9 citations · 10 across the 12 of their papers we have counts for
6 papers · 1 filter
CI-PINN: Causal Integral Physics-Informed Neural Network for Solving Evolution Equations
Xiaodong Feng, Ziyu Sun, Tao Tang +2
Physics-informed neural networks (PINNs) solve partial differential equations (PDEs) by incorporating governing physical laws into the training loss. For evolution equations, howev…
Moving sample method for solving time-dependent partial differential equations
Beining Xu, Haijun Yu, Jiayu Zhai +2
Solving time-dependent partial differential equations (PDEs) that exhibit sharp gradients or local singularities is computationally demanding, as traditional physics-informed neura…
Overcoming Spectral Bias via Cross-Attention
Xiaodong Feng, Tao Tang, Xiaoliang Wan +1
Spectral bias implies an imbalance in training dynamics, whereby high-frequency components may converge substantially more slowly than low-frequency ones. To alleviate this issue,…
Integral regularization PINNs for evolution equations
Xiaodong Feng, Haojiong Shangguan, Tao Tang +1
Evolution equations, including both ordinary differential equations (ODEs) and partial differential equations (PDEs), play a pivotal role in modeling dynamic systems. However, achi…
A hybrid FEM-PINN method for time-dependent partial differential equations
Xiaodong Feng, Haojiong Shangguan, Tao Tang +2
In this work, we present a hybrid numerical method for solving evolution partial differential equations (PDEs) by merging the time finite element method with deep neural networks.…
Deep adaptive sampling for surrogate modeling without labeled data
Xili Wang, Kejun Tang, Jiayu Zhai +2
Surrogate modeling is of great practical significance for parametric differential equation systems. In contrast to classical numerical methods, using physics-informed deep learning…