Can Physics-Informed Neural Networks beat the Finite Element Method?

Can Physics-Informed Neural Networks beat the Finite Element Method?

8 February 2023

T. G. Grossmann

U. J. Komorowska

Carola-Bibiane Schönlieb

Papers citing "Can Physics-Informed Neural Networks beat the Finite Element Method?"

11 / 11 papers shown

Title
ANaGRAM: A Natural Gradient Relative to Adapted Model for efficient PINNs learning Nilo Schwencke Cyril Furtlehner 64 1 0 14 Dec 2024
Lie Algebra Canonicalization: Equivariant Neural Operators under arbitrary Lie Groups Zakhar Shumaylov Peter Zaika James Rowbottom Ferdia Sherry Melanie Weber Carola-Bibiane Schönlieb 34 1 0 03 Oct 2024
Improved physics-informed neural network in mitigating gradient related failures Pancheng Niu Yongming Chen Jun Guo Yuqian Zhou Minfu Feng Yanchao Shi PINN AI4CE 23 0 0 28 Jul 2024
Weak baselines and reporting biases lead to overoptimism in machine learning for fluid-related partial differential equations N. McGreivy Ammar Hakim AI4CE 29 42 0 09 Jul 2024
Error Analysis of Kernel/GP Methods for Nonlinear and Parametric PDEs Pau Batlle Yifan Chen Bamdad Hosseini H. Owhadi Andrew M. Stuart 26 17 0 08 May 2023
Monte Carlo Neural PDE Solver for Learning PDEs via Probabilistic Representation Rui Zhang Qi Meng Rongchan Zhu Yue Wang Wenlei Shi Shihua Zhang Zhi-Ming Ma Tie-Yan Liu DiffM AI4CE 44 4 0 10 Feb 2023
Finite Basis Physics-Informed Neural Networks (FBPINNs): a scalable domain decomposition approach for solving differential equations Benjamin Moseley Andrew Markham T. Nissen‐Meyer PINN 45 209 0 16 Jul 2021
$NVIDIA SimNet^{TM}: an AI-accelerated multi-physics simulation framework$ NVIDIA SimNet^{TM}: an AI-accelerated multi-physics simulation framework O. Hennigh S. Narasimhan M. A. Nabian Akshay Subramaniam Kaustubh Tangsali M. Rietmann J. Ferrandis Wonmin Byeon Z. Fang S. Choudhry PINN AI4CE 93 126 0 14 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 205 2,282 0 18 Oct 2020
B-PINNs: Bayesian Physics-Informed Neural Networks for Forward and Inverse PDE Problems with Noisy Data Liu Yang Xuhui Meng George Karniadakis PINN 180 758 0 13 Mar 2020
hp-VPINNs: Variational Physics-Informed Neural Networks With Domain Decomposition E. Kharazmi Zhongqiang Zhang George Karniadakis 125 508 0 11 Mar 2020