| 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 | 9674 | 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 |
| Microflows and nanoflows: fundamentals and simulation G Karniadakis, A Beskok, N Aluru Springer Science & Business Media, 2006 | 4054* | 2006 |
| Physics-informed machine learning GE Karniadakis, IG Kevrekidis, L Lu, P Perdikaris, S Wang, L Yang Nature Reviews Physics 3 (6), 422-440, 2021 | 3578 | 2021 |
| Spectral/hp element methods for computational fluid dynamics G Karniadakis, SJ Sherwin Oxford University Press, USA, 2005 | 3493 | 2005 |
| Discontinuous Galerkin methods: theory, computation and applications B Cockburn, GE Karniadakis, CW Shu Springer Science & Business Media, 2012 | 2989* | 2012 |
| 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 | 1780 | 1991 |
| Modeling uncertainty in flow simulations via generalized polynomial chaos D Xiu, GE Karniadakis Journal of computational physics 187 (1), 137-167, 2003 | 1764 | 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 | 1589 | 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 | 1513 | 1999 |
| 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 | 1481 | 2021 |
| Hidden fluid mechanics: Learning velocity and pressure fields from flow visualizations M Raissi, A Yazdani, GE Karniadakis Science 367 (6481), 1026-1030, 2020 | 1452 | 2020 |
| 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 | 1389 | 2017 |
| Hidden physics models: Machine learning of nonlinear partial differential equations M Raissi, GE Karniadakis Journal of Computational Physics 357, 125-141, 2018 | 1242 | 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 | 866 | 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 | 861 | 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 | 826 | 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 | 772* | 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 | 730 | 2002 |
| An adaptive multi-element generalized polynomial chaos method for stochastic differential equations X Wan, GE Karniadakis Journal of Computational Physics 209 (2), 617-642, 2005 | 728 | 2005 |
Ali BeskokSouthern Methodist UniversityVerified email at smu.edu
