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05/31/2023
A scalable domain decomposition method for FEM discretizations of nonlocal equations of integrable and fractional type
Nonlocal models allow for the description of phenomena which cannot be c...
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03/28/2023
GNN-based physics solver for time-independent PDEs
Physics-based deep learning frameworks have shown to be effective in acc...
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01/11/2023
Towards a unified nonlocal, peridynamics framework for the coarse-graining of molecular dynamics data with fractures
Molecular dynamics (MD) has served as a powerful tool for designing mate...
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10/06/2022
Probabilistic partition of unity networks for high-dimensional regression problems
We explore the probabilistic partition of unity network (PPOU-Net) model...
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03/15/2022
An asymptotically compatible coupling formulation for nonlocal interface problems with jumps
We introduce a mathematically rigorous formulation for a nonlocal interf...
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01/28/2022
Efficient optimization-based quadrature for variational discretization of nonlocal problems
Casting nonlocal problems in variational form and discretizing them with...
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01/26/2022
Machine-learning of nonlocal kernels for anomalous subsurface transport from breakthrough curves
Anomalous behavior is ubiquitous in subsurface solute transport due to t...
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01/06/2022
Nonlocal Kernel Network (NKN): a Stable and Resolution-Independent Deep Neural Network
Neural operators have recently become popular tools for designing soluti...
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10/22/2021
Fractional Modeling in Action: A Survey of Nonlocal Models for Subsurface Transport, Turbulent Flows, and Anomalous Materials
Modeling of phenomena such as anomalous transport via fractional-order d...
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10/09/2021
An optimization-based strategy for peridynamic-FEM coupling and for the prescription of nonlocal boundary conditions
We develop and analyze an optimization-based method for the coupling of ...
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07/09/2021
On the prescription of boundary conditions for nonlocal Poisson's and peridynamics models
We introduce a technique to automatically convert local boundary conditi...
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05/15/2021
A FETI approach to domain decomposition for meshfree discretizations of nonlocal problems
We propose a domain decomposition method for the efficient simulation of...
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01/28/2021
A fractional model for anomalous diffusion with increased variability. Analysis, algorithms and applications to interface problems
Fractional equations have become the model of choice in several applicat...
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01/21/2021
Efficient quadrature rules for finite element discretizations of nonlocal equations
In this paper we design efficient quadrature rules for finite element di...
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01/12/2021
Analysis of Anisotropic Nonlocal Diffusion Models: Well-posedness of Fractional Problems for Anomalous Transport
We analyze the well-posedness of an anisotropic, nonlocal diffusion equa...
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01/04/2021
A machine-learning framework for peridynamic material models with physical constraints
As a nonlocal extension of continuum mechanics, peridynamics has been wi...
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12/08/2020
Data-driven learning of nonlocal models: from high-fidelity simulations to constitutive laws
We show that machine learning can improve the accuracy of simulations of...
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10/07/2020
An optimization-based approach to parameter learning for fractional type nonlocal models
Nonlocal operators of fractional type are a popular modeling choice for ...
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08/26/2020
A general framework for substructuring-based domain decomposition methods for models having nonlocal interactions
A rigorous mathematical framework is provided for a substructuring-based...
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05/21/2020
A cookbook for finite element methods for nonlocal problems, including quadrature rules and approximate Euclidean balls
The implementation of finite element methods (FEMs) for nonlocal models ...
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05/17/2020
Data-driven learning of robust nonlocal physics from high-fidelity synthetic data
A key challenge to nonlocal models is the analytical complexity of deriv...
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04/08/2020
nPINNs: nonlocal Physics-Informed Neural Networks for a parametrized nonlocal universal Laplacian operator. Algorithms and Applications
Physics-informed neural networks (PINNs) are effective in solving invers...
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02/04/2020
Numerical methods for nonlocal and fractional models
Partial differential equations (PDEs) are used, with huge success, to mo...
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01/11/2020
An energy-based coupling approach to nonlocal interface problems
Nonlocal models provide accurate representations of physical phenomena r...
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11/16/2019
A Thermodynamically Consistent Fractional Visco-Elasto-Plastic Model with Memory-Dependent Damage for Anomalous Materials
We develop a thermodynamically consistent, fractional visco-elasto-plast...
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10/24/2019