| Learning nonlinear operators via DeepONet based on the universal approximation theorem of operators L Lu, P Jin, G Pang, Z Zhang, GE Karniadakis Nature machine intelligence 3 (3), 218-229, 2021 | 1289 | 2021 |
| fPINNs: Fractional physics-informed neural networks G Pang, L Lu, GE Karniadakis SIAM Journal on Scientific Computing 41 (4), A2603-A2626, 2019 | 623 | 2019 |
| 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 404, 109009, 2020 | 339 | 2020 |
| nPINNs: nonlocal Physics-Informed Neural Networks for a parametrized nonlocal universal Laplacian operator. Algorithms and Applications G Pang, M D'Elia, M Parks, GE Karniadakis Journal of Computational Physics 422, 109760, 2020 | 139 | 2020 |
| Space-fractional advection–dispersion equations by the Kansa method G Pang, W Chen, Z Fu Journal of Computational Physics 293, 280-296, 2015 | 139 | 2015 |
| What is the fractional Laplacian? A Lischke, G Pang, M Gulian, F Song, C Glusa, X Zheng, Z Mao, W Cai, ... arXiv preprint arXiv:1801.09767, 2018 | 97 | 2018 |
| Neural-net-induced Gaussian process regression for function approximation and PDE solution G Pang, L Yang, GE Karniadakis Journal of Computational Physics 384, 270-288, 2019 | 84 | 2019 |
| A new definition of fractional Laplacian with application to modeling three-dimensional nonlocal heat conduction W Chen, G Pang Journal of Computational Physics 309, 350-367, 2016 | 69 | 2016 |
| Discovering variable fractional orders of advection–dispersion equations from field data using multi-fidelity Bayesian optimization G Pang, P Perdikaris, W Cai, GE Karniadakis Journal of Computational Physics 348, 694-714, 2017 | 55 | 2017 |
| Discovering a universal variable-order fractional model for turbulent Couette flow using a physics-informed neural network PP Mehta, G Pang, F Song, GE Karniadakis Fractional calculus and applied analysis 22 (6), 1675-1688, 2019 | 39 | 2019 |
| Gauss–Jacobi-type quadrature rules for fractional directional integrals G Pang, W Chen, KY Sze Computers & Mathematics with Applications 66 (5), 597-607, 2013 | 38 | 2013 |
| A fast semi-discrete Kansa method to solve the two-dimensional spatiotemporal fractional diffusion equation HG Sun, X Liu, Y Zhang, G Pang, R Garrard Journal of Computational Physics 345, 74-90, 2017 | 33 | 2017 |
| Physics-informed learning machines for partial differential equations: Gaussian processes versus neural networks G Pang, GE Karniadakis Emerging Frontiers in Nonlinear Science, 323-343, 2020 | 26 | 2020 |
| A comparative study of finite element and finite difference methods for two-dimensional space-fractional advection-dispersion equation G Pang, W Chen, KY Sze Advances in Applied Mathematics and Mechanics 8 (1), 166-186, 2016 | 16 | 2016 |
| Differential quadrature and cubature methods for steady-state space-fractional advection-diffusion equations GF Pang, W Chen, KY Sze Comput. Model. Eng. Sci 97, 299-322, 2014 | 14 | 2014 |
| Fractional biharmonic operator equation model for arbitrary frequency-dependent scattering attenuation in acoustic wave propagation W Chen, J Fang, G Pang, S Holm The Journal of the Acoustical Society of America 141 (1), 244-253, 2017 | 13 | 2017 |
| Singular boundary method for acoustic eigenanalysis W Li, W Chen, G Pang Computers & Mathematics with Applications 72 (3), 663-674, 2016 | 13 | 2016 |
| Solving fractional Laplacian visco-acoustic wave equations on complex-geometry domains using Grünwald-formula based radial basis collocation method Y Xu, J Li, X Chen, G Pang Computers & Mathematics with Applications 79 (8), 2153-2167, 2020 | 6 | 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 | 6 | 2018 |
| Fractional calculus and numerical methods for fractional PDEs E Kharazmi, Z Mao, G Pang, M Zayernouri, GE Karniadakis First Congress of Greek Mathematicians: Proceedings of the Congress held in …, 2018 | 4 | 2018 |
