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 | 8870* | 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 | 2895 | 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 | 844* | 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 | 841 | 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 | 586 | 2022 |

Machine learning of linear differential equations using Gaussian processes M Raissi, P Perdikaris, G Karniadakis Journal of Computational Physics 348, 683-693, 2017 | 558 | 2017 |

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 | 485 | 2021 |

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 | 410 | 2020 |

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 | 401 | 2021 |

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 | 401 | 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 | 369 | 2017 |

Adversarial uncertainty quantification in physics-informed neural networks Y Yang, P Perdikaris Journal of Computational Physics 394, 136-152, 2019 | 364 | 2019 |

Multistep neural networks for data-driven discovery of nonlinear dynamical systems M Raissi, P Perdikaris, GE Karniadakis arXiv preprint arXiv:1801.01236, 2018 | 326 | 2018 |

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 | 292 | 2018 |

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 | 286 | 2020 |

Inferring solutions of differential equations using noisy multi-fidelity data M Raissi, P Perdikaris, GE Karniadakis Journal of Computational Physics 335, 736-746, 2017 | 274 | 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 | 273 | 2021 |

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 | 270 | 2020 |

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 | 232 | 2021 |

Multi-fidelity modelling via recursive co-kriging and Gaussian–Markov random fields P Perdikaris, D Venturi, JO Royset, GE Karniadakis Proceedings of the Royal Society A: Mathematical, Physical and Engineering …, 2015 | 215 | 2015 |