An explainable multitask deep learning framework based on QC multiscale modeling of nanoindentation in thin films
Hasan Ghahremani and Soheil Mohammadi
Results in Engineering, 28, 107729 (2025).

ABSTRACT

Nanoindentation is a powerful technique for assessing the mechanical properties of materials at the atomic scale, yet its computational modeling remains a challenge due to the complexity of deformation mechanisms. In this study, a deep learning framework is developed to predict the mechanical response of nanoindentation using the data generated via the quasicontinuum (QC) method. The dataset includes simulations of copper thin films with various indenter shapes and sizes, surface roughness levels, and crystallographic orientations. Three different neural network models are implemented and compared: (1) a multioutput model, which predicts all mechanical parameters simultaneously; (2) a two-network approach, which separates displacement predictions from other mechanical properties to increase accuracy; and (3) a multitask learning (MTL) model, which optimizes shared learning between interdependent variables. The MTL model demonstrates the highest accuracy and generalization capability, effectively capturing the nonlinear relationships between critical loads, load drops, penetration depths, hardness, and absorbed energy. To validate the proposed framework, two case studies are conducted: (1) a Berkovich indenter on a rough surface with a specific crystallographic orientation and (2) a cylindrical indenter on a smooth surface with a different orientation. The results show strong agreement between the deep learning predictions and the QC simulations, confirming the model robustness. The proposed deep learning approach provides a computationally efficient and accurate tool for predicting the mechanical behavior of materials at the atomic scale, paving the way for further advancements in data-driven nanomechanical analysis.