Methods for assimilating blood velocity measures in hemodynamics simulations: Preliminary results. - Marta D'Elia; Alessandro Veneziani (ICCS, 2010)

A Variational Data Assimilation Procedure for the Incompressible Navier-Stokes Equations in Hemodynamics. - Marta D'Elia; Mauro Perego; Alessandro Veneziani (J. Sci. Comput., 2012)

The fractional Laplacian operator on bounded domains as a special case of the nonlocal diffusion operator. - Marta D'Elia; Max D. Gunzburger (Comput. Math. Appl., 2013)

Coarse-Grid Sampling Interpolatory Methods for Approximating Gaussian Random Fields. - Marta D'Elia; Max D. Gunzburger (SIAM/ASA J. Uncertain. Quantification, 2013)

Optimal Distributed Control of Nonlocal Steady Diffusion Problems. - Marta D'Elia; Max D. Gunzburger (SIAM J. Control. Optim., 2014)

A coupling strategy for nonlocal and local diffusion models with mixed volume constraints and boundary conditions. - Marta D'Elia; Mauro Perego; Pavel B. Bochev; David J. Littlewood (Comput. Math. Appl., 2016)

Optimization-based mesh correction with volume and convexity constraints. - Marta D'Elia; Denis Ridzal; Kara J. Peterson; Pavel B. Bochev; Mikhail J. Shashkov (J. Comput. Phys., 2016)

Nonlocal Convection-Diffusion Problems on Bounded Domains and Finite-Range Jump Processes. - Marta D'Elia; Qiang Du 001; Max D. Gunzburger; Richard B. Lehoucq (Comput. Methods Appl. Math., 2017)

Embedded Ensemble Propagation for Improving Performance, Portability, and Scalability of Uncertainty Quantification on Emerging Computational Architectures. - Eric T. Phipps; Marta D'Elia; H. Carter Edwards; Mark Hoemmen; Jonathan J. Hu; Sivasankaran Rajamanickam (SIAM J. Sci. Comput., 2017)

Ensemble Grouping Strategies for Embedded Stochastic Collocation Methods Applied to Anisotropic Diffusion Problems. - Marta D'Elia; H. Carter Edwards; Jonathan J. Hu; Eric T. Phipps; Sivasankaran Rajamanickam (SIAM/ASA J. Uncertain. Quantification, 2018)

Formulation, analysis and computation of an optimization-based local-to-nonlocal coupling method. - Marta D'Elia; Pavel B. Bochev (CoRR, 2019)

A Thermodynamically Consistent Fractional Visco-Elasto-Plastic Model with Memory-Dependent Damage for Anomalous Materials. - Jorge L. Suzuki; Yongtao Zhou; Marta D'Elia; Mohsen Zayernouri (CoRR, 2019)

A Priori Error Estimates for the Optimal Control of the Integral Fractional Laplacian. - Marta D'Elia; Christian Glusa; Enrique Otárola (SIAM J. Control. Optim., 2019)

Nonlocal Physics-Informed Neural Networks - A Unified Theoretical and Computational Framework for Nonlocal Models. - Marta D'Elia; George E. Karniadakis; Guofei Pang; Michael L. Parks (AAAI Spring Symposium: MLPS, 2020)

Numerical methods for nonlocal and fractional models. - Marta D'Elia; Qiang Du 001; Christian Glusa; Max D. Gunzburger; Xiaochuan Tian; Zhi Zhou 002 (Acta Numer., 2020)

An energy-based coupling approach to nonlocal interface problems. - Giacomo Capodaglio; Marta D'Elia; Pavel B. Bochev; Max D. Gunzburger (CoRR, 2020)

Data-driven learning of robust nonlocal physics from high-fidelity synthetic data. - Huaiqian You; Yue Yu; Nathaniel Trask; Mamikon A. Gulian; Marta D'Elia (CoRR, 2020)

A cookbook for finite element methods for nonlocal problems, including quadrature rules and approximate Euclidean balls. - Marta D'Elia; Max D. Gunzburger; Christian Vollmann (CoRR, 2020)

A general framework for substructuring-based domain decomposition methods for models having nonlocal interactions. - Giacomo Capodaglio; Marta D'Elia; Max D. Gunzburger; Pavel B. Bochev; Manuel Klar 001; Christian Vollmann (CoRR, 2020)

nPINNs: Nonlocal physics-informed neural networks for a parametrized nonlocal universal Laplacian operator. Algorithms and applications. - Guofei Pang; Marta D'Elia; Michael L. Parks; George E. Karniadakis (J. Comput. Phys., 2020)

A Physically Consistent, Flexible, and Efficient Strategy to Convert Local Boundary Conditions into Nonlocal Volume Constraints. - Marta D'Elia; Xiaochuan Tian; Yue Yu (SIAM J. Sci. Comput., 2020)

Data-driven Learning of Nonlocal Models: from high-fidelity simulations to constitutive laws. - Huaiqian You; Yue Yu; Stewart Silling; Marta D'Elia (AAAI Spring Symposium: MLPS, 2021)

A machine-learning framework for peridynamic material models with physical constraints. - Xiao Xu; Marta D'Elia; John T. Foster (CoRR, 2021)

