209 citations · 596 across the 42 of their papers we have counts for
9 papers · 1 filter
Data-driven learning of nonlocal models: from high-fidelity simulations to constitutive laws
Huaiqian You, Yue Yu, Stewart Silling +1
We show that machine learning can improve the accuracy of simulations of stress waves in one-dimensional composite materials. We propose a data-driven technique to learn nonlocal c…
An optimization-based approach to parameter learning for fractional type nonlocal models
Olena Burkovska, Christian Glusa, Marta D'Elia
Nonlocal operators of fractional type are a popular modeling choice for applications that do not adhere to classical diffusive behavior; however, one major challenge in nonlocal si…
A general framework for substructuring-based domain decomposition methods for models having nonlocal interactions
Giacomo Capodaglio, Marta D'Elia, Max Gunzburger +3
A rigorous mathematical framework is provided for a substructuring-based domain-decomposition approach for nonlocal problems that feature interactions between points separated by a…
A cookbook for finite element methods for nonlocal problems, including quadrature rules and approximate Euclidean balls
Marta D'Elia, Max Gunzburger, Christian Vollmann
The implementation of finite element methods (FEMs) for nonlocal models with a finite range of interaction poses challenges not faced in the partial differential equations (PDEs) s…
Data-driven learning of robust nonlocal physics from high-fidelity synthetic data
Huaiqian You, Yue Yu, Nathaniel Trask +2
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…
Towards a Unified Theory of Fractional and Nonlocal Vector Calculus
Marta D'Elia, Mamikon Gulian, Hayley Olson +1
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 engineer…
nPINNs: nonlocal Physics-Informed Neural Networks for a parametrized nonlocal universal Laplacian operator. Algorithms and Applications
Guofei Pang, Marta D'Elia, Michael Parks +1
Physics-informed neural networks (PINNs) are effective in solving inverse problems based on differential and integral equations with sparse, noisy, unstructured, and multi-fidelity…
Numerical methods for nonlocal and fractional models
Marta D'Elia, Qiang Du, Christian Glusa +3
Partial differential equations (PDEs) are used, with huge success, to model phenomena arising across all scientific and engineering disciplines. However, across an equally wide swa…
An energy-based coupling approach to nonlocal interface problems
Giacomo Capodaglio, Marta D'Elia, Pavel Bochev +1
Nonlocal models provide accurate representations of physical phenomena ranging from fracture mechanics to complex subsurface flows, where traditional partial differential equations…