| 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 | 3704 | 2021 |
| fPINNs: Fractional physics-informed neural networks G Pang, L Lu, GE Karniadakis SIAM Journal on Scientific Computing 41 (4), A2603-A2626, 2019 | 1188 | 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 | 533 | 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 | 213 | 2020 |
| Space-fractional advection–dispersion equations by the Kansa method G Pang, W Chen, Z Fu Journal of Computational Physics 293, 280-296, 2015 | 156 | 2015 |
| 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 | 111 | 2019 |
| 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 | 104 | 2018 |
| 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 | 76 | 2016 |
| 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 | 63 | 2019 |
| 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 | 62 | 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 | 52 | 2020 |
| Gauss–Jacobi-type quadrature rules for fractional directional integrals G Pang, W Chen, KY Sze Computers & Mathematics with Applications 66 (5), 597-607, 2013 | 40 | 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 | 34 | 2017 |
| Singular boundary method for acoustic eigenanalysis W Li, W Chen, G Pang Computers & Mathematics with Applications 72 (3), 663-674, 2016 | 18 | 2016 |
| A deep learning framework for solving forward and inverse problems of power-law fluids R Zhai, D Yin, G Pang Physics of Fluids 35 (9), 2023 | 17 | 2023 |
| 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 | 17 | 2016 |
| Differential quadrature and cubature methods for steady-state space-fractional advection-diffusion equations G Pang, W Chen, KY Sze Computer Modeling in Engineering & Sciences 97 (4), 299, 2014 | 15 | 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 | 14 | 2017 |
| Learning nonlinear operators via DeepONet L Lu, P Jin, GE Karniadakis Nature Machine Intelligence 3 (3), 218-229, 2021 | 10 | 2021 |
| 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 |
