5 papers
Physics-Informed Tailored Finite Point Operator Network for Parametric Interface Problems
Ting Du, Xianliang Xu, Wang Kong +2
Learning operators for parametric partial differential equations (PDEs) using neural networks has gained significant attention in recent years. However, standard approaches like De…
Tailored Finite Point Operator Networks for Interface problems
Ye Li, Ting Du, Zhongyi Huang
Interface problems pose significant challenges due to the discontinuity of their solutions, particularly when they involve singular perturbations or high-contrast coefficients, res…
Component Fourier Neural Operator for Singularly Perturbed Differential Equations
Ye Li, Ting Du, Yiwen Pang +1
Solving Singularly Perturbed Differential Equations (SPDEs) poses computational challenges arising from the rapid transitions in their solutions within thin regions. The effectiven…
Convergence Analysis of Natural Gradient Descent for Over-parameterized Physics-Informed Neural Networks
Xianliang Xu, Ting Du, Wang Kong +3
In the context of over-parameterization, there is a line of work demonstrating that randomly initialized (stochastic) gradient descent (GD) converges to a globally optimal solution…
Convergence of Implicit Gradient Descent for Training Two-Layer Physics-Informed Neural Networks
Xianliang Xu, Ting Du, Wang Kong +3
The optimization algorithms are crucial in training physics-informed neural networks (PINNs), as unsuitable methods may lead to poor solutions. Compared to the common gradient desc…