From legacy finite element modeling to explainable simulation: Technical requirements for XAI in computational mechanics

This paper establishes technical requirements for explainable artificial intelligence (XAI) in computational mechanics, with an emphasis on controlling both the model-form and discretization errors in finite element analysis. We argue that explanation accuracy and the identification of knowledge limits—central requirements of XAI—can be satisfied only when these error sources are systematically estimated and controlled. A model-centric framework is developed in which hierarchical discretization and model hierarchies enable traceability of modeling assumptions and quantitative assessment of their impact on quantities of interest. The approach is illustrated through numerical studies of the stability and post-buckling behavior of spherical and hemispherical shells. The results indicate that achieving XAI in engineering requires a transition from legacy element-centric implementations to formulations grounded in the science of finite element analysis, with important implications for software architecture and simulation workflows.