3 papers
cs.LG2026
Sinc Kolmogorov-Arnold network and its application for solving PDEs with singularities
Tianchi Yu, Jingwei Qiu, Jiang Yang +1
In this paper, we propose to use Sinc interpolation in the context of Kolmogorov-Arnold Networks, neural networks with learnable activation functions, which recently gained attenti…
math.NA2026
A second-order product-type implicit-explicit Runge-Kutta method preserving unit length and energy dissipation structures for gradient flows of vector fields
Jianan Li, Shuang Liu, Tao Tang +1
Gradient flows of unit vector fields arise in a wide range of physical models such as harmonic map heat flows, nematic liquid crystals, and magnetization dynamics. Designing numeri…
math.NA2026
Energy Dissipation Preserving Feature-based DNN Galerkin Methods for Gradient Flows
Tao Tang, Jiang Yang, Yuxiang Zhao +1
In recent years, deep learning methods, exemplified by Physics-Informed Neural Networks (PINNs), have been widely applied to the numerical solution of differential equations. Howev…