6 papers · 1 filter
A semi-generating function approach to the stability of implicit-explicit multistep methods for nonlinear parabolic equations
Hong-lin Liao, Chaoyu Quan, Tao Tang +1
The rigorous stability analysis of high-order implicit-explicit linear multistep (IELM) methods for nonlinear parabolic equations by using discrete energy arguments is a long stand…
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 class of refined implicit-explicit Runge-Kutta methods with robust time adaptability and unconditional convergence for the Cahn-Hilliard model
Hong-lin Liao, Tao Tang, Xuping Wang +1
One of main obstacles in verifying the energy dissipation laws of implicit-explicit Runge-Kutta (IERK) methods for phase field equations is to establish the uniform boundedness of…
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.…
Failure-informed adaptive sampling for PINNs, Part II: combining with re-sampling and subset simulation
Zhiwei Gao, Tao Tang, Liang Yan +1
This is the second part of our series works on failure-informed adaptive sampling for physic-informed neural networks (FI-PINNs). In our previous work \cite{gao2022failure}, we hav…