Computing residual field distributions resulting from the thermomechanical history and interactions experienced by materials build by additive manufacturing (AM) methods, can be a very inefficient and computationally expensive process. To address this issue, the present work proposes and demonstrates a data-driven surrogate modeling approach that does not require solving the thermal-structural simulation of the AM process explicitly. Instead, it introduces the employment of various types of physics-agnostic surrogate models that are trained to data produced by full order physics-informed models. This enables to efficiently predict the resulting residual fields (e.g. distortions and residual stress) throughout the entire component. More specifically, two types of surrogate models for two different requirements scenarios are selected for the proposed work: Non-Uniform Rational B-Splines (NURBs) for a regularly sampled parametric space and k-simplex interpolants approach based on a two-step 3 + 1 dimensional interpolation that can operate on irregularly sampled spaces and grids. It is demonstrated that both methodologies can operate with low error and high performance (solution can be obtained within a few seconds on a desktop computer) on additively manufactured components of complex geometries.