| The fractional Laplacian operator on bounded domains as a special case of the nonlocal diffusion operator M D’Elia, M Gunzburger Computers & Mathematics with Applications 66 (7), 1245-1260, 2013 | 270 | 2013 |
| Numerical methods for nonlocal and fractional models M D’Elia, Q Du, C Glusa, M Gunzburger, X Tian, Z Zhou Acta Numerica 29, 1-124, 2020 | 218 | 2020 |
| nPINNs: nonlocal Physics-Informed Neural Networks for a parametrized nonlocal universal Laplacian operator. Algorithms and Applications G Pang, M D'Elia, M Parks, GE Karniadakis Journal of Computational Physics 422, 109760, 2020 | 175 | 2020 |
| A variational data assimilation procedure for the incompressible Navier-Stokes equations in hemodynamics M D’Elia, M Perego, A Veneziani Journal of Scientific Computing 52, 340-359, 2012 | 125 | 2012 |
| Fractional diffusion on bounded domains O Defterli, M D’Elia, Q Du, M Gunzburger, R Lehoucq, MM Meerschaert Fractional Calculus and Applied Analysis 18 (2), 342-360, 2015 | 116 | 2015 |
| Nonlocal convection-diffusion problems on bounded domains and finite-range jump processes M D’Elia, Q Du, M Gunzburger, R Lehoucq Computational Methods in Applied Mathematics 17 (4), 707-722, 2017 | 113* | 2017 |
| Data-driven learning of nonlocal physics from high-fidelity synthetic data H You, Y Yu, N Trask, M Gulian, M D’Elia Computer Methods in Applied Mechanics and Engineering 374, 113553, 2021 | 91 | 2021 |
| Nonlocal kernel network (NKN): A stable and resolution-independent deep neural network H You, Y Yu, M D'Elia, T Gao, S Silling Journal of Computational Physics 469, 111536, 2022 | 76 | 2022 |
| Towards a unified theory of fractional and nonlocal vector calculus M D’Elia, M Gulian, H Olson, GE Karniadakis Fractional Calculus and Applied Analysis 24 (5), 1301-1355, 2021 | 73 | 2021 |
| A coupling strategy for nonlocal and local diffusion models with mixed volume constraints and boundary conditions M D’Elia, M Perego, P Bochev, D Littlewood Computers & Mathematics with Applications 71 (11), 2218-2230, 2016 | 73 | 2016 |
| Optimal distributed control of nonlocal steady diffusion problems M D'Elia, M Gunzburger SIAM Journal on Control and Optimization 52 (1), 243-273, 2014 | 73 | 2014 |
| Applications of variational data assimilation in computational hemodynamics M D’Elia, L Mirabella, T Passerini, M Perego, M Piccinelli, C Vergara, ... Modeling of physiological flows, 363-394, 2012 | 70 | 2012 |
| Bilevel parameter learning for nonlocal image denoising models M D’Elia, JC De Los Reyes, A Miniguano-Trujillo Journal of Mathematical Imaging and Vision 63 (6), 753-775, 2021 | 69* | 2021 |
| A review of local-to-nonlocal coupling methods in nonlocal diffusion and nonlocal mechanics M D’Elia, X Li, P Seleson, X Tian, Y Yu Journal of Peridynamics and Nonlocal Modeling, 1-50, 2021 | 67 | 2021 |
| Identification of the diffusion parameter in nonlocal steady diffusion problems M D’Elia, M Gunzburger Applied Mathematics & Optimization 73, 227-249, 2016 | 63 | 2016 |
| A priori error estimates for the optimal control of the integral fractional Laplacian M D'elia, C Glusa, E Otárola SIAM Journal on Control and Optimization 57 (4), 2775-2798, 2019 | 56 | 2019 |
| Nonlocal Operator Learning for Homogenized Models: From High-fidelity Simulations to Constitutive Laws H You, Y Yu, S Silling, M D’Elia Journal of Peridynamics and Nonlocal Modeling, 1-16, 2024 | 53* | 2024 |
| Fractional modeling in action: A survey of nonlocal models for subsurface transport, turbulent flows, and anomalous materials JL Suzuki, M Gulian, M Zayernouri, M D’Elia Journal of Peridynamics and Nonlocal modeling 5 (3), 392-459, 2023 | 51 | 2023 |
| A data-driven peridynamic continuum model for upscaling molecular dynamics H You, Y Yu, S Silling, M D’Elia Computer Methods in Applied Mechanics and Engineering 389, 114400, 2022 | 48 | 2022 |
| A machine-learning framework for peridynamic material models with physical constraints X Xu, M D’Elia, JT Foster Computer Methods in Applied Mechanics and Engineering 386, 114062, 2021 | 44 | 2021 |
Pavel BochevDistinguished Member of technical Staff, Sandia National LaboratoriesAdresse e-mail validée de sandia.gov
