4 papers · 1 filter
Convergence analysis of wide shallow neural operators within the framework of Neural Tangent Kernel
Xianliang Xu, Ye Li, Zhongyi Huang
Neural operators are aiming at approximating operators mapping between Banach spaces of functions, achieving much success in the field of scientific computing. Compared to certain…
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…