5 papers · 1 filter
A Geometry-Aware Operator Learning Framework for Interface Problems on Varying Domains
Shanshan Xiao, Ye Li, Zhongyi Huang +1
Solving Partial Differential Equation (PDE) interface problems on varying domains is a critical task in design and optimization, yet it remains computationally prohibitive for trad…
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…
A Priori Estimation of the Approximation, Optimization and Generalization Errors of Random Neural Networks for Solving Partial Differential Equations
Xianliang Xu, Ye Li, Zhongyi Huang
In recent years, neural networks have achieved remarkable progress in various fields and have also drawn much attention in applying them on scientific problems. A line of methods i…
Refined generalization analysis of the Deep Ritz Method and Physics-Informed Neural Networks
Xianliang Xu, Ye Li, Zhongyi Huang
In this paper, we derive refined generalization bounds for the Deep Ritz Method (DRM) and Physics-Informed Neural Networks (PINNs). For the DRM, we focus on two prototype elliptic…