Our research is motivated by the desire to better understand, model and simulate complex vibrations and waves. Complexity here often arises from multi-scale and multi-physics problems, and the interplay between nonlinearity, problem size, and non-stationarity. Application fields include the structural and wave dynamics of mechanical systems from mechanical, aerospace, and offshore engineering. We study novel phenomena, including rare and extreme events. And we develop new engineering methods for complex dynamical systems. Often integrating physics based approaches with data driven methods from machine learning.