After Chris Anderson's statement: "The End of Theory: The Data Deluge Makes the Scientific Method Obsolete" published in Wired in 2008, a big discussion arose about the role of modelling schemes in the digital era. The Big Data paradigm, with its overwhelming impact on technology and science, proposes, in some sense, a purely inductive alternative to the physical, model-based, description of reality. It is thus very natural and important to raise the question, about the limits of such a description. In what circumstances can one learn (predict, extract-features, etc.) efficiently from the data without the use of models, theories or hierarchical hypotheses? What is behind the apparent success of tools like deep learning and what is its link with well-known theoretical tools, e.g., the renormalisation group? It is even more important to raise the question about the positive synergies that theoretical schemes and data can jointly trigger. The notable examples of weather forecast and epidemic spreading have proved that suitable data-driven computational schemes can effectively tame the high dimensionality embedding complex phenomena. Still the whole matter is far from being settled. This project aims at addressing this set of problems by blending in a unique effort several tools and approaches: dynamical systems and information theory, neural networks and machine learning approaches, data-driven modelling schemes. Several case studies will be considered in several areas: e.g., modelling and predicting social dynamics (opinions, mobility, information dynamics), statistical mechanics in "non standard" situations, i.e., systems far from equilibrium and/or without an Hamiltonian structure, modelling innovation dynamics, textual analysis and classification, extraction of features from images, etc.
