Mamikon A. Gulian
R&D Computer Science
R&D Computer Science
(925) 294-2732
Sandia National Laboratories, California
P.O. Box 969
Livermore, CA 94551-0969
I am a computational scientist with a background in mathematics, modeling, data science, and software engineering. I work at Sandia National Laboratories in Livermore, California in the department of Quantitative Modeling and Software Engineering (8734). Previously, I was the John von Neumann Postdoctoral Fellow at Sandia Labs in Albuquerque, NM.
My current research interests include (1) nonlocal and fractional-order coarse grained models for subsurface transport through fracture networks, (2) data-driven surrogate models for circuits and climate systems, (3) time-series forecasting of extreme weather events, and (4) verification, validation, and uncertainty quantification in support of national security. A unifying theme of my projects involves developing scientific machine learning methods for regression, model calibration, and operator learning. My work in this area has led to tools that incorporate prior physics/system knowledge within machine learning algorithms, thereby improving robustness and fidelity while accelerating training. In parallel, I’ve done foundational work on nonlocal and fractional-order vector calculus, building theoretical frameworks and stochastic methods for applying nonlocal methods to multivariate multi-scale systems.
Education
Ph.D. in Mathematics, Brown University (2018)
M.S. in Mathematics, Brown University (2015)
B.S. in Mathematics, University of Maryland Baltimore County (2013)
Publications
Marta D’Elia, Mamikon Gulian, Tadele Mengesha, James Scott, (2022). Connections between nonlocal operators: from vector calculus identities to a fractional Helmholtz decomposition Fractional Calculus and Applied Analysis https://doi.org/10.2172/1855046 Publication ID: 77052
Marta D’Elia, Pavel Bochev, John Foster, Christian Glusa, Mamikon Gulian, Max Gunzburger, Jeremy Trageser, Kristopher Kuhlman, Mario Martinez, Habib Najm, Stewart Silling, Michael Tupek, Xiao Xu, (2022). Mathematical Foundations for Nonlocal Interface Problems: Multiscale Simulations of Heterogeneous Materials (Final LDRD Report) https://doi.org/10.2172/1888162 Publication ID: 80232
Jorge Suzuki, Mamikon Gulian, Mohsen Zayernouri, Marta D’Elia, (2022). Fractional Modeling in Action: a Survey of Nonlocal Models for Subsurface Transport, Turbulent Flows, and Anomalous Materials Journal of Peridynamics and Nonlocal Modeling https://doi.org/10.2172/1820001 Publication ID: 75627
Mamikon Gulian, A. Frankel, L. Swiler, (2022). Gaussian process regression constrained by boundary value problems Computer Methods in Applied Mechanics and Engineering https://doi.org/10.1016/j.cma.2021.114117 Publication ID: 75489
Mamikon Gulian, (2021). Robust architectures, initialization, and training for deep neural networks via the adaptive basis interpretation https://doi.org/10.2172/1889595 Publication ID: 75730
Mamikon Gulian, (2021). Data-driven learning of nonlocal physics from high-fidelity synthetic data https://doi.org/10.2172/1888123 Publication ID: 75404
Marta D’Elia, Hayley Olson, Mamikon Gulian, (2021). Comparison of Tempered and Truncated Fractional Models https://doi.org/10.2172/1888466 Publication ID: 79402
Mamikon Gulian, (2021). Partition of Unity Networks for Deterministic and Probabilistic Regression https://www.osti.gov/servlets/purl/1888667 Publication ID: 79485
Mamikon Gulian, (2021). Robust architectures, initialization, and training for deep neural networks https://www.osti.gov/servlets/purl/1888396 Publication ID: 79244
Mamikon Gulian, (2021). Gaussian Process Regression constrained by Boundary Value Problems https://doi.org/10.2172/1883509 Publication ID: 79507
Eric Cyr, Mamikon Gulian, Kookjin Lee, Ravi Patel, Mauro Perego, Nathaniel Trask, (2021). An Adaptive Basis Perspective to Improve Initialization and Accelerate Training of DNNs https://www.osti.gov/servlets/purl/1872708 Publication ID: 78814
Mamikon Gulian, (2021). Analysis of Anisotropic Nonlocal Diffusion Models: Well-posedness of Fractional Problems for Anomalous Transport https://doi.org/10.2172/1870369 Publication ID: 78630
