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From Legacy Finite Element Modeling to Explainable Simulation: Technical Requirements for XAI in Computational Mechanics

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DOI:

https://doi.org/10.31224/7229

Keywords:

numerical simulation, solid mechanics, hierarchical shell models, model form errors, XAI integration

Abstract

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.

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Author Biography

Barna Szabo, Washington University in St. Louis

Barna A. Szabó is Senior Professor in the Department of Mechanical Engineering and Materials Science at Washington University in St. Louis, Missouri. He is widely recognized for his pioneering work on the p- and hp-versions of the finite element method. He has authored or co-authored more than 100 technical papers, primarily on the finite element method. Together with Ivo Babuška, he wrote the influential book Finite Element Analysis, published by John Wiley & Sons in 1991, with substantially revised editions appearing in 2011 and 2021.

His principal research focuses on mathematical modeling techniques, with particular emphasis on ensuring the reliability and accuracy of computed results.

Professor Szabó is co-founder and Chairman of Engineering Software Research and Development, Inc. (ESRD), the company that develops StressCheck, an advanced finite element analysis software tool for structural and mechanical design and analysis with a focus on aerospace applications.

 

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Posted

2026-06-03

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Copyright (c) 2026 Barna Szabo

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This work is licensed under a Creative Commons Attribution 4.0 International License.