Data-driven bond-based peridynamics with nonlocal influence function for crack propagation

Deep learning method for predicting the strengths of microcracked brittle materials

(2022) Bo-Wen Xu et al.   ENGINEERING FRACTURE MECHANICS

Fuzzy fractional differential equations under the Mittag-Leffler kernel differential operator of the ABC approach: Theorems and applications

(2021) Mohammed Al-Smadi et al.   CHAOS SOLITONS & FRACTALS

Identification of the interfacial cohesive law parameters of FRP strips externally bonded to concrete using machine learning techniques

(2021) Miao Su et al.   ENGINEERING FRACTURE MECHANICS

Deep-learning of parametric partial differential equations from sparse and noisy data

(2021) Hao Xu et al.   PHYSICS OF FLUIDS

Data-driven fatigue life prediction in additive manufactured titanium alloy: A damage mechanics based machine learning framework

(2021) Zhixin Zhan et al.   ENGINEERING FRACTURE MECHANICS

A data-driven peridynamic continuum model for upscaling molecular dynamics

(2021) Huaiqian You et al.   COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING

Deep-learning based discovery of partial differential equations in integral form from sparse and noisy data

(2021) Hao Xu et al.   JOURNAL OF COMPUTATIONAL PHYSICS

An improved data-free surrogate model for solving partial differential equations using deep neural networks

(2021) Xinhai Chen et al.   Scientific Reports

Data-driven multiscale finite element method: From concurrence to separation

(2020) Rui Xu et al.   COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING

nPINNs: Nonlocal physics-informed neural networks for a parametrized nonlocal universal Laplacian operator. Algorithms and applications

(2020) G. Pang et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Existence of traveling wave solutions to a nonlocal scalar equation with sign-changing kernel

(2020) Shin-Ichiro Ei et al.   JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

Data-driven molecular modeling with the generalized Langevin equation

(2020) Francesca Grogan et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Data-driven multiscale simulation of FRP based on material twins

(2020) Wei Huang et al.   COMPOSITE STRUCTURES

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

(2020) Huaiqian You et al.   COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING

A study of pattern forming systems with a fully nonlocal interaction kernel of possibly changing sign

(2019) Xiaofeng Ren et al.   PHYSICA D-NONLINEAR PHENOMENA

A data-driven framework for sparsity-enhanced surrogates with arbitrary mutually dependent randomness

(2019) Huan Lei et al.   COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING

XFEM and experimental simulation of failure mechanism of non-persistent joints in mortar under compression

(2019) Hadi Haeri et al.   CONSTRUCTION AND BUILDING MATERIALS

Data-driven discovery of partial differential equations

(2017) Samuel H. Rudy et al.   Science Advances

Discovering governing equations from data by sparse identification of nonlinear dynamical systems

(2016) Steven L. Brunton et al.   PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA

New fractional derivatives with nonlocal and non-singular kernel: Theory and application to heat transfer model

(2016) Abdon Atangana et al.   Thermal Science

Cohesive Dynamics and Brittle Fracture

(2015) Robert Lipton   JOURNAL OF ELASTICITY

Analysis of a scalar nonlocal peridynamic model with a sign changing kernel

(2013) Tadele Mengesha et al.   DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B

A reproducing kernel method for solving nonlocal fractional boundary value problems

(2011) Fazhan Geng et al.   APPLIED MATHEMATICS LETTERS

Statistical mechanical foundation of the peridynamic nonlocal continuum theory: Energy and momentum conservation laws

(2011) R. B. Lehoucq et al.   PHYSICAL REVIEW E

From Local Kernel to Nonlocal Multiple-Model Image Denoising

(2009) Vladimir Katkovnik et al.   INTERNATIONAL JOURNAL OF COMPUTER VISION

Nonlocal anisotropic dispersal with monostable nonlinearity

(2008) Jérôme Coville et al.   JOURNAL OF DIFFERENTIAL EQUATIONS