Artificial intelligence methods, especially artificial neural networks (ANNs), have increasingly been utilized for the mathematical description of physical phenomena in (metallic) material processing. Traditional methods often fall short in explaining the complex, real-world data ob-served in production. While ANN models, typically functioning as "black boxes," improve pro-duction efficiency, a deeper understanding of the phenomena, akin to that provided by explicit mathematical formulas, could enhance this efficiency further. This article proposes a general framework that leverages (CAE) ANNs to explain predicted results alongside their graphical presentation, marking a significant improvement over previous approaches and those relied on expert assessments. Unlike existing Explainable AI (XAI) methods, the proposed framework mimics the standard scientific methodology, utilizing minimal parameters for the mathematical representation of physical phenomena and their derivatives. Additionally, it analyzes the relia-bility and accuracy of the predictions using well-known statistical metrics, transitioning from deterministic to probabilistic descriptions for better handling of real-world phenomena. The proposed approach addresses both aleatory and epistemic uncertainties inherent in the data. The concept is demonstrated through the hot extrusion of aluminum alloy 6082, where CAE ANN models and predicts key parameters, and ChatGPT explains the results, enabling researchers and/or engineers to better understand the phenomena and outcomes obtained by ANNs.