Kevrekidis, Yannis G.Wu, Yan2014-07-292026-09-292014-07-292026-09-292014-04-142014-07-29http://arks.princeton.edu/ark:/88435/dsp01fj236230rhttps://theses-dissertations.princeton.edu/handle/88435/dsp01fj236230rGranularity is the level of detail with which a system is described. A fine-grained system looks at small sub-components, while a coarse-grained system looks at larger components that are made up of those small sub-components. Coarse-graining a system can be an effective way to reduce the computational resources needed to model the system, while also summarizing essential system characteristics. We propose a computational method for coarse-graining the dynamics of heterogeneous, coupled oscillators using the technique of Stochastic Collocation. While our technique can be applied to general systems of coupled oscillators, we will demonstrate our method on the Kuramoto system. We will show that our coarse-grained model faithfully reproduces the dynamics of the fine-grained Kuramoto system, with a substantial reduction in computational cost.57 pagesen-USPrinceton University Senior Theses