533 citations · 623 across the 21 of their papers we have counts for
6 papers · 1 filter
Nonuniqueness of Leray-Hopf solutions to the unforced incompressible 3D Navier-Stokes Equation
Thomas Hou, Yixuan Wang, Changhe Yang
The nonuniqueness of Leray-Hopf solutions to the unforced incompressible 3D Navier-Stokes equations is one of the central open problems in mathematical fluid dynamics. In this pape…
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…
Finite time blowup for Keller-Segel equation with logistic damping in three dimensions
Jiaqi Liu, Yixuan Wang, Tao Zhou
The Keller-Segel equation, a classical chemotaxis model, and many of its variants have been extensively studied for decades. In this work, we focus on 3D Keller-Segel equation with…