Abstract A novel mathematical framework called materials knowledge systems (MKS) was recently formulated to extract, store and recall computationally efficient hierarchical linkages that are at the core of multi-scale modeling of materials phenomena. A salient feature of this new framework is that it facilitates flow of high-fidelity information in both directions between the constituent length scales, and thereby offers a new strategy for concurrent multi-scale modeling. The viability of this new framework has thus far been largely explored for capturing the mechanical response of composite material systems. This paper extends the MKS framework to applications involving microstructure evolution, where the local states are typically defined in a continuous local state space. In particular, it will be shown that it is possible to obtain an efficient discretization of the local state space to produce a sufficiently accurate description of the linearized structure–structure evolution linkages for modeling spinodal decomposition. Furthermore, it will be shown that these linkages can be used successfully to accurately predict the continuous evolution of microstructure over the long time periods involved in such problems.