This project is a trans-disciplinary effort toward inference and prediction of complex physical systems. Such systems are often ineffectively described by first principles models and should be modeled via a data-driven approach. However, difficulties arise from the high dimensional and multi-scale nature of these systems. Further, only limited and poorly informative observations are typically available. Prototypical of these situations is subsurface ocean inference or the prevention of seizures in neurosciences. For many applications however, some degree of expertise is available. The goal of this project is to leverage both the theoretical and the data science pillars to infer computable models informed from the existing prior knowledge (Physics first principles and theories) and providing new hints into the principles satisfied by the proposed abstractions, amenable to interpretation and refutation. More precisely, building upon the pluridisciplinary expertise of the team in the domains of Fluid Mechanics and Deep Neural Networks (DNN), the goal of the proposal is: - i) to make the model space (neural architecture and computational flow) compliant with the known Physics of the system under consideration, - ii) to exploit the data and inference tools to train efficient models built on first principles, thereby enhancing their robustness and reducing their data-hunger, - iii) to form and inspect the abstractions built by the DNN systems, to check whether they satisfy the expected properties and understand the properties they satisfy. Methods and tools will be first developed with low-dimensional dynamical systems but will then be illustrated and demonstrated on a full-scale turbulent fluid flow numerical simulation.