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 | 1343 | 2019 |

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 | 1343 | 2019 |

Physics informed deep learning (part ii): Data-driven discovery of nonlinear partial differential equations M Raissi, P Perdikaris, GE Karniadakis arXiv preprint arXiv:1711.10566, 2017 | 414* | 2017 |

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 | 414 | 2017 |

Machine learning of linear differential equations using Gaussian processes M Raissi, P Perdikaris, G Karniadakis Journal of Computational Physics 348, 683-693, 2017 | 257 | 2017 |

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 | 239 | 2019 |

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 | 143 | 2018 |

Multistep neural networks for data-driven discovery of nonlinear dynamical systems M Raissi, P Perdikaris, GE Karniadakis arXiv preprint arXiv:1801.01236, 2018 | 142 | 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 | 140 | 2017 |

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 | 139 | 2015 |

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 | 134 | 2017 |

Adversarial uncertainty quantification in physics-informed neural networks Y Yang, P Perdikaris Journal of Computational Physics 394, 136-152, 2019 | 123 | 2019 |

Integrating machine learning and multiscale modeling—perspectives, challenges, and opportunities in the biological, biomedical, and behavioral sciences M Alber, AB Tepole, WR Cannon, S De, S Dura-Bernal, K Garikipati, ... NPJ digital medicine 2 (1), 1-11, 2019 | 99 | 2019 |

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 | 93* | 2020 |

Fractional-order viscoelasticity in one-dimensional blood flow models P Perdikaris, GE Karniadakis Annals of biomedical engineering 42 (5), 1012-1023, 2014 | 88 | 2014 |

Model inversion via multi-fidelity Bayesian optimization: a new paradigm for parameter estimation in haemodynamics, and beyond P Perdikaris, GE Karniadakis Journal of The Royal Society Interface 13 (118), 20151107, 2016 | 69 | 2016 |

Understanding and mitigating gradient pathologies in physics-informed neural networks S Wang, Y Teng, P Perdikaris arXiv preprint arXiv:2001.04536, 2020 | 64 | 2020 |

Multi-fidelity Gaussian process regression for prediction of random fields L Parussini, D Venturi, P Perdikaris, GE Karniadakis Journal of Computational Physics 336, 36-50, 2017 | 64 | 2017 |

Learning parameters and constitutive relationships with physics informed deep neural networks AM Tartakovsky, CO Marrero, P Perdikaris, GD Tartakovsky, ... arXiv preprint arXiv:1808.03398, 2018 | 58 | 2018 |

Multifidelity information fusion algorithms for high-dimensional systems and massive data sets P Perdikaris, D Venturi, GE Karniadakis SIAM Journal on Scientific Computing 38 (4), B521-B538, 2016 | 58 | 2016 |