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

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 · 14.4K citations · Full text

Engineering, Pde-constrained Optimization, Deep Learning Framework +6

Artificial neural networks for solving ordinary and partial differential equations

IEEE Transactions on Neural Networks · 1998 · 2.1K citations · Full text

Numerical Analysis, Method Of Fundamental Solution, Evolving Neural Network +13

Automatic Differentiationin Machine Learning: a Survey

Atılım Güneş Baydin, Barak A. Pearlmutter, Alexey Radul et al. · MURAL - Maynooth University Research Archive Library (National University of Ireland, Maynooth) · 2018 · 2.1K citations

Hidden fluid mechanics: Learning velocity and pressure fields from flow visualizations

Maziar Raissi, Alireza Yazdani, George Em Karniadakis · Science · 2020 · 1.8K citations · Full text

Geometric Learning, Real-time Visualization, Convolutional Neural Network +23

When and why PINNs fail to train: A neural tangent kernel perspective

Sifan Wang, Xinling Yu, Paris Perdikaris · Journal of Computational Physics · 2021 · 991 citations · Full text

Cognitive Science, Engineering, Machine Learning +10