Scientific Machine Learning Through Physics–Informed Neural Networks: Where we are and What’s Next

Scientific Machine Learning Through Physics–Informed Neural Networks: Where we are and What’s Next Abstract Physics-Informed Neural Networks (PINN) are neural networks (NNs) that encode model equations, like Partial Differential Equations (PDE), as a component of the neural network itself. PINNs are nowadays used to solve PDEs, fractional equations, integral-differential equations, and stochastic PDEs. This novel methodology has arisen as a multi-task learning framework in which a NN must fit o...