4 papers
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…
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…