533 citations · 623 across the 21 of their papers we have counts for
10 papers · 1 filter
SS-ESOAP: Self-Scaled Adaptive Preconditioning for Physics-Informed Learning
Guangyuan Wang, Mads Toftrup, Sebastian Loeschcke +2
Physics-informed neural networks (PINNs) often face ill-conditioned objectives that limit high-accuracy training. Dense quasi-Newton methods improve local conditioning but require…
Fourier Feature Pyramids for Physics-Informed Neural Networks
Brandon Zhao, Yixuan Wang, Jonathan T. Barron +3
We present an improved neural field architecture for solving partial differential equations (PDEs). Current physics-informed neural networks (PINNs) provide a flexible framework fo…
KANO: Kolmogorov-Arnold Neural Operator
Jin Lee, Ziming Liu, Xinling Yu +4
We introduce Kolmogorov--Arnold Neural Operator (KANO), a dual-domain neural operator jointly parameterized by both spectral and spatial bases with intrinsic symbolic interpretabil…
Initialization Schemes for Kolmogorov-Arnold Networks: An Empirical Study
Spyros Rigas, Dhruv Verma, Georgios Alexandridis +1
Kolmogorov-Arnold Networks (KANs) are a recently introduced neural architecture that replace fixed nonlinearities with trainable activation functions, offering enhanced flexibility…
Scale-Consistent Learning for Partial Differential Equations
Zongyi Li, Samuel Lanthaler, Catherine Deng +4
Machine learning (ML) models have emerged as a promising approach for solving partial differential equations (PDEs) in science and engineering. Previous ML models typically cannot…
High precision PINNs in unbounded domains: application to singularity formulation in PDEs
Yixuan Wang, Ziming Liu, Zongyi Li +2
We investigate the high-precision training of Physics-Informed Neural Networks (PINNs) in unbounded domains, with a special focus on applications to singularity formulation in PDEs…
On the expressiveness and spectral bias of KANs
Yixuan Wang, Jonathan W. Siegel, Ziming Liu +1
Kolmogorov-Arnold Networks (KAN) \cite{liu2024kan} were very recently proposed as a potential alternative to the prevalent architectural backbone of many deep learning models, the…
KAN 2.0: Kolmogorov-Arnold Networks Meet Science
Ziming Liu, Pingchuan Ma, Yixuan Wang +2
A major challenge of AI + Science lies in their inherent incompatibility: today's AI is primarily based on connectionism, while science depends on symbolism. To bridge the two worl…
KAN: Kolmogorov-Arnold Networks
Ziming Liu, Yixuan Wang, Sachin Vaidya +5
Inspired by the Kolmogorov-Arnold representation theorem, we propose Kolmogorov-Arnold Networks (KANs) as promising alternatives to Multi-Layer Perceptrons (MLPs). While MLPs have…
FC-PINO: High Precision Physics-Informed Neural Operators via Fourier Continuation
Adarsh Ganeshram, Haydn Maust, Valentin Duruisseaux +6
The physics-informed neural operator (PINO) is a machine learning paradigm that has demonstrated promising results for learning solutions to partial differential equations (PDEs).…