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Mamikon Gulian
Mamikon Gulian
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Title
Cited by
Cited by
Year
What Is the Fractional Laplacian? A Comparative Review with New Results
A Lischke, G Pang, M Gulian, F Song, C Glusa, X Zheng, Z Mao, W Cai, ...
Journal of Computational Physics, 109009, 2019
420*2019
A survey of constrained Gaussian process regression: Approaches and implementation challenges
LP Swiler, M Gulian, AL Frankel, C Safta, JD Jakeman
Journal of Machine Learning for Modeling and Computing 1 (2), 2020
1092020
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
822021
Robust training and initialization of deep neural networks: An adaptive basis viewpoint
EC Cyr, MA Gulian, RG Patel, M Perego, NA Trask
Mathematical and Scientific Machine Learning, 512-536, 2020
732020
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
632021
Machine learning of space-fractional differential equations
M Gulian, M Raissi, P Perdikaris, G Karniadakis
SIAM Journal on Scientific Computing 41 (4), A2485-A2509, 2019
632019
Partition of unity networks: deep hp-approximation
K Lee, NA Trask, RG Patel, MA Gulian, EC Cyr
arXiv preprint arXiv:2101.11256, 2021
372021
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
292023
Gaussian process regression constrained by boundary value problems
M Gulian, A Frankel, L Swiler
Computer Methods in Applied Mechanics and Engineering 388, 114117, 2022
232022
Free boundary minimal surfaces in the unit ball with low cohomogeneity
B Freidin, M Gulian, P McGrath
Proceedings of the American Mathematical Society 145 (4), 1671-1683, 2017
202017
Analysis of anisotropic nonlocal diffusion models: Well-posedness of fractional problems for anomalous transport
M D'Elia, M Gulian
arXiv preprint arXiv:2101.04289, 2021
172021
Connections between nonlocal operators: from vector calculus identities to a fractional Helmholtz decomposition
M D’Elia, M Gulian, T Mengesha, JM Scott
Fractional Calculus and Applied Analysis 25 (6), 2488-2531, 2022
132022
Probabilistic partition of unity networks: clustering based deep approximation
N Trask, M Gulian, A Huang, K Lee
arXiv preprint arXiv:2107.03066, 2021
102021
A block coordinate descent optimizer for classification problems exploiting convexity
RG Patel, NA Trask, MA Gulian, EC Cyr
arXiv preprint arXiv:2006.10123, 2020
102020
Stochastic solution of elliptic and parabolic boundary value problems for the spectral fractional Laplacian
M Gulian, G Pang
arXiv preprint arXiv:1812.01206, 2018
62018
The tempered fractional Laplacian as a special case of the nonlocal Laplace operator
HA Olson, M Gulian, M D’Elia
Computer Science Research Institute Summer Proceedings, 111-126, 2020
52020
Distribution and pressure of active Lévy swimmers under confinement
T Zhou, Z Peng, M Gulian, JF Brady
Journal of Physics A: Mathematical and Theoretical 54 (27), 275002, 2021
42021
Error-in-variables modelling for operator learning
R Patel, I Manickam, M Lee, M Gulian
Mathematical and Scientific Machine Learning, 142-157, 2022
32022
Fractional Path Integral Monte Carlo
M Gulian, H Yang, BM Rubenstein
arXiv preprint arXiv:1709.09089, 2017
22017
Solving High-Dimensional Inverse Problems with Auxiliary Uncertainty via Operator Learning with Limited Data
J Hart, M Gulian, I Manickam, LP Swiler
Journal of Machine Learning for Modeling and Computing 4 (2), 2023
12023
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