27 citations · 118 across the 26 of their papers we have counts for
4 papers · 1 filter
Weights initialization of neural networks for function approximation
Xinwen Hu, Yunqing Huang, Nianyu Yi +1
Neural network-based function approximation plays a pivotal role in the advancement of scientific computing and machine learning. Yet, training such models faces several challenges…
A positivity-preserving hybrid DDG method for Poisson--Nernst--Planck systems
Hailiang Liu, Zhongming Wang, Peimeng Yin
In earlier work [H. Liu and Z. Wang, J. Comput. Phys., 328(2017)], an arbitrary high-order conservative and energy-dissipative direct discontinuous Galerkin (DDG) scheme was develo…
Neural network-enhanced -adaptive finite element algorithm for parabolic equations
Jiaxiong Hao, Yunqing Huang, Nianyu Yi +1
In this paper, we propose a novel -adaptive finite element method, enhanced by neural networks, for parabolic equations. The main challenge of the conventional -adaptive fin…
A second-order dynamical low-rank mass-lumped finite element method for the Allen-Cahn equation
Jun Yang, Nianyu Yi, Peimeng Yin
In this paper, we propose a novel second-order dynamical low-rank mass-lumped finite element method for solving the Allen-Cahn (AC) equation, a semilinear parabolic partial differe…