A review of local-to-nonlocal coupling methods in nonlocal diffusion and nonlocal mechanics

M D'Elia, X Li, P Seleson, X Tian, Y Yu - Journal of Peridynamics and …, 2022 - Springer
Abstract Local-to-nonlocal (LtN) coupling refers to a class of methods aimed at combining
nonlocal and local modeling descriptions of a given system into a unified coupled …

Nonlocal attention operator: Materializing hidden knowledge towards interpretable physics discovery

Y Yu, N Liu, F Lu, T Gao… - Advances in Neural …, 2025 - proceedings.neurips.cc
Despite recent popularity of attention-based neural architectures in core AI fields like natural
language processing (NLP) and computer vision (CV), their potential in modeling complex …

Towards a unified theory of fractional and nonlocal vector calculus

M D'Elia, M Gulian, H Olson… - Fractional Calculus and …, 2021 - degruyter.com
Nonlocal and fractional-order models capture effects that classical partial differential
equations cannot describe; for this reason, they are suitable for a broad class of engineering …

Data-driven learning of nonlocal physics from high-fidelity synthetic data

H You, Y Yu, N Trask, M Gulian, M D'Elia - Computer Methods in Applied …, 2021 - Elsevier
A key challenge to nonlocal models is the analytical complexity of deriving them from first
principles, and frequently their use is justified a posteriori. In this work we extract nonlocal …

Peridynamic neural operators: A data-driven nonlocal constitutive model for complex material responses

S Jafarzadeh, S Silling, N Liu, Z Zhang, Y Yu - Computer Methods in …, 2024 - Elsevier
Neural operators, which can act as implicit solution operators of hidden governing
equations, have recently become popular tools for learning the responses of complex real …

A data-driven peridynamic continuum model for upscaling molecular dynamics

H You, Y Yu, S Silling, M D'Elia - Computer Methods in Applied Mechanics …, 2022 - Elsevier
Nonlocal models, including peridynamics, often use integral operators that embed
lengthscales in their definition. However, the integrands in these operators are difficult to …

Heterogeneous peridynamic neural operators: Discover biotissue constitutive law and microstructure from digital image correlation measurements

S Jafarzadeh, S Silling, L Zhang, C Ross… - arxiv preprint arxiv …, 2024 - arxiv.org
Human tissues are highly organized structures with collagen fiber arrangements varying
from point to point. Anisotropy of the tissue arises from the natural orientation of the fibers …

Towards a unified theory of fractional and nonlocal vector calculus

M D'Elia, M Gulian, H Olson, GE Karniadakis - arxiv preprint arxiv …, 2020 - arxiv.org
Nonlocal and fractional-order models capture effects that classical partial differential
equations cannot describe; for this reason, they are suitable for a broad class of engineering …

Peridynamic micromechanics of composites: a review

VA Buryachenko - Journal of Peridynamics and Nonlocal Modeling, 2024 - Springer
A static peridynamic (proposed by Silling, see J. Mech. Phys. Solids 2000; 48: 175–209)
composite materials (CMs) of both the random and periodic structures are considered. In the …

Nonlocal diffusion models with consistent local and fractional limits

Q Du, X Tian, Z Zhou - … , Applications, and Analysis of Nonlocal, Nonlinear …, 2023 - Springer
For some spatially nonlocal diffusion models with a finite range of nonlocal interactions
measured by a positive parameter δ, we review their formulation defined on a bounded …