Mamikon A. Gulian

R&D Computer Science

(505) 844-4363

Sandia National Laboratories, California
P.O. Box 969
Livermore, CA 94551-0969

Greetings! I’m a mathematician and computational scientist at Sandia National Labs in Livermore, CA, within the Quantitative Modeling & Analysis group. Previously, I was the John von Neumann Postdoctoral Fellow at Sandia Labs in Albuquerque, NM.

My current research interests include nonlocal and fractional-order coarse grained models for subsurface transport through fracture networks, data-driven surrogate models for circuits and climate systems, and verification and validation studies of electromagnetic codes. A unifying theme of my projects is the development of improved scientific machine learning methods for mission applications, ranging from statistical and Bayesian methods to deep learning approaches for regression, model calibration, and operator learning. My foundational work in this area has led to tools that incorporate prior physics/system knowledge as constraints in machine learning methods, in addition to accelerated and more numerically stable training methods and training methods that are more robust to noise in variables. In parallel, I’ve done foundational work on nonlocal and fractional-order vector calculus, building theoretical frameworks and stochastic methods that allow for highly successful nonlocal methods to applied 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

Mamikon Gulian, Christian Alexander Glusa, Jeffrey Hyman, Marta D’Elia, (2022). Calibrating Fractional-Order Models for Anomalous Subsurface Flow through Fractures SIAM Mathematics of Data Science Document ID: 1641165

MartaD’Elia, Pavel B. Bochev, JohnT.Foster, Christian Alexander Glusa, Mamikon Gulian, MaxGunzburger, Jeremy Trageser, Kristopher L Kuhlman, Mario Alberto Martinez, Habib N. Najm, Stewart A. Silling, MichaelTupek, XiaoXu, (2022). Mathematical Foundations for Nonlocal Interface Problems: Multiscale Simulations of Heterogeneous Materials. Final LDRD Report https://www.osti.gov/search/identifier:1888162 Document ID: 1630446

Mamikon Gulian, (2022). Gaussian Process Regression Constrained by Boundary Value Problems IMSI WorkshopExpressing and Exploiting Structure in Modeling, Theory, and Computation with Gaussian Processes Document ID: 1618558

Ravi Ghanshyam Patel, Indu Manickam, Myoungkyu Lee, Mamikon Gulian, (2022). Error-in-variables modelling for operator learning Msml22 Document ID: 1606857

Mamikon Gulian, Ravi Ghanshyam Patel, Indu Manickam, Lee Myoungkyu, (2022). Error-in-variables modelling for operator learning Mathematical and Scientific Machine Learning 2022 (MSML2022) Document ID: 1482408

Marta D’Elia, Mamikon Gulian, Tadele Mengesha, James M. Scott, (2021). Connections between nonlocal operators: from vector calculus identities to a fractional Helmholtz decomposition https://www.osti.gov/search/identifier:1855046 Document ID: 1403812

Marta D’Elia, Mamikon Gulian, Jorge Suzuki, Mohsen Zayernouri, (2021). Fractional Modeling in Action: A Survey of Nonlocal Models for Subsurface Transport, Turbulent Flows, and Anomalous Materials https://www.osti.gov/search/identifier:1820001 Document ID: 1357040

Mamikon Gulian, Ari Louis Frankel, Laura Painton Swiler, (2021). Gaussian Process Regression constrained by Boundary Value Problems Computer Methods in Applied Mechanics and Engineering https://www.osti.gov/search/identifier:1831157 Document ID: 1355823

Mamikon Gulian, Ravi Ghanshyam Patel, Nathaniel Albert Trask, Eric Christopher Cyr, (2021). A block coordinate descent optimizer for classification problems exploiting convexity Aaai-mlps 2021 https://www.osti.gov/search/identifier:1855748 Document ID: 1281385

Marta D’Elia, Mamikon Gulian, (2021). Analysis of Anisotropic Nonlocal Diffusion Models: Well-posedness of Fractional Problems for Anomalous Transport https://www.osti.gov/search/identifier:1763574 Document ID: 1255267

Lee Kookjin, Nathaniel Albert Trask, Ravi Ghanshyam Patel, Mamikon Gulian, Eric Christopher Cyr, (2020). Partition of unity networks: data-driven meshfree hp-approximation AAAI 2021 Spring Symposium on Combining Artificial Intelligence and Machine Learning with Physics Sciences https://www.osti.gov/search/identifier:1835970 Document ID: 1243888

Laura Painton Swiler, Mamikon Gulian, Ari Louis Frankel, Cosmin Safta, John Davis Jakeman, (2020). A Survey of Constrained Gaussian Process: Approaches and Implementation Challenges Journal of Machine Learning for Modeling and Computing https://www.osti.gov/search/identifier:1725870 Document ID: 1127442

Ravi Ghanshyam Patel, Nathaniel Albert Trask, Mamikon Gulian, Eric Christopher Cyr, (2020). A block coordinate descent optimizer for classification problems exploiting convexity Arxiv https://www.osti.gov/search/identifier:1834091 Document ID: 1140140

Huaiqian You, Yue Yu, Nathaniel Albert Trask, Mamikon Gulian, Marta D’Elia, (2020). Data-driven learning of robust nonlocal physics from high-fidelity synthetic data Arxiv https://www.osti.gov/search/identifier:1765754 Document ID: 1128470

Eric Christopher Cyr, Mamikon Gulian, Ravi Ghanshyam Patel, Mauro Perego, Nathaniel Albert Trask, (2019). Robust Training and Initialization of Deep Neural Networks: An Adaptive Basis Viewpoint Mathematical and Scientific Machine Learning Conference https://www.osti.gov/search/identifier:1643463 Document ID: 1067715

Anna Lischke, Guofei Pang, Mamikon Gulian, Fangying Song, Christian Alexander Glusa, Xiaoning Zheng, Zhiping Mao, Wei Cai, Mark Meerschaert, Mark Ainsworth, George Karniadakis, (2019). What Is the Fractional Laplacian? A Comparative Review with New Results Journal of Computational Physics https://www.osti.gov/search/identifier:1574478 Document ID: 1054211

Mamikon Gulian, Maziar Raissi, Paris Georgios Perdikaris, George Karniadakis, (2019). Machine Learning of Space-Fractional Differential Equations RICAM Special Semester Optimization Workshop 2Optimal control and optimization for nonlocal models https://www.osti.gov/search/identifier:1642956 Document ID: 1043897

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