In parallel to the theory based WP 1.1 and the applications based WP 3.1 and WP 3.2, the question here is how to suitably discretise an underlying dynamical system while maintaining important structures, e.g. invariants, symmetries (continuous and discrete), and symplectic / Hamiltonian structures. The focus here will be to develop the new area of Physics Informed Neural Networks (PINNS) in the broader context of Physics Informed Learning (PIL). Such properties play a fundamental role in mathematical modelling, which will be used for developing DL based generative models in WP 3.1 and the solvers for computational physics in WP 3.2, whereas generic DNNs are largely agnostic to structures. These aspects of computational methods have been studied in the numerical analysis literature in the areas of geometric integration and structure preserving algorithms. In this WP, we shall systematically explore the connection between such structure preserving methods, and the DL based PINNs and generative models.