Virtual Metrology (VM) generally refers to a model based prediction of some process outcome in place of, or in the absence of, an actual physical measurement of that outcome. The underlying models are learned from histories of the actual physical outcomes and predictors that may include process trace data, tool consumable status, and incoming work characteristics. If the models are sufficiently accurate predictors of process outcomes, VM applications present the opportunity to reduce the number of physical measurements made to monitor a process, while maintaining or even improving quality control. Such applications are especially attractive for highly complex, capital intensive semiconductor manufacturing lines, in which measurements monitoring processes may add significant processing time and cost. In this paper, we propose a model for metrology variable prediction with tensor input process variables by directly operating on the tensor. Experimental results demonstrate the good performance of this model compared to others that are widely discussed in the literature of VM and deal with only one-dimensional inputs. We also propose three VM embedded run-to-run (R2R) control schemes that can facilitate feedback control based on the actual and virtual metrology values. We demonstrate the ability of the proposed control schemes to effectively reduce the process variation based on experiment results.