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"

24 / 24 papers shown

Title
Rational-WENO: A lightweight, physically-consistent three-point weighted essentially non-oscillatory scheme S. Shahane Sheide Chammas Deniz A. Bezgin Aaron B. Buhendwa Steffen J. Schmidt ... Spencer H. Bryngelson Yi-Fan Chen Qing Wang Fei Sha Leonardo Zepeda-Núñez 70 2 0 13 Sep 2024
Full error analysis of the random deep splitting method for nonlinear parabolic PDEs and PIDEs Ariel Neufeld Philipp Schmocker Sizhou Wu 97 7 0 08 May 2024
DySLIM: Dynamics Stable Learning by Invariant Measure for Chaotic Systems Yair Schiff Zhong Yi Wan Jeffrey B. Parker Stephan Hoyer Volodymyr Kuleshov Fei Sha Leonardo Zepeda-Núñez 137 15 0 06 Feb 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 85 11 0 01 Jun 2023
A Neural PDE Solver with Temporal Stencil Modeling Zhiqing Sun Yiming Yang Shinjae Yoo DiffM AI4CE 98 17 0 16 Feb 2023
Evolve Smoothly, Fit Consistently: Learning Smooth Latent Dynamics For Advection-Dominated Systems Z. Y. Wan Leonardo Zepeda-Núñez Anudhyan Boral Fei Sha BDL AI4CE 86 13 0 25 Jan 2023
Learning Relaxation for Multigrid Dmitry Kuznichov AI4CE 46 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 88 62 0 01 Jul 2022
Multigoal-oriented dual-weighted-residual error estimation using deep neural networks Ayan Chakraborty T. Wick X. Zhuang Timon Rabczuk 58 8 0 21 Dec 2021
Learning optimal multigrid smoothers via neural networks Ru Huang Ruipeng Li Yuanzhe Xi AI4CE 69 30 0 24 Feb 2021
STENCIL-NET: Data-driven solution-adaptive discretization of partial differential equations Suryanarayana Maddu D. Sturm B. Cheeseman Christian L. Müller I. Sbalzarini 45 8 0 15 Jan 2021
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 90 77 0 13 Aug 2020
An unsupervised learning approach to solving heat equations on chip based on Auto Encoder and Image Gradient Haiyang He Jay Pathak 66 24 0 19 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 109 267 0 29 Jun 2020
Estimates on the generalization error of Physics Informed Neural Networks (PINNs) for approximating PDEs Siddhartha Mishra Roberto Molinaro PINN 79 173 0 29 Jun 2020
Enhancing accuracy of deep learning algorithms by training with low-discrepancy sequences Siddhartha Mishra T. Konstantin Rusch 82 50 0 26 May 2020
Mean-Field and Kinetic Descriptions of Neural Differential Equations Michael Herty T. Trimborn G. Visconti 118 6 0 07 Jan 2020
A Multi-level procedure for enhancing accuracy of machine learning algorithms K. Lye Siddhartha Mishra Roberto Molinaro 66 32 0 20 Sep 2019
Variational training of neural network approximations of solution maps for physical models Yingzhou Li Jianfeng Lu Anqi Mao GAN 81 36 0 07 May 2019
Constraint-Aware Neural Networks for Riemann Problems Jim Magiera Deep Ray J. Hesthaven C. Rohde AI4CE PINN 73 60 0 29 Apr 2019
Deep learning observables in computational fluid dynamics K. Lye Siddhartha Mishra Deep Ray OOD AI4CE 126 159 0 07 Mar 2019
Learning to Optimize Multigrid PDE Solvers D. Greenfeld Meirav Galun Ron Kimmel I. Yavneh Ronen Basri AI4CE 99 119 0 25 Feb 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 73 119 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 86 171 0 07 Sep 2018