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Abstract Energy 3D printing processes have enabled energy storage devices with complex structures, high energy density, and high power density. Among these processes, Freeze Nano Printing (FNP) has risen as a promising process. However, quality problems are among the biggest barriers for FNP. Particularly, the droplet solidification time in FNP governs thermal distribution, and subsequently determines product solidification, formation, and quality. To describe the solidification time, physical-based heat transfer model is built. But it is computationally intensive. The objective of this work is to build an efficient emulator for the physical model. There are several challenges unaddressed: 1) the solidification time at various locations, which is a multi-dimensional array response, needs to be modeled; 2) the construction and evaluation of the emulator at new process settings need to be quick and accurate. We integrate joint tensor decomposition and Nearest Neighbor Gaussian Process (NNGP) to construct an efficient multi-dimensional array response emulator with process settings as inputs. Specifically, structured joint tensor decomposition decomposes the multi-dimensional array responses at various process settings into the setting-specific core tensors and shared low dimensional factorization matrices. Then, each independent entry of the core tensor is modeled with an NNGP, which addresses the computationally intensive model estimation problem by sampling the nearest neighborhood samples. Finally, tensor reconstruction is performed to make predictions of solidification time for new process settings. The proposed framework is demonstrated by emulating the physical model of FNP, and compared with alternative tensor (multi-dimensional array) regression models. 

Abstract 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.