A Deep Neural Network Surrogate for High-Dimensional Random Partial Differential Equations

8 June 2018

Papers citing "A Deep Neural Network Surrogate for High-Dimensional Random Partial Differential Equations"

22 / 22 papers shown

Title
Optimization Landscapes Learned: Proxy Networks Boost Convergence in Physics-based Inverse Problems Girnar Goyal Philipp Holl Sweta Agrawal Nils Thuerey AI4CE 53 0 0 27 Jan 2025
Physics-Aware Neural Implicit Solvers for multiscale, parametric PDEs with applications in heterogeneous media Matthaios Chatzopoulos P. Koutsourelakis AI4CE 41 3 0 29 May 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
Approximation of Solution Operators for High-dimensional PDEs Nathan Gaby Xiaojing Ye 30 0 0 18 Jan 2024
Bayesian deep learning framework for uncertainty quantification in high dimensions Jeahan Jung Minseok Choi BDL UQCV 26 1 0 21 Oct 2022
MultiAuto-DeepONet: A Multi-resolution Autoencoder DeepONet for Nonlinear Dimension Reduction, Uncertainty Quantification and Operator Learning of Forward and Inverse Stochastic Problems Jiahao Zhang Shiqi Zhang Guang Lin 25 14 0 07 Apr 2022
PI-VAE: Physics-Informed Variational Auto-Encoder for stochastic differential equations Weiheng Zhong Hadi Meidani DRL 30 37 0 21 Mar 2022
Computing the Invariant Distribution of Randomly Perturbed Dynamical Systems Using Deep Learning Bo Lin Qianxiao Li W. Ren 29 8 0 22 Oct 2021
Predicting the spread of COVID-19 in Delhi, India using Deep Residual Recurrent Neural Networks S. Vadyala S. N. Betgeri 41 2 0 09 Oct 2021
A Deep Collocation Method for the Bending Analysis of Kirchhoff Plate Hongwei Guo X. Zhuang Timon Rabczuk AI4CE 27 433 0 04 Feb 2021
An overview on deep learning-based approximation methods for partial differential equations C. Beck Martin Hutzenthaler Arnulf Jentzen Benno Kuckuck 35 146 0 22 Dec 2020
Weak error analysis for stochastic gradient descent optimization algorithms A. Bercher Lukas Gonon Arnulf Jentzen Diyora Salimova 36 4 0 03 Jul 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
PyDEns: a Python Framework for Solving Differential Equations with Neural Networks A. Koryagin R. Khudorozhkov S. Tsimfer OOD AI4CE 6 32 0 25 Sep 2019
DeepXDE: A deep learning library for solving differential equations Lu Lu Xuhui Meng Zhiping Mao George Karniadakis PINN AI4CE 52 1,491 0 10 Jul 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 46 854 0 18 Jan 2019
Physics-Informed Generative Adversarial Networks for Stochastic Differential Equations Siyu Dai Shawn Schaffert Andreas G. Hofmann 17 355 0 05 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
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
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 29 116 0 19 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 21 167 0 07 Sep 2018
Deep convolutional encoder-decoder networks for uncertainty quantification of dynamic multiphase flow in heterogeneous media S. Mo Yinhao Zhu N. Zabaras Xiaoqing Shi Jichun Wu AI4CE 16 272 0 02 Jul 2018