An overview on deep learning-based approximation methods for partial
differential equations

An overview on deep learning-based approximation methods for partial differential equations

22 December 2020

Martin Hutzenthaler

Papers citing "An overview on deep learning-based approximation methods for partial differential equations"

18 / 18 papers shown

Title
Practical Aspects on Solving Differential Equations Using Deep Learning: A Primer Georgios Is. Detorakis 16 0 0 21 Aug 2024
Gradient Flow Based Phase-Field Modeling Using Separable Neural Networks R. Mattey Susanta Ghosh AI4CE 38 1 0 09 May 2024
Full error analysis of the random deep splitting method for nonlinear parabolic PDEs and PIDEs Ariel Neufeld Philipp Schmocker Sizhou Wu 24 7 0 08 May 2024
Global Convergence of Deep Galerkin and PINNs Methods for Solving Partial Differential Equations Deqing Jiang Justin A. Sirignano Samuel N. Cohen 20 6 0 10 May 2023
Algorithmically Designed Artificial Neural Networks (ADANNs): Higher order deep operator learning for parametric partial differential equations Arnulf Jentzen Adrian Riekert Philippe von Wurstemberger 11 1 0 07 Feb 2023
Mean-field neural networks: learning mappings on Wasserstein space H. Pham X. Warin 11 13 0 27 Oct 2022
$r-$ Adaptive Deep Learning Method for Solving Partial Differential Equations Ángel J. Omella David Pardo AI4CE 11 4 0 19 Oct 2022
Clifford Neural Layers for PDE Modeling Johannes Brandstetter Rianne van den Berg Max Welling Jayesh K. Gupta AI4CE 60 79 0 08 Sep 2022
Pricing options on flow forwards by neural networks in Hilbert space F. Benth Nils Detering Luca Galimberti 11 7 0 17 Feb 2022
Convergence of a robust deep FBSDE method for stochastic control Kristoffer Andersson Adam Andersson C. Oosterlee 21 19 0 18 Jan 2022
Interpolating between BSDEs and PINNs: deep learning for elliptic and parabolic boundary value problems Nikolas Nusken Lorenz Richter PINN DiffM 28 27 0 07 Dec 2021
Deep Neural Network Algorithms for Parabolic PIDEs and Applications in Insurance Mathematics R. Frey Verena Köck 16 16 0 23 Sep 2021
On the eigenvector bias of Fourier feature networks: From regression to solving multi-scale PDEs with physics-informed neural networks Sifan Wang Hanwen Wang P. Perdikaris 131 437 0 18 Dec 2020
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 203 2,272 0 18 Oct 2020
hp-VPINNs: Variational Physics-Informed Neural Networks With Domain Decomposition E. Kharazmi Zhongqiang Zhang George Karniadakis 117 506 0 11 Mar 2020
Deep neural network solution of the electronic Schrödinger equation J. Hermann Zeno Schätzle Frank Noé 144 445 0 16 Sep 2019
An Energy Approach to the Solution of Partial Differential Equations in Computational Mechanics via Machine Learning: Concepts, Implementation and Applications E. Samaniego C. Anitescu S. Goswami Vien Minh Nguyen-Thanh Hongwei Guo Khader M. Hamdia Timon Rabczuk X. Zhuang PINN AI4CE 145 1,333 0 27 Aug 2019
Deep splitting method for parabolic PDEs C. Beck S. Becker Patrick Cheridito Arnulf Jentzen Ariel Neufeld 14 125 0 08 Jul 2019