209 citations · 596 across the 42 of their papers we have counts for
43 papers
A scalable domain decomposition method for FEM discretizations of nonlocal equations of integrable and fractional type
Manuel Klar, Giacomo Capodaglio, Marta D'Elia +3
Nonlocal models allow for the description of phenomena which cannot be captured by classical partial differential equations. The availability of efficient solvers is one of the mai…
GNN-based physics solver for time-independent PDEs
Rini Jasmine Gladstone, Helia Rahmani, Vishvas Suryakumar +3
Physics-based deep learning frameworks have shown to be effective in accurately modeling the dynamics of complex physical systems with generalization capability across problem inpu…
Towards a unified nonlocal, peridynamics framework for the coarse-graining of molecular dynamics data with fractures
Huaiqian You, Xiao Xu, Yue Yu +3
Molecular dynamics (MD) has served as a powerful tool for designing materials with reduced reliance on laboratory testing. However, the use of MD directly to treat the deformation…
Control of fractional diffusion problems via dynamic programming equations
Alessandro Alla, Marta D'Elia, Christian Glusa +1
We explore the approximation of feedback control of integro-differential equations containing a fractional Laplacian term. To obtain feedback control for the state variable of this…
Bayesian Nonlocal Operator Regression (BNOR): A Data-Driven Learning Framework of Nonlocal Models with Uncertainty Quantification
Yiming Fan, Marta D'Elia, Yue Yu +2
We consider the problem of modeling heterogeneous materials where micro-scale dynamics and interactions affect global behavior. In the presence of heterogeneities in material micro…
Probabilistic partition of unity networks for high-dimensional regression problems
Tiffany Fan, Nathaniel Trask, Marta D'Elia +1
We explore the probabilistic partition of unity network (PPOU-Net) model in the context of high-dimensional regression problems and propose a general framework focusing on adaptive…
Nonlocal Machine Learning of Micro-Structural Defect Evolutions in Crystalline Materials
Eduardo Augusto Barros de Moraes, Marta D'Elia, Mohsen Zayernouri
The presence and evolution of defects that appear in the manufacturing process play a vital role in the failure mechanisms of engineering materials. In particular, the collective b…
An asymptotically compatible coupling formulation for nonlocal interface problems with jumps
Christian Glusa, Marta D'Elia, Giacomo Capodaglio +2
We introduce a mathematically rigorous formulation for a nonlocal interface problem with jumps and propose an asymptotically compatible finite element discretization for the weak f…
Efficient optimization-based quadrature for variational discretization of nonlocal problems
Marco Pasetto, Zhaoxiang Shen, Marta D'Elia +3
Casting nonlocal problems in variational form and discretizing them with the finite element (FE) method facilitates the use of nonlocal vector calculus to prove well-posedeness, co…
Machine-learning of nonlocal kernels for anomalous subsurface transport from breakthrough curves
Xiao Xu, Marta D'Elia, Christian Glusa +1
Anomalous behavior is ubiquitous in subsurface solute transport due to the presence of high degrees of heterogeneity at different scales in the media. Although fractional models ha…
Nonlocal Kernel Network (NKN): a Stable and Resolution-Independent Deep Neural Network
Huaiqian You, Yue Yu, Marta D'Elia +2
Neural operators have recently become popular tools for designing solution maps between function spaces in the form of neural networks. Differently from classical scientific machin…
Connections between nonlocal operators: from vector calculus identities to a fractional Helmholtz decomposition
Marta D'Elia, Mamikon Gulian, Tadele Mengesha +1
Nonlocal vector calculus, which is based on the nonlocal forms of gradient, divergence, and Laplace operators in multiple dimensions, has shown promising applications in fields suc…
Fractional Modeling in Action: A Survey of Nonlocal Models for Subsurface Transport, Turbulent Flows, and Anomalous Materials
Jorge Suzuki, Mamikon Gulian, Mohsen Zayernouri +1
Modeling of phenomena such as anomalous transport via fractional-order differential equations has been established as an effective alternative to partial differential equations, du…
An optimization-based strategy for peridynamic-FEM coupling and for the prescription of nonlocal boundary conditions
Marta D'Elia, David Littlewood, Jeremy Trageser +2
We develop and analyze an optimization-based method for the coupling of a static peri-dynamic (PD) model and a static classical elasticity model. The approach formulates the coupli…
Peridynamic Model for Single-Layer Graphene Obtained from Coarse Grained Bond Forces
Stewart A. Silling, Marta D'Elia, Yue Yu +2
An ordinary state-based peridynamic material model is proposed for single sheet graphene. The model is calibrated using coarse grained molecular dynamics simulations. The coarse gr…
On the fractional Laplacian of variable order
Eric Darve, Marta D'Elia, Roberto Garrappa +2
We present a novel definition of variable-order fractional Laplacian on Rn based on a natural generalization of the standard Riesz potential. Our definition holds for values of the…
A data-driven peridynamic continuum model for upscaling molecular dynamics
Huaiqian You, Yue Yu, Stewart Silling +1
Nonlocal models, including peridynamics, often use integral operators that embed lengthscales in their definition. However, the integrands in these operators are difficult to defin…
On the prescription of boundary conditions for nonlocal Poisson's and peridynamics models
Marta D'Elia, Yue Yu
We introduce a technique to automatically convert local boundary conditions into nonlocal volume constraints for nonlocal Poisson's and peridynamic models. The proposed strategy is…
A FETI approach to domain decomposition for meshfree discretizations of nonlocal problems
Xiao Xu, Christian Glusa, Marta D'Elia +1
We propose a domain decomposition method for the efficient simulation of nonlocal problems. Our approach is based on a multi-domain formulation of a nonlocal diffusion problem wher…
A fractional model for anomalous diffusion with increased variability. Analysis, algorithms and applications to interface problems
Marta D'Elia, Christian Glusa
Fractional equations have become the model of choice in several applications where heterogeneities at the microstructure result in anomalous diffusive behavior at the macroscale. I…
Efficient quadrature rules for finite element discretizations of nonlocal equations
Eugenio Aulisa, Giacomo Capodaglio, Andrea Chierici +1
In this paper we design efficient quadrature rules for finite element discretizations of nonlocal diffusion problems with compactly supported kernel functions. Two of the main chal…
Analysis of Anisotropic Nonlocal Diffusion Models: Well-posedness of Fractional Problems for Anomalous Transport
Marta D'Elia, Mamikon Gulian
We analyze the well-posedness of an anisotropic, nonlocal diffusion equation. Establishing an equivalence between weighted and unweighted anisotropic nonlocal diffusion operators i…
A machine-learning framework for peridynamic material models with physical constraints
Xiao Xu, Marta D'Elia, John T. Foster
As a nonlocal extension of continuum mechanics, peridynamics has been widely and effectively applied in different fields where discontinuities in the field variables arise from an…
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…