Data-And model-driven computer simulations are increasingly critical in many application domains. These simulations may track 10s or 100s of parameters, affected by complex inter-dependent dynamic processes. Moreover, decision makers usually need to run large simulation ensembles, containing 1000s of simulations. In this paper, we rely on a tensor-based framework to represent and analyze patterns in large simulation ensemble data sets to obtain a high-level understanding of the dynamic processes implied by a given ensemble of simulations.We, further, note that the inherent sparsity of the simulation ensembles (relative to the space of potential simulations one can run) constitutes a significant problem in discovering these underlying patterns. To address this challenge, we propose a partition-stitch sampling scheme, which divides the parameter space into subspaces to collect several lower modal ensembles, and complement this with a novel Multi-Task Tensor Decomposition (M2TD), technique which helps effectively and efficiently stitch these subensembles back. Experiments showed that, for a given budget of simulations, the proposed structured sampling scheme leads to significantly better overall accuracy relative to traditional sampling approaches, even when the user does not have a perfect information to help guide the structured partitioning process.