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Paris Perdikaris
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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
10715*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
36942021
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
1026*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
9322019
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
7442022
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
6422021
Machine learning of linear differential equations using Gaussian processes
M Raissi, P Perdikaris, G Karniadakis
Journal of Computational Physics 348, 683-693, 2017
6072017
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
5522021
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
4752020
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
4712019
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
4092017
Adversarial uncertainty quantification in physics-informed neural networks
Y Yang, P Perdikaris
Journal of Computational Physics 394, 136-152, 2019
3942019
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
3662021
Multistep neural networks for data-driven discovery of nonlinear dynamical systems
M Raissi, P Perdikaris, GE Karniadakis
arXiv preprint arXiv:1801.01236, 2018
3412018
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
3292020
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
3182018
Inferring solutions of differential equations using noisy multi-fidelity data
M Raissi, P Perdikaris, GE Karniadakis
Journal of Computational Physics 335, 736-746, 2017
3052017
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
3022020
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
2662021
Respecting causality for training physics-informed neural networks
S Wang, S Sankaran, P Perdikaris
Computer Methods in Applied Mechanics and Engineering 421, 116813, 2024
224*2024
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Articles 1–20