| 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 | 510* | 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 | 176 | 2020 |
| 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 |
| 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 | 90 | 2020 |
| 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 | 74 | 2021 |
| 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 | 74 | 2019 |
| 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 | 52 | 2023 |
| Partition of unity networks: deep hp-approximation K Lee, NA Trask, RG Patel, MA Gulian, EC Cyr arXiv preprint arXiv:2101.11256, 2021 | 46 | 2021 |
| Gaussian process regression constrained by boundary value problems M Gulian, A Frankel, L Swiler Computer Methods in Applied Mechanics and Engineering 388, 114117, 2022 | 31 | 2022 |
| 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 | 24 | 2021 |
| 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 | 21 | 2017 |
| 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 | 20 | 2022 |
| Probabilistic partition of unity networks: clustering based deep approximation N Trask, M Gulian, A Huang, K Lee arXiv preprint arXiv:2107.03066, 2021 | 12 | 2021 |
| A block coordinate descent optimizer for classification problems exploiting convexity RG Patel, NA Trask, MA Gulian, EC Cyr arXiv preprint arXiv:2006.10123, 2020 | 11 | 2020 |
| Stochastic solution of elliptic and parabolic boundary value problems for the spectral fractional Laplacian M Gulian, G Pang arXiv preprint arXiv:1812.01206, 2018 | 9 | 2018 |
| 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 | 6 | 2023 |
| 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 | 6 | 2021 |
| Stratospheric aerosol source inversion: Noise, variability, and uncertainty quantification J Hart, I Manickam, M Gulian, LP Swiler, D Bull, T Ehrmann, H Brown, ... Journal of Machine Learning for Modeling and Computing 6 (2), 2025 | 5 | 2025 |
| 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 | 5 | 2020 |
| Error-in-variables modelling for operator learning R Patel, I Manickam, M Lee, M Gulian Mathematical and Scientific Machine Learning, 142-157, 2022 | 3 | 2022 |
