The data-driven rogue waves of the Hirota equation by using Mix-training PINNs approach

Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations

Maziar Raissi, Paris Perdikaris, George Em Karniadakis · Journal of Computational Physics · 2018 · 16.9K citations · Full text

Natural Sciences, Computer Science, Physics +16

Conservative physics-informed neural networks on discrete domains for conservation laws: Applications to forward and inverse problems

Ameya D. Jagtap, Ehsan Kharazmi, George Em Karniadakis · Computer Methods in Applied Mechanics and Engineering · 2020 · 1.1K citations · Full text

Natural Sciences, Mathematics, Physics +16

Gradient-enhanced physics-informed neural networks for forward and inverse PDE problems

Jeremy Yu, Lu Lu, Xuhui Meng et al. · Computer Methods in Applied Mechanics and Engineering · 2022 · 634 citations · Full text

Natural Sciences, Mathematics, Physics +14

Machine learning in cardiovascular flows modeling: Predicting arterial blood pressure from non-invasive 4D flow MRI data using physics-informed neural networks

Georgios Kissas, Yibo Yang, Eileen Hwuang et al. · Computer Methods in Applied Mechanics and Engineering · 2019 · 629 citations · Full text

Engineering, Biomedical Engineering, Computer Science +17

Rogue waves and rational solutions of the Hirota equation

Adrian Ankiewicz, J. M. Soto‐Crespo, Nail Akhmediev · Physical Review E · 2010 · 510 citations · Full text

Natural Sciences, Mathematics, Oceanography +17