The last few years have been marked by the rise of Machine Learning (ML), which has allowed significant performance gains in several application areas. In addition to the undeniable methodological advances, these gains are often attributed to large amounts of training data and computing power, which have led to advances in speech recognition, computer vision and automatic speech processing. language (I will put information in general).

While in many applications machine learning has become the predominant methodology, there are also areas and / or situations where exact modeling of a system or phenomenon is (at present) essential. This dichotomy between manual design (by integrating expert knowledge) and machine learning from data is typical of artificial intelligence at its interface with other fields. It is widely discussed, for example, in computer vision (manually designed features vs. learned features) in natural language processing (linguistic knowledge vs. learning), in statistics (causal models vs. learned predictors) and in control ( control theory vs. reinforcement learning) etc.

This thesis deals with problems involving physical phenomena, such as the control of mechanical processes or mechanical agents, traditionally approached by control theory, or weather prediction, traditionally treated by numerical modeling based on equations with partial derivatives (PDE), on a discretization in the form of a grid, etc. Most physical phenomena are governed by infinite dimensional systems (Navier-Stockes for fluid mechanics, Maxwell for electromagnetism, heat equation, etc.). The modeling of these natural phenomena remains a discipline for which "data-driven" methods suffer from a lack of precision, stability and robustness of the discretization schemes often necessary for their implementations in practice.

By approaching this problem in a hybrid way, combining the modeling of the physical phenomena studied and machine learning from big data, we will address the underlying methodological questions.