3 papers
math.AP2025
On parameterized nonlocal-fractional transmission problems and associated function spaces
Qiang Du, Zhaolong Han, Tadele Mengesha +2
In this paper, we consider a family of seamlessly coupled nonlocal models associated with transmission conditions across an interface. The models are derived from the variation of…
cs.LG2025
Monotone Peridynamic Neural Operator for Nonlinear Material Modeling with Conditionally Unique Solutions
Jihong Wang, Xiaochuan Tian, Zhongqiang Zhang +3
Data-driven methods have emerged as powerful tools for modeling the responses of complex nonlinear materials directly from experimental measurements. Among these methods, the data-…
math.AP2024
Compactness results for a Dirichlet energy of nonlocal gradient with applications
Zhaolong Han, Tadele Mengesha, Xiaochuan Tian
We prove two compactness results for function spaces with finite Dirichlet energy of half-space nonlocal gradients. In each of these results, we provide sufficient conditions on a…