Error analysis for deep neural network approximations of parametric hyperbolic conservation laws

15 July 2022

Papers citing "Error analysis for deep neural network approximations of parametric hyperbolic conservation laws"

18 / 18 papers shown

Title
wPINNs: Weak Physics informed neural networks for approximating entropy solutions of hyperbolic conservation laws Tim De Ryck Siddhartha Mishra Roberto Molinaro PINN 61 30 0 18 Jul 2022
Generic bounds on the approximation error for physics-informed (and) operator learning Tim De Ryck Siddhartha Mishra PINN 104 62 0 23 May 2022
Error estimates for physics informed neural networks approximating the Navier-Stokes equations Tim De Ryck Ameya Dilip Jagtap S. Mishra PINN 83 118 0 17 Mar 2022
On the approximation of functions by tanh neural networks Tim De Ryck S. Lanthaler Siddhartha Mishra 48 138 0 18 Apr 2021
Fourier Neural Operator for Parametric Partial Differential Equations Zong-Yi Li Nikola B. Kovachki Kamyar Azizzadenesheli Burigede Liu K. Bhattacharya Andrew M. Stuart Anima Anandkumar AI4CE 494 2,401 0 18 Oct 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 58 76 0 13 Aug 2020
Overall error analysis for the training of deep neural networks via stochastic gradient descent with random initialisation Arnulf Jentzen Timo Welti 43 17 0 03 Mar 2020
On the approximation of rough functions with deep neural networks Tim De Ryck Siddhartha Mishra Deep Ray 18 7 0 13 Dec 2019
Full error analysis for the training of deep neural networks C. Beck Arnulf Jentzen Benno Kuckuck 43 47 0 30 Sep 2019
A Multi-level procedure for enhancing accuracy of machine learning algorithms K. Lye Siddhartha Mishra Roberto Molinaro 48 32 0 20 Sep 2019
A Theoretical Analysis of Deep Neural Networks and Parametric PDEs Gitta Kutyniok P. Petersen Mones Raslan R. Schneider 69 198 0 31 Mar 2019
Deep learning observables in computational fluid dynamics K. Lye Siddhartha Mishra Deep Ray OOD AI4CE 98 159 0 07 Mar 2019
Deep Neural Network Approximation Theory Dennis Elbrächter Dmytro Perekrestenko Philipp Grohs Helmut Bölcskei 54 210 0 08 Jan 2019
Analysis of the Generalization Error: Empirical Risk Minimization over Deep Artificial Neural Networks Overcomes the Curse of Dimensionality in the Numerical Approximation of Black-Scholes Partial Differential Equations Julius Berner Philipp Grohs Arnulf Jentzen 51 182 0 09 Sep 2018
Hidden Physics Models: Machine Learning of Nonlinear Partial Differential Equations M. Raissi George Karniadakis AI4CE PINN 67 1,137 0 02 Aug 2017
Deep learning-based numerical methods for high-dimensional parabolic partial differential equations and backward stochastic differential equations Weinan E Jiequn Han Arnulf Jentzen 119 797 0 15 Jun 2017
Error bounds for approximations with deep ReLU networks Dmitry Yarotsky 193 1,227 0 03 Oct 2016
Adam: A Method for Stochastic Optimization Diederik P. Kingma Jimmy Ba ODL 1.8K 150,039 0 22 Dec 2014