| 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 | 10889 | 2019 |
| The Wiener--Askey polynomial chaos for stochastic differential equations D Xiu, GE Karniadakis SIAM journal on scientific computing 24 (2), 619-644, 2002 | 5861 | 2002 |
| Physics-informed machine learning GE Karniadakis, IG Kevrekidis, L Lu, P Perdikaris, S Wang, L Yang Nature Reviews Physics 3 (6), 422-440, 2021 | 4138 | 2021 |
| Microflows and nanoflows: fundamentals and simulation G Karniadakis, A Beskok, N Aluru Springer Science & Business Media, 2006 | 4096* | 2006 |
| Spectral/hp element methods for computational fluid dynamics G Karniadakis, SJ Sherwin Oxford University Press, USA, 2005 | 3541 | 2005 |
| Discontinuous Galerkin methods: theory, computation and applications B Cockburn, GE Karniadakis, CW Shu Springer Science & Business Media, 2012 | 3032* | 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 | 1800 | 1991 |
| Modeling uncertainty in flow simulations via generalized polynomial chaos D Xiu, GE Karniadakis Journal of computational physics 187 (1), 137-167, 2003 | 1785 | 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 | 1762 | 2021 |
| 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 | 1717 | 2021 |
| Hidden fluid mechanics: Learning velocity and pressure fields from flow visualizations M Raissi, A Yazdani, GE Karniadakis Science 367 (6481), 1026-1030, 2020 | 1581 | 2020 |
| 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 | 1527 | 1999 |
| 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 | 1498 | 2017 |
| Hidden physics models: Machine learning of nonlinear partial differential equations M Raissi, GE Karniadakis Journal of Computational Physics 357, 125-141, 2018 | 1314 | 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 | 1046 | 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 | 954 | 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 | 899 | 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 | 857* | 2020 |
| fPINNs: Fractional physics-informed neural networks G Pang, L Lu, GE Karniadakis SIAM Journal on Scientific Computing 41 (4), A2603-A2626, 2019 | 757 | 2019 |
| Conservative physics-informed neural networks on discrete domains for conservation laws: Applications to forward and inverse problems AD Jagtap, E Kharazmi, GE Karniadakis Computer Methods in Applied Mechanics and Engineering 365, 113028, 2020 | 755 | 2020 |
Ali BeskokSouthern Methodist UniversityVerified email at smu.edu
