Essays and reviews on new trends in kinetic theory, active particles, and hyperbolic systems toward scientific machine learning

This editorial paper introduces the articles published in a special issue focused on essays and reviews, which offer a forward-looking perspectives on new frontiers of applied mathematics. First, a brief description of the scientific contributions of the papers published in this issue is provided. Then, based on the papers’ contents, a forward look at research perspectives is brought to the reader’s attention. These perspectives focus on new developments of the kinetic theory of classical and active particles, behavioral swarms, and numerical and analytical study of hyperbolic systems. Finally, our editorial explores how the contents of this issue can have an impact on mathematical tools of Scientific Machine learning Applied to the study of collective dynamics of living systems.