In this talk we will introduce physics informed neural networks (PINNs) which are neural networks designed to solve PDE. We will discuss some of their specificity related to the low-dimensionality of the input data and a strong spectral bias issue which require to identify and address separately optimization and learning shortcomings. The analysis of the geometric structure of the NN tangent space will lead us to propose state of the art optimization algorithms to these problem and to design a principled active learning strategy.