Machine Learning of Space-Fractional Differential Equations. - Mamikon A. Gulian; Maziar Raissi; Paris Perdikaris; George E. Karniadakis (SIAM J. Sci. Comput., 2019)

Robust Training and Initialization of Deep Neural Networks: An Adaptive Basis Viewpoint. - Eric C. Cyr; Mamikon A. Gulian; Ravi G. Patel; Mauro Perego; Nathaniel A. Trask (MSML, 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 Survey of Constrained Gaussian Process Regression: Approaches and Implementation Challenges. - Laura P. Swiler; Mamikon A. Gulian; Ari Frankel; Cosmin Safta; John D. Jakeman (CoRR, 2020)

Gaussian Process Regression constrained by Boundary Value Problems. - Mamikon A. Gulian; Ari Frankel; Laura P. Swiler (CoRR, 2020)

What is the fractional Laplacian? A comparative review with new results. - Anna Lischke; Guofei Pang; Mamikon A. Gulian; Fangying Song; Christian Glusa; Xiaoning Zheng; Zhiping Mao; Wei Cai 003; Mark M. Meerschaert; Mark Ainsworth; George Em Karniadakis (J. Comput. Phys., 2020)

Partition of Unity Networks: Deep HP-Approximation. - Kookjin Lee; Nathaniel Trask; Ravi G. Patel; Mamikon A. Gulian; Eric C. Cyr (AAAI Spring Symposium: MLPS, 2021)

A Block Coordinate Descent Optimizer for Classification Problems Exploiting Convexity. - Ravi G. Patel; Nathaniel Trask; Mamikon A. Gulian; Eric C. Cyr (AAAI Spring Symposium: MLPS, 2021)

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

Probabilistic partition of unity networks: clustering based deep approximation. - Nathaniel Trask; Mamikon A. Gulian; Andy Huang; Kookjin Lee (CoRR, 2021)

Error-in-variables modelling for operator learning. - Ravi G. Patel; Indu Manickam; Myoungkyu Lee; Mamikon A. Gulian (MSML, 2022)

Solving High-Dimensional Inverse Problems with Auxiliary Uncertainty via Operator Learning with Limited Data. - Joseph L. Hart; Mamikon A. Gulian; Indu Manickam; Laura P. Swiler (CoRR, 2023)

Stratospheric aerosol source inversion: Noise, variability, and uncertainty quantification. - Joseph L. Hart; Indu Manickam; Mamikon A. Gulian; Laura P. Swiler; Diana Bull; T. Ehrmann; H. Brown; B. Wagman; Jerry Watkins (CoRR, 2024)