Mamikon Gulian, (2021). Robust architectures initialization and training for deep neural networks via the adaptive basis interpretation https://www.osti.gov/servlets/purl/1866561 Publication ID: 78329
Mamikon Gulian, (2021). Data-driven learning of nonlocal physics from high-fidelity synthetic data https://doi.org/10.2172/1854073 Publication ID: 77436
Mamikon Gulian, (2021). A block coordinate descent optimizer for classification problems exploiting convexity https://doi.org/10.2172/1859695 Publication ID: 77748
Huaiqian You, Yue Yu, Nathaniel Trask, Mamikon Gulian, Marta D’Elia, (2021). Data-driven learning of nonlocal physics from high-fidelity synthetic data Computer Methods in Applied Mechanics and Engineering https://doi.org/10.1016/j.cma.2020.113553 Publication ID: 73539
Eric Cyr, Mamikon Gulian, Ravi Patel, Mauro Perego, Nathaniel Trask, (2021). An Adaptive Basis Perspective to Improve Initialization and Accelerate Training of DNNs https://doi.org/10.2172/1847582 Publication ID: 77381
Laura Swiler, Mamikon Gulian, A. Frankel, Cosmin Safta, John Jakeman, (2021). Constrained Gaussian Processes: A Survey https://doi.org/10.2172/1847480 Publication ID: 77280
Marta D’Elia, Mamikon Gulian, (2021). Analysis of Anisotropic Nonlocal Diffusion Models: Well-posedness of Fractional Problems for Anomalous Transport https://doi.org/10.2172/1763574 Publication ID: 75004
Ravi Patel, Nathaniel Trask, Mamikon Gulian, Eric Cyr, (2021). A block coordinate descent optimizer for classification problems exploiting convexity CEUR Workshop Proceedings https://www.osti.gov/servlets/purl/1855748 Publication ID: 77621
Mamikon Gulian, (2021). A Unified Theory of Fractional Nonlocal and Weighted Nonlocal Vector Calculus https://doi.org/10.2172/1841821 Publication ID: 75102
Lee Kookjin, Nathaniel Trask, Ravi Patel, Mamikon Gulian, Eric Cyr, (2020). Partition of unity networks: data-driven meshfree hp-approximation https://www.osti.gov/servlets/purl/1835970 Publication ID: 72183
Mamikon Gulian, Laura Swiler, A. Frankel, Cosmin Safta, John Jakeman, (2020). A Survey of Constrained Gaussian Process Regression: Approaches and Implementation Challenges https://www.osti.gov/servlets/purl/1814448 Publication ID: 74592
Mamikon Gulian, Eric Cyr, Ravi Patel, Mauro Perego, Nathaniel Trask, (2020). Robust training and initialization of deep neural networks: an adaptive basis viewpoint https://www.osti.gov/servlets/purl/1808257 Publication ID: 74043
Mamikon Gulian, Laura Swiler, A. Frankel, John Jakeman, Cosmin Safta, (2020). A Survey of Constrained Gaussian Process Regression: Approaches and Implementation Challenges https://www.osti.gov/servlets/purl/1812282 Publication ID: 74359
Eric Cyr, Mamikon Gulian, Ravi Patel, Mauro Perego, Nathaniel Trask, (2020). Robust Training and Initialization of Deep Neural Networks An Adaptive Basis Viewpoint https://www.osti.gov/servlets/purl/1810691 Publication ID: 74202
Ravi Patel, Nathaniel Trask, Mamikon Gulian, Eric Cyr, (2020). A block coordinate descent optimizer for classification problems exploiting convexity Arxiv https://www.osti.gov/servlets/purl/1834091 Publication ID: 73782
Anna Lischke, Guofei Pang, Mamikon Gulian, Fangying Song, Christian Glusa, Xiaoning Zheng, Zhiping Mao, Wei Cai, Mark Meerschaert, Mark Ainsworth, George Karniadakis, (2020). What is the fractional Laplacian? A comparative review with new results Journal of Computational Physics https://doi.org/10.1016/j.jcp.2019.109009 Publication ID: 66165
Eric Cyr, Mamikon Gulian, Ravi Patel, Mauro Perego, Nathaniel Trask, Denis Ridzal, Stefanie Guenther, Lars Ruthotto, Jacob Schroder, Nico Gauger, (2019). Improved Neural Network Training: Layer-Parallelism Least-squares and Initialization https://www.osti.gov/servlets/purl/1643364 Publication ID: 66945
Eric Cyr, Mamikon Gulian, Ravi Patel, Mauro Perego, Nathaniel Trask, (2019). Robust Training and Initialization of Deep Neural Networks: An Adaptive Basis Viewpoint https://www.osti.gov/servlets/purl/1643463 Publication ID: 66738
Mamikon Gulian, Maziar Raissi, George Karniadakis, (2019). Machine Learning of Space-Fractional Differential Equations https://doi.org/10.1137/18M1204991 Publication ID: 65842
Showing Results.