Freeze nano 3D printing is a novel process that seamlessly integrates freeze casting and inkjet printing processes. It can fabricate flexible energy products with both macroscale and microscale features. These multi-scale features enable good mechanical and electrical properties with lightweight structures. However, the quality issues are among the biggest barriers that freeze nano printing, and other 3D printing processes, need to come through. In particular, the droplet solidification behavior is crucial for the product quality. The physical based heat transfer models are computationally inefficient for the online solidification time prediction during the printing process. In this paper, we integrate machine learning (i.e., tensor decomposition) methods and physical models to emulate the tensor responses of droplet solidification time from the physical based models. The tensor responses are factorized with joint tensor decomposition, and represented with low dimensional vectors. We then model these low dimensional vectors with Gaussian process models. We demonstrate the proposed framework for emulating the physical models of freeze nano 3D printing, which can help the future real-time process optimization.