Before revision: Physics-Informed Neural Networks (PINN) are neural networks that encode the problem governing equations, such as Partial Differential Equations (PDE), as a part of the neural network training . PINNs have emerged as an essential tool to solve various challenging problems, such as computing linear and non-linear PDEs, completing data assimilation and uncertainty quantification tasks .
After revision: Physics-Informed Neural Networks (PINN) are neural networks that encode the problem governing equations, such as Partial Differential Equations (PDE), as a part of the neural network training . PINNs have emerged as an essential tool to solve various challenging problems, including computing linear systems arising from PDEs, a task for which several traditional methods exist .