Scientific machine learning for collective systems: Physics-brain-guided social-learning to decision-making

This work is dedicated to the study, modeling and simulation of the collective dynamics of interacting living system. The core mathematical contribution is a coupled kinetic system for the distribution function [Formula: see text] and the learned distribution [Formula: see text], where social learning and decision-making interact bidirectionally through physics-brain-guided operators. The first objective is to develop some perspective ideas toward the approach of theoretical tools of Artificial Intelligence methods, specifically Scientific Machine Learning, with focus on the study of the collective dynamics of several interacting entities. The study will be developed specifically focusing on the collective behavior of living entities, real or artificial, e.g. imitated by robots, with application to the dynamics of different situations of social life. The second perspective is to develop the conceptual tools for a theory of artificial intelligence. The aim is to model a dynamic in which interacting entities learn from other entities as well as from the environment and external actions. Then, out of this collective social-learning process, each entity develops a strategy to pursue specific goals through a decision-making process that leads to the dynamics. The approach is based on developments in the kinetic theory of active particles. This paper does not naively claim that the problem of artificial intelligence for collective dynamics has been considered exhaustively, but some hints are proposed to contribute to such a challenging perspective in view of further developments.