In this talk we follow two roads. The first one explores the approach taken by formal methods in constructing and evaluating software systems. This means applying mathematics for modelling and analyzing systems, from specification to implementation, so that we can verify the implemented properties. The second road inspects what it takes for machines to learn, from the basic concepts to a review of current machine learning techniques. We aim to arrive at an intersection of the two roads, where we can apply the strictness of mathematical modelling and the predictive power of machine learning in order to better understand the problematics of gravitational waves and laser physics.