Unveiling the Implicitness: Kolmogorov-Arnold Networks for Structural Reliability Problems

Abstract

The analysis and design process in structural engineering relies on the results obtained of the structural model from the black-box finite element analysis which causes implicit limit state function (i-LSF) in the structural reliability analysis (SRA). The current surrogate modeling techniques are based on evaluating the i-LSF to construct surrogates. However, even though their computational efficiencies and accuracies, the developed surrogates are mainly still implicit or yield highly complex i-LSFs. In this work, the Kolmogorov-Arnold Network (KAN) is used to discover an equivalent explicit LSF (ee-LSF) by generating a symbolic function for a given dataset. The discovered ee-LSF can be used in SRA since the expensive FEA is now able to be replaced by a simple explicit function. This paradigm allows us to unveil the implicitness of LSFs by discovering equivalent formulations through KANs which is novel to this work. Two examples are covered in this paper to present the ee-LSF approach. The ee-LSF approach demonstrates high accuracy, though its computational efficiency is currently lower compared to other surrogate modeling techniques. This limitation presents an opportunity for enhancement in future studies, particularly through integration with advanced sampling techniques.