Advances in mathematics and physics: From complexity to machine learning—A review

In this Focus Issue, we explore recent advances in complexity and machine learning applied to nonlinear and emergent phenomena in mathematics, physics, and interdisciplinary science. The collected papers address topics, including chaos, turbulence, dissipative solitons, active matter, complex networks, stochastic dynamics, bifurcations, and quantum systems. Several contributions investigate self-organization, synchronization, multistability, and pattern formation in physical, biological, ecological, and socioeconomic systems, while others employ neural networks, physics-informed learning, reservoir computing, and data-driven approaches to model, predict, and analyze complex dynamical behaviors. These studies demonstrate the broad impact of complexity and machine learning across modern interdisciplinary research.