Adaptive Training of Grid-Dependent Physics-Informed Kolmogorov-Arnold Networks

24 July 2024

Spyros Rigas

M. Papachristou

Theofilos Papadopoulos

Fotios Anagnostopoulos

Georgios Alexandridis

AI4CE

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Papers citing "Adaptive Training of Grid-Dependent Physics-Informed Kolmogorov-Arnold Networks"

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Title
Anant-Net: Breaking the Curse of Dimensionality with Scalable and Interpretable Neural Surrogate for High-Dimensional PDEs Sidharth S. Menon Ameya D. Jagtap PINN 331 0 0 06 May 2025
Low Tensor-Rank Adaptation of Kolmogorov--Arnold Networks Yihang Gao Michael K. Ng Vincent Y. F. Tan 220 0 0 17 Feb 2025
KAA: Kolmogorov-Arnold Attention for Enhancing Attentive Graph Neural Networks Taoran Fang Tianhong Gao Chunping Wang Yihao Shang Wei Chow Lei Chen Yang Yang 151 2 0 23 Jan 2025
Deep Learning Alternatives of the Kolmogorov Superposition Theorem Leonardo Ferreira Guilhoto P. Perdikaris 84 7 0 02 Oct 2024
On the expressiveness and spectral bias of KANs Yixuan Wang Jonathan W. Siegel Ziming Liu Thomas Y. Hou 87 12 0 02 Oct 2024
KAN we improve on HEP classification tasks? Kolmogorov-Arnold Networks applied to an LHC physics example Johannes Erdmann F. Mausolf Jan Lukas Späh 188 4 0 05 Aug 2024
Deep State Space Recurrent Neural Networks for Time Series Forecasting Hugo Inzirillo AI4TS 47 6 0 21 Jul 2024
U-KAN Makes Strong Backbone for Medical Image Segmentation and Generation Chenxin Li Xinyu Liu Wenbo Li Cheng Wang Hengyu Liu Yifan Liu Zhen Chen Yixuan Yuan MedIm DiffM SSeg 102 132 0 05 Jun 2024
A Temporal Kolmogorov-Arnold Transformer for Time Series Forecasting Remi Genet Hugo Inzirillo AI4TS 90 44 0 04 Jun 2024
RoPINN: Region Optimized Physics-Informed Neural Networks Haixu Wu Huakun Luo Yuezhou Ma Jianmin Wang Mingsheng Long AI4CE 53 8 0 23 May 2024
Kolmogorov-Arnold Networks are Radial Basis Function Networks Ziyao Li 91 76 0 10 May 2024
KAN: Kolmogorov-Arnold Networks Ziming Liu Yixuan Wang Sachin Vaidya Fabian Ruehle James Halverson Marin Soljacic Thomas Y. Hou Max Tegmark 235 546 0 30 Apr 2024
An Expert's Guide to Training Physics-informed Neural Networks Sizhuang He Shyam Sankaran Hanwen Wang P. Perdikaris PINN 90 107 0 16 Aug 2023
A comprehensive study of non-adaptive and residual-based adaptive sampling for physics-informed neural networks Chen-Chun Wu Min Zhu Qinyan Tan Yadhu Kartha Lu Lu 75 374 0 21 Jul 2022
Efficient training of physics-informed neural networks via importance sampling M. A. Nabian R. J. Gladstone Hadi Meidani DiffM PINN 116 233 0 26 Apr 2021
When and why PINNs fail to train: A neural tangent kernel perspective Sizhuang He Xinling Yu P. Perdikaris 130 909 0 28 Jul 2020
On the Spectral Bias of Neural Networks Nasim Rahaman A. Baratin Devansh Arpit Felix Dräxler Min Lin Fred Hamprecht Yoshua Bengio Aaron Courville 141 1,438 0 22 Jun 2018
Physics Informed Deep Learning (Part II): Data-driven Discovery of Nonlinear Partial Differential Equations M. Raissi P. Perdikaris George Karniadakis PINN AI4CE 81 613 0 28 Nov 2017
Physics Informed Deep Learning (Part I): Data-driven Solutions of Nonlinear Partial Differential Equations M. Raissi P. Perdikaris George Karniadakis PINN AI4CE 75 924 0 28 Nov 2017
Automatic differentiation in machine learning: a survey A. G. Baydin Barak A. Pearlmutter Alexey Radul J. Siskind PINN AI4CE ODL 156 2,803 0 20 Feb 2015
Adam: A Method for Stochastic Optimization Diederik P. Kingma Jimmy Ba ODL 1.8K 150,039 0 22 Dec 2014