| Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations M Raissi, P Perdikaris, GE Karniadakis Journal of Computational physics 378, 686-707, 2019 | 9442 | 2019 |
| The Wiener--Askey polynomial chaos for stochastic differential equations D Xiu, GE Karniadakis SIAM journal on scientific computing 24 (2), 619-644, 2002 | 5731 | 2002 |
| Spectral/hp element methods for computational fluid dynamics G Karniadakis, SJ Sherwin Oxford University Press, USA, 2005 | 3502 | 2005 |
| Physics-informed machine learning GE Karniadakis, IG Kevrekidis, L Lu, P Perdikaris, S Wang, L Yang Nature Reviews Physics 3 (6), 422-440, 2021 | 3444 | 2021 |
| Discontinuous Galerkin methods: theory, computation and applications B Cockburn, GE Karniadakis, CW Shu Springer Science & Business Media, 2012 | 3033* | 2012 |
| Microflows and nanoflows: fundamentals and simulation G Karniadakis, A Beskok, N Aluru Springer Science & Business Media, 2006 | 2746 | 2006 |
| High-order splitting methods for the incompressible Navier-Stokes equations GE Karniadakis, M Israeli, SA Orszag Journal of computational physics 97 (2), 414-443, 1991 | 1787 | 1991 |
| Modeling uncertainty in flow simulations via generalized polynomial chaos D Xiu, GE Karniadakis Journal of computational physics 187 (1), 137-167, 2003 | 1757 | 2003 |
| DeepXDE: A deep learning library for solving differential equations L Lu, X Meng, Z Mao, GE Karniadakis SIAM review 63 (1), 208-228, 2021 | 1557 | 2021 |
| Report: a model for flows in channels, pipes, and ducts at micro and nano scales A Beskok, GE Karniadakis Microscale thermophysical engineering 3 (1), 43-77, 1999 | 1519 | 1999 |
| Hidden fluid mechanics: Learning velocity and pressure fields from flow visualizations M Raissi, A Yazdani, GE Karniadakis Science 367 (6481), 1026-1030, 2020 | 1437 | 2020 |
| 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 | 1417 | 2021 |
| Micro flows: fundamentals and simulation GE Karniadakis, A Beskok, M Gad-el-Hak Appl. Mech. Rev. 55 (4), B76-B76, 2002 | 1371 | 2002 |
| Physics informed deep learning (part i): Data-driven solutions of nonlinear partial differential equations M Raissi, P Perdikaris, GE Karniadakis arXiv preprint arXiv:1711.10561, 2017 | 1352 | 2017 |
| Hidden physics models: Machine learning of nonlinear partial differential equations M Raissi, GE Karniadakis Journal of Computational Physics 357, 125-141, 2018 | 1233 | 2018 |
| Physics-informed neural networks (PINNs) for fluid mechanics: A review S Cai, Z Mao, Z Wang, M Yin, GE Karniadakis Acta Mechanica Sinica 37 (12), 1727-1738, 2021 | 844 | 2021 |
| Physics-informed neural networks for high-speed flows Z Mao, AD Jagtap, GE Karniadakis Computer Methods in Applied Mechanics and Engineering 360, 112789, 2020 | 841 | 2020 |
| NSFnets (Navier-Stokes flow nets): Physics-informed neural networks for the incompressible Navier-Stokes equations X Jin, S Cai, H Li, GE Karniadakis Journal of Computational Physics 426, 109951, 2021 | 809 | 2021 |
| Adaptive activation functions accelerate convergence in deep and physics-informed neural networks AD Jagtap, K Kawaguchi, GE Karniadakis Journal of Computational Physics 404, 109136, 2020 | 757* | 2020 |
| Modeling uncertainty in steady state diffusion problems via generalized polynomial chaos D Xiu, GE Karniadakis Computer methods in applied mechanics and engineering 191 (43), 4927-4948, 2002 | 740 | 2002 |
Ali BeskokSouthern Methodist University在 smu.edu 的电子邮件经过验证
