Grid infrastructures and computing environments have progressed significantly in the past few years. The vision of truly seamless Grid usage relies on runtime systems support that is cognizant of the operational issues underlying grid computations and, at the same time, is flexible enough to accommodate diverse application scenarios. This paper addresses the twin aspects of Grid infrastructure and application support through a novel combination of two computational technologies: Weaves - a source-language independent parallel runtime compositional framework that operates through reverse-analysis of compiled object files, and runtime recommender systems that aid in dynamic knowledge-based application composition. Domain-specific adaptivity is exploited through a novel compositional system that supports runtime recommendation of code modules and a sophisticated checkpointing and runtime migration solution that can be transparently deployed over Grid infrastructures. A core set of "adaptivity schemas" are provided as templates for adaptive composition of large-scale scientific computations. Implementation issues, motivating application contexts, and preliminary results are described.