Schillings 31 3 0 23 Feb 2024
Neural Operators for Accelerating Scientific Simulations and Design Kamyar Azzizadenesheli Nikola B. Kovachki Zong-Yi Li Miguel Liu-Schiaffini Jean Kossaifi Anima Anandkumar AI4CE 43 128 0 27 Sep 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 37 5 0 26 Apr 2023
Multilevel CNNs for Parametric PDEs Cosmas Heiß Ingo Gühring Martin Eigel AI4CE 25 8 0 01 Apr 2023
NeuralStagger: Accelerating Physics-constrained Neural PDE Solver with Spatial-temporal Decomposition Xinquan Huang Wenlei Shi Qi Meng Yue Wang Xiaotian Gao Jia Zhang Tie-Yan Liu AI4CE 23 8 0 20 Feb 2023
An optimal control perspective on diffusion-based generative modeling Julius Berner Lorenz Richter Karen Ullrich DiffM 44 81 0 02 Nov 2022
Robust SDE-Based Variational Formulations for Solving Linear PDEs via Deep Learning Lorenz Richter Julius Berner 27 19 0 21 Jun 2022
LordNet: An Efficient Neural Network for Learning to Solve Parametric Partial Differential Equations without Simulated Data Xinquan Huang Wenlei Shi Xiaotian Gao Xinran Wei Jia Zhang Jiang Bian Mao Yang Tie-Yan Liu PINN 27 10 0 19 Jun 2022