2 citations · 3 across the 3 of their papers we have counts for
4 papers
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…
A deformation-based framework for learning solution mappings of PDEs defined on varying domains
Shanshan Xiao, Pengzhan Jin, Yifa Tang
In this work, we establish a deformation-based framework for learning solution mappings of PDEs defined on varying domains. The union of functions defined on varying domains can be…
Learning solution operators of PDEs defined on varying domains via MIONet
Shanshan Xiao, Pengzhan Jin, Yifa Tang
In this work, we propose a method to learn the solution operators of PDEs defined on varying domains via MIONet, and theoretically justify this method. We first extend the approxim…
Generalized Lagrangian Neural Networks
Shanshan Xiao, Jiawei Zhang, Yifa Tang
Incorporating neural networks for the solution of Ordinary Differential Equations (ODEs) represents a pivotal research direction within computational mathematics. Within neural net…