| 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 | 12593* | 2019 |
| Physics-informed machine learning GE Karniadakis, IG Kevrekidis, L Lu, P Perdikaris, S Wang, L Yang Nature Reviews Physics 3 (6), 422-440, 2021 | 4492 | 2021 |
| Understanding and mitigating gradient flow pathologies in physics-informed neural networks S Wang, Y Teng, P Perdikaris SIAM Journal on Scientific Computing 43 (5), A3055-A3081, 2021 | 1224* | 2021 |
| Physics-constrained deep learning for high-dimensional surrogate modeling and uncertainty quantification without labeled data Y Zhu, N Zabaras, PS Koutsourelakis, P Perdikaris Journal of Computational Physics 394, 56-81, 2019 | 1014 | 2019 |
| When and why PINNs fail to train: A neural tangent kernel perspective S Wang, X Yu, P Perdikaris Journal of Computational Physics 449, 110768, 2022 | 915 | 2022 |
| Physics-informed neural networks for heat transfer problems S Cai, Z Wang, S Wang, P Perdikaris, GE Karniadakis Journal of Heat Transfer 143 (6), 060801, 2021 | 794 | 2021 |
| Learning the solution operator of parametric partial differential equations with physics-informed DeepONets S Wang, H Wang, P Perdikaris Science advances 7 (40), eabi8605, 2021 | 671 | 2021 |
| Machine learning of linear differential equations using Gaussian processes M Raissi, P Perdikaris, G Karniadakis Journal of Computational Physics 348, 683-693, 2017 | 651 | 2017 |
| Machine learning in cardiovascular flows modeling: Predicting arterial blood pressure from non-invasive 4D flow MRI data using physics-informed neural networks G Kissas, Y Yang, E Hwuang, WR Witschey, JA Detre, P Perdikaris Computer Methods in Applied Mechanics and Engineering 358, 112623, 2020 | 544 | 2020 |
| Integrating machine learning and multiscale modeling—perspectives, challenges, and opportunities in the biological, biomedical, and behavioral sciences M Alber, A Buganza Tepole, WR Cannon, S De, S Dura-Bernal, ... NPJ digital medicine 2 (1), 115, 2019 | 521 | 2019 |
| Nonlinear information fusion algorithms for data-efficient multi-fidelity modelling P Perdikaris, M Raissi, A Damianou, ND Lawrence, GE Karniadakis Proceedings of the Royal Society A: Mathematical, Physical and Engineering …, 2017 | 450 | 2017 |
| On the eigenvector bias of Fourier feature networks: From regression to solving multi-scale PDEs with physics-informed neural networks S Wang, H Wang, P Perdikaris Computer Methods in Applied Mechanics and Engineering 384, 113938, 2021 | 443 | 2021 |
| Adversarial uncertainty quantification in physics-informed neural networks Y Yang, P Perdikaris Journal of Computational Physics 394, 136-152, 2019 | 424 | 2019 |
| Physics-informed neural networks for cardiac activation mapping F Sahli Costabal, Y Yang, P Perdikaris, DE Hurtado, E Kuhl Frontiers in Physics 8, 42, 2020 | 371 | 2020 |
| Multistep neural networks for data-driven discovery of nonlinear dynamical systems M Raissi, P Perdikaris, GE Karniadakis arXiv preprint arXiv:1801.01236, 2018 | 351 | 2018 |
| Physics‐informed deep neural networks for learning parameters and constitutive relationships in subsurface flow problems AM Tartakovsky, CO Marrero, P Perdikaris, GD Tartakovsky, ... Water Resources Research 56 (5), e2019WR026731, 2020 | 340 | 2020 |
| Numerical Gaussian processes for time-dependent and nonlinear partial differential equations M Raissi, P Perdikaris, GE Karniadakis SIAM Journal on Scientific Computing 40 (1), A172-A198, 2018 | 339 | 2018 |
| Inferring solutions of differential equations using noisy multi-fidelity data M Raissi, P Perdikaris, GE Karniadakis Journal of Computational Physics 335, 736-746, 2017 | 328 | 2017 |
| Multiscale modeling meets machine learning: What can we learn? GCY Peng, M Alber, A Buganza Tepole, WR Cannon, S De, ... Archives of Computational Methods in Engineering 28, 1017-1037, 2021 | 310 | 2021 |
| Respecting causality for training physics-informed neural networks S Wang, S Sankaran, P Perdikaris Computer Methods in Applied Mechanics and Engineering 421, 116813, 2024 | 297* | 2024 |
George Em KarniadakisThe Charles Pitts Robinson and John Palmer Barstow Professor of Applied Mathematics and EngineeringEmail verificata su brown.edu