## 1 Introduction  
Additive manufacturing (AM) or 3D printing refers to a set of manufacturing processes that can fabricate a three-dimensional (3D) physical object from a digital computer-aided design (CAD) model by directly joining materials in a layer-by-layer fashion. In contrast, traditional manufacturing processes are subtractive since a part is mainly produced by removing unnecessary parts from a bulk material, which typically increases material waste, and thereby production cost. Additionally, the manufacturing time of a subtractive process is highly dependent on the geometrical complexity of products. However, AM builds a product in a layer-by-layer fashion, making it possible to construct products in a complex geometry without increasing manufacturing time or cost. Given these advantages, AM is increasingly used to produce a wide range of parts and products and replace traditional manufacturing processes [1; 2]. Furthermore, AM even allows for the creation of sophisticated geometries that would not be possible to realize otherwise. For example, AM is used to fabricate lightweight cellular structures with an unprecedented capability to sustain high external loads while maintaining an extremely low density [3; 4]. Highly ordered cellular structures that comprise spatially arranged thin struts result in high stiffness and toughness per unit weight and high surface-to-volume ratios. Several applications of cellular structures are suggested, including energy absorbing systems [5; 6; 7], thermal applications [8; 9], and biomimetic materials [10]. Despite significant advances in AM techniques, distinctive geometrical deviations continue to exist between a CAD model and a final printed product due to various sources, such as digitization of 3D models, non-uniform material forming, and defects from the printing processes [11; 12]. The staircase sidewall profile is one of the most prominent problems observed in most AM parts. Given that the use of AM gradually shifts from creating prototyping to manufacturing of functional end products, the accurate prediction of mechanical properties of AM parts is increasingly important. Recent studies indicate that dimensional accuracy, geometrical alignment, and surface roughness of micro and nanostructures fabricated by AM techniques can lead to high deviations in the mechanical properties [13; 14]. In particular, the impact of geometrical uncertainties on mechanical performance is increasingly pronounced when the length scale of the AM parts approaches the spatial deviations caused by the manufacturing process. There has been a previous study in which the stiffness variations of additively manufactured microlattice structures resulting from geometrical uncertainties were quantified [13]. However, the geometrical difference investigated is limited to in-plane radial deviations, and the effects from the staircase sidewall profile and roughness are not considered. In addition, previous studies do not consider the actual deviation between planned and manufactured geometries to investigate the effect of topological uncertainties on the mechanical performance of AM parts. Figure 1a shows a schematic illustration of additive manufacturing process of a 3D microlattice using a mask projection stereolithography technique. The manufactured microlattice has a hierarchical structure of repeating unit cells which consist of thin struts arranged in multiple directions. In the study, we present a probabilistic modeling framework that can predict the spatial variations of printed geometry via digital images of AM parts. We limit our interest to the spatial variations of a single strut given that it is a unit building block of various types of 3D microlattices and that the load-bearing characteristics of a single strut determine the mechanical behavior of the overall lattice structure.