A machine learning framework for data driven acceleration of computations of differential equations

25 July 2018

Papers citing "A machine learning framework for data driven acceleration of computations of differential equations"

16 / 16 papers shown

Title
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
Neural Ideal Large Eddy Simulation: Modeling Turbulence with Neural Stochastic Differential Equations Anudhyan Boral Z. Y. Wan Leonardo Zepeda-Núñez James Lottes Qing Wang Yi-fan Chen John R. Anderson Fei Sha AI4CE PINN 29 11 0 01 Jun 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
Invariant preservation in machine learned PDE solvers via error correction N. McGreivy Ammar Hakim AI4CE PINN 29 8 0 28 Mar 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
Learning Relaxation for Multigrid Dmitry Kuznichov AI4CE 24 1 0 25 Jul 2022
Learning to correct spectral methods for simulating turbulent flows Gideon Dresdner Dmitrii Kochkov Peter C. Norgaard Leonardo Zepeda-Núñez Jamie A. Smith M. Brenner Stephan Hoyer AI4CE 23 56 0 01 Jul 2022
Learning optimal multigrid smoothers via neural networks Ru Huang Ruipeng Li Yuanzhe Xi AI4CE 18 27 0 24 Feb 2021
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
Enhancing accuracy of deep learning algorithms by training with low-discrepancy sequences Siddhartha Mishra T. Konstantin Rusch 24 49 0 26 May 2020
Mean-Field and Kinetic Descriptions of Neural Differential Equations Michael Herty T. Trimborn G. Visconti 36 6 0 07 Jan 2020
A Multi-level procedure for enhancing accuracy of machine learning algorithms K. Lye Siddhartha Mishra Roberto Molinaro 17 32 0 20 Sep 2019
Variational training of neural network approximations of solution maps for physical models Yingzhou Li Jianfeng Lu Anqi Mao GAN 19 35 0 07 May 2019
Deep learning observables in computational fluid dynamics K. Lye Siddhartha Mishra Deep Ray OOD AI4CE 15 158 0 07 Mar 2019
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 16 116 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 11 167 0 07 Sep 2018