Renormalized Mori-Zwanzig-reduced models for systems without scale separation

Model reduction for complex systems is a rather active area of research. For many real-world systems, constructing an accurate reduced model is prohibitively expensive. The main difficulty stems from the tremendous range of spatial and temporal scales present in the solution of such systems. This leads to the need to develop reduced models where, inevitably, the resolved variables do not exhibit (spatial and/or temporal) scale separation from the unresolved ones. We present a brief survey of recent results on the construction of Mori-Zwanzig-reduced models for such systems. The construction is inspired by the concepts of scale dependence and renormalization which first appeared in the context of high-energy and statistical physics.