The first part of the talk is about the design of parameter free limiter for hyperbolic conservation laws, which is agnostic to the mathematical model and underlying numerical method. A neural network is trained to identify cells which are in need of limiting without having to fix a parameter which often depends on initial data (when such parameter is poorly tuned, the cost is shown through excessive smooth extrema clipping, excessive dissipation or unstable schemes). A 2-d extension defined on a cartesian mesh for Runge-Kutta Discontinuous Galerkin scheme is obtained. One way to generalize the limiter to other numerical schemes can be to see this as a transfer learning problem. We use the blackbox shock detector on a residual distribution scheme (cartesian mesh and triangular mesh), by performing feature projection and retraining the neural network with a reduced dataset generated with the residual distribution scheme. The last part of the talk is a by product of the study described above. We found interest on the question of how to enforce relevant approximation properties (e.g. symmetry of the approximating function) when using neural networks as approximators. I will talk about some of our efforts into constructing structure preserving (or often called physics aware) learning algorithms, and the importance of these developments for applying machine learning in natural sciences.