Analysis of Anisotropic Nonlocal Diffusion Models: Well-posedness of Fractional Problems for Anomalous Transport. - Marta D'Elia; Mamikon A. Gulian (CoRR, 2021)

Efficient quadrature rules for finite element discretizations of nonlocal equations. - Eugenio Aulisa; Giacomo Capodaglio; Andrea Chierici; Marta D'Elia (CoRR, 2021)

A fractional model for anomalous diffusion with increased variability. Analysis, algorithms and applications to interface problems. - Marta D'Elia; Christian Glusa (CoRR, 2021)

A FETI approach to domain decomposition for meshfree discretizations of nonlocal problems. - Xiao Xu; Christian Glusa; Marta D'Elia; John T. Foster (CoRR, 2021)

On the prescription of boundary conditions for nonlocal Poisson's and peridynamics models. - Marta D'Elia; Yue Yu (CoRR, 2021)

A data-driven peridynamic continuum model for upscaling molecular dynamics. - Huaiqian You; Yue Yu; Stewart Silling; Marta D'Elia (CoRR, 2021)

An optimization-based strategy for peridynamic-FEM coupling and for the prescription of nonlocal boundary conditions. - Marta D'Elia; David J. Littlewood; Jeremy Trageser; Mauro Perego; Pavel B. Bochev (CoRR, 2021)

Bilevel Parameter Learning for Nonlocal Image Denoising Models. - Marta D'Elia; Juan Carlos de los Reyes; Andrés Miniguano-Trujillo (J. Math. Imaging Vis., 2021)

A Fast Solver for the Fractional Helmholtz Equation. - Christian Glusa; Harbir Antil; Marta D'Elia; Bart G. van Bloemen Waanders; Chester J. Weiss (SIAM J. Sci. Comput., 2021)

An optimization-based approach to parameter learning for fractional type nonlocal models. - Olena Burkovska; Christian Glusa; Marta D'Elia (Comput. Math. Appl., 2022)

Machine-learning of nonlocal kernels for anomalous subsurface transport from breakthrough curves. - Xiao Xu; Marta D'Elia; Christian Glusa; John T. Foster (CoRR, 2022)

Efficient optimization-based quadrature for variational discretization of nonlocal problems. - Marco Pasetto; Zhaoxiang Shen; Marta D'Elia; Xiaochuan Tian; Nathaniel Trask; David Kamensky (CoRR, 2022)

Machine Learning in Heterogeneous Porous Materials. - Marta D'Elia; Hang Deng; Cedric G. Fraces; Krishna C. Garikipati; Lori Graham-Brady; Amanda A. Howard; George Em Karniadakis; Vahid Keshavarzzadeh; Robert M. Kirby; J. Nathan Kutz; Chunhui Li; Xing Liu; et al. (CoRR, 2022)

Probabilistic partition of unity networks for high-dimensional regression problems. - Tiffany Fan; Nathaniel Trask; Marta D'Elia; Eric Darve (CoRR, 2022)

Bayesian Nonlocal Operator Regression (BNOR): A Data-Driven Learning Framework of Nonlocal Models with Uncertainty Quantification. - Yiming Fan; Marta D'Elia; Yue Yu; Habib N. Najm; Stewart Silling (CoRR, 2022)

Nonlocal kernel network (NKN): A stable and resolution-independent deep neural network. - Huaiqian You; Yue Yu; Marta D'Elia; Tian Gao; Stewart Silling (J. Comput. Phys., 2022)

Towards a unified nonlocal, peridynamics framework for the coarse-graining of molecular dynamics data with fractures. - Huaiqian You; Xiao Xu; Yue Yu; Stewart Silling; Marta D'Elia; John T. Foster (CoRR, 2023)

GNN-based physics solver for time-independent PDEs. - Rini Jasmine Gladstone; Helia Rahmani; Vishvas Suryakumar; Hadi Meidani; Marta D'Elia; Ahmad Zareei (CoRR, 2023)

An Asymptotically Compatible Coupling Formulation for Nonlocal Interface Problems with Jumps. - Christian Glusa; Marta D'Elia; Giacomo Capodaglio; Max D. Gunzburger; Pavel B. Bochev (SIAM J. Sci. Comput., 2023)

A scalable domain decomposition method for FEM discretizations of nonlocal equations of integrable and fractional type. - Manuel Klar 001; Giacomo Capodaglio; Marta D'Elia; Christian Glusa; Max D. Gunzburger; Christian Vollmann (Comput. Math. Appl., 2023)

ML-based identification of the interface regions for coupling local and nonlocal models. - Noujoud Nader; Patrick Diehl; Marta D'Elia; Christian Glusa; Serge Prudhomme (CoRR, 2024)

Embedded Nonlocal Operator Regression (ENOR): Quantifying model error in learning nonlocal operators. - Yiming Fan; Habib N. Najm; Yue Yu; Stewart Silling; Marta D'Elia (CoRR, 2024)

Physically Interpretable Representation and Controlled Generation for Turbulence Data. - Tiffany Fan; Murray Cutforth; Marta D'Elia; Alexandre Cortiella; Alireza Doostan; Eric Darve (CoRR, 2025)