## 1 Introduction  
During the operation of a pipeline, various types of flaws can occur, including volumetric flaws (e.g., pores, inclusions, undercuts, and overlaps) as well as crack-like flaws characterized by planar flaws with a sharp root radius [1, 2]. According to the recommendations outlined in API 579-1/ASME FFS-1 [3], it is advisable to treat volumetric flaws in the close vicinity as crack-like flaws, the severity of which could be characterized by length and depth. A crack-like flaw intends to create an idealized crack geometry that is intentionally conservative (i.e., more severe than the actual volumetric flaws). Under the combination of mechanical action and environment, the propagation of a surface crack is possible and becomes a serious risk to the structural integrity of the pipeline system. The severity of a crack can be quantified by a linear-elastic fracture mechanics parameter, known as the stress intensity factor or \(K\)[4]. If \(K\) is higher than the fracture toughness of pipe material (i.e., the critical stress intensity factor or \(K_{\text{C}}\)), the crack propagates rapidly, and a sudden fracture of the pipeline is possible. On the other hand, if \(K\) is lower than \(K_{\text{C}}\) but still high enough to initiate crack propagation, the crack could propagate in the thickness of the pipe (i.e., a propagating crack), eventually leading to leakage (i.e., a through-thickness crack). With periodic observation and life assessment, the service of a cracked pipeline may be allowed to continue until appropriate maintenance is performed [2]. For a pipe under internal pressure, the semi-elliptical crack-like flaws are likely to nucleate at an inner wall and in the longitudinal direction due to the influence of hoop stress [5]. Because the \(K\) under opening mode (i.e., \(K_{\rm I}\)) at the deepest point of an infinitely long crack could be considered the upper limit of \(K_{\rm I}\) for the pressurized pipe with semi-elliptical surface cracks [3; 6]; the \(K_{\rm I}\) solution for an infinitely long crack is recommended by API 579-1/ASME FFS-1 for a cracked pipe under internal pressure. For a pressurized pipe with an infinitely long internal surface crack in the longitudinal direction, \(K_{\rm I}\) can be numerically calculated using finite element analysis (FEA). However, the FEA for an accurate \(K_{\rm I}\) requires various resources, such as numerical skills, computational hardware, and time. As an alternative, the \(K_{\rm I}\) values obtained from FEA are mathematically arranged into a simple function based on applied pressure, geometry, and crack size, as presented in API 579-1/ASME FFS-1. Interpolations are necessary to obtain the required geometry function when the geometry of a cracked pipe does not exactly match those provided in API 579-1/ASME FFS-1. Although the geometry functions for various crack sizes and pipe thicknesses are nonlinear, linear interpolation is typically employed for the required geometry function. [PERSON] et al. [7] found that for shallow cracks in a pipe, linear interpolation does not yield a significant difference in \(K_{\rm I}\) when compared with nonlinear interpolation. However, for deep cracks in a pipe, the difference becomes more pronounced (i.e., up to 6%). As an intelligence created by machines to solve complex problems, artificial intelligence (AI) has successfully been applied in various engineering domains. These applications include predicting the compressive strength of concrete [8], determining the stiffness matrix of functionally-graded nanoplates [9], generating performance data for a steam methane reformer (SMR) [10], forecasting electric energy consumption [11], analyzing fuel efficiency for cargo vessel operation [12], and identifying damages in components as well as determining the fracture toughness of materials [13; 14]. Among various AI methods, the artificial neural network (ANN) method [15] simulates a brain by using artificial neurons that transmit and process signals between each other.