Quantifying Training Difficulty and Accelerating Convergence in Neural
Network-Based PDE Solvers

Quantifying Training Difficulty and Accelerating Convergence in Neural Network-Based PDE Solvers

8 October 2024

Yang Xiang

Tao Luo

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Papers citing "Quantifying Training Difficulty and Accelerating Convergence in Neural Network-Based PDE Solvers"

14 / 14 papers shown

Title
Initialization-enhanced Physics-Informed Neural Network with Domain Decomposition (IDPINN) Chenhao Si Ming Yan AI4CE PINN 68 4 0 05 Jun 2024
Automatic Differentiation is Essential in Training Neural Networks for Solving Differential Equations Chuqi Chen Yahong Yang Yang Xiang Wenrui Hao 62 2 0 23 May 2024
HomPINNs: homotopy physics-informed neural networks for solving the inverse problems of nonlinear differential equations with multiple solutions Haoyang Zheng Yao Huang Ziyang Huang Wenrui Hao Guang Lin PINN 25 13 0 06 Apr 2023
GPT-4 Technical Report OpenAI OpenAI OpenAI Josh Achiam Steven Adler Sandhini Agarwal Lama Ahmad ... Shengjia Zhao Tianhao Zheng Juntang Zhuang William Zhuk Barret Zoph LLMAG MLLM 1.4K 14,631 0 15 Mar 2023
DOSnet as a Non-Black-Box PDE Solver: When Deep Learning Meets Operator Splitting Yuan Lan Zerui Li Jie Sun Yang Xiang 52 11 0 11 Dec 2022
Parallel Physics-Informed Neural Networks via Domain Decomposition K. Shukla Ameya Dilip Jagtap George Karniadakis PINN 162 284 0 20 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 500 2,414 0 18 Oct 2020
When and why PINNs fail to train: A neural tangent kernel perspective Sizhuang He Xinling Yu P. Perdikaris 141 914 0 28 Jul 2020
Language Models are Few-Shot Learners Tom B. Brown Benjamin Mann Nick Ryder Melanie Subbiah Jared Kaplan ... Christopher Berner Sam McCandlish Alec Radford Ilya Sutskever Dario Amodei BDL 814 42,055 0 28 May 2020
Frequency Bias in Neural Networks for Input of Non-Uniform Density Ronen Basri Meirav Galun Amnon Geifman David Jacobs Yoni Kasten S. Kritchman 84 185 0 10 Mar 2020
DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators Lu Lu Pengzhan Jin George Karniadakis 248 2,131 0 08 Oct 2019
Frequency Principle: Fourier Analysis Sheds Light on Deep Neural Networks Zhi-Qin John Xu Yaoyu Zhang Yaoyu Zhang Yan Xiao Zheng Ma 124 516 0 19 Jan 2019
On the Spectral Bias of Neural Networks Nasim Rahaman A. Baratin Devansh Arpit Felix Dräxler Min Lin Fred Hamprecht Yoshua Bengio Aaron Courville 154 1,451 0 22 Jun 2018
The Deep Ritz method: A deep learning-based numerical algorithm for solving variational problems E. Weinan Ting Yu 121 1,387 0 30 Sep 2017