  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 observed data while reducing a PDE residual. This article provides a
comprehensive review of the literature on PINNs: while the primary goal of the
study was to characterize these networks and their related advantages and
disadvantages. The review also attempts to incorporate publications on a
broader range of collocation-based physics informed neural networks, which
stars form the vanilla PINN, as well as many other variants, such as
physics-constrained neural networks (PCNN), variational hp-VPINN, and
conservative PINN (CPINN). The study indicates that most research has focused
on customizing the PINN through different activation functions, gradient
optimization techniques, neural network structures, and loss function
structures. Despite the wide range of applications for which PINNs have been
used, by demonstrating their ability to be more feasible in some contexts than
classical numerical techniques like Finite Element Method (FEM), advancements
are still possible, most notably theoretical issues that remain unresolved.
