New trends in mathematics for scientific machine learning

This editorial introduces a special issue devoted to recent developments in scientific machine learning. The issue brings together contributions that illustrate, from complementary viewpoints, how mathematical analysis, modeling, scientific computing, control, and learning are becoming increasingly intertwined in the study of complex systems. Beyond presenting the papers collected in this volume, the editorial aims to place them within a broader conceptual landscape and to highlight a number of emerging directions that, in our view, will shape the future of the field. The presentation is organized in three parts: first, the motivations and scientific context underlying the special issue, second, a brief overview of the contributions included in the volume, and third, a discussion of some challenging perspectives at the interface of mathematics, scientific computing, and artificial intelligence.