Additive manufacturing (AM) is a process of creating objects from 3D model data by adding layers of material. AM technologies present several advantages compared to traditional manufacturing technologies, such as producing less material waste and being capable of producing parts with greater geometric complexity. However, deficiencies in the printing process due to high process uncertainty can affect the microstructural properties of a fabricated part leading to defects. In metal AM, previous studies have linked defects in parts with melt pool temperature fluctuations, with the size of the melt pool and the scan pattern being key factors associated with part defects. Thus being able to adjust certain process parameters during a part's fabrication, and knowing when to adjust these parameters, is critical to producing reliable parts. To know when to effectively adjust these parameters it is necessary to have models that can both identify when a defect has occurred and forecast the behavior of the process to identify if a defect will occur. This study focuses on the development of accurate forecasting models of the melt pool temperature distribution. Researchers at Mississippi State University have collected in-situ pyrometer data of a direct laser deposition process which captures the temperature distribution of the melt pool. The high-dimensionality and noise of the data pose unique challenges in developing accurate forecasting models. To overcome these challenges, a tensor decomposition modeling framework is developed that can actively learn and adapt to new data. The framework is evaluated on two datasets which demonstrates its ability to generate accurate forecasts and adjust to new data.