Prediction and Inference: From Models and Data to Artificial Intelligence

Abstract

In this paper we present a discussion of the basic aspects of the well-known problem of prediction and inference in physics, with specific attention to the role of models, the use of data and the application of recent developments in artificial intelligence. By focussing in the time evolution of dynamic system, it is shown that main difficulties in predictions arise due to the presence of few factors as: the occurrence of chaotic dynamics, the existence of many variables with very different characteristic time-scales and the lack of an accurate understanding of the underlying physical phenomena. It is shown that a crucial role is assigned to the preliminary identification of the proper variables, their selection and the identification of an appropriate level of description (coarse-graining procedure). Moreover, it is discussed the relevance, even in modern practical issues, of old well-known fundamental results, like the Poincaré recurrence theorem, the Kac’s lemma and the Richard’s paradox.