Dimensional analysis-guided neural network for nanoindentation tests of composites

Abstract

Machine learning holds a great promise for applications in the experimental characterization of the mechanical properties of composites. However, conventional neural networks often suffer from low training efficiency, limited predictive accuracy, and strong dependence on the amount and quality of experimental data. In this paper, we propose a generalizable framework, referred to as a dimensional analysis-guided neural network (DANN), by integrating dimensional analysis with the neural network architecture. Through the introduction of a dimensionless transformation layer, DANN converts both the inputs and outputs into dimensionless groups, thereby embedding the principle of physical similarity into the learning process. The framework is validated via an inverse indentation problem involving fiber-reinforced composites. In comparison with conventional neural networks, DANN demonstrates higher accuracy, improved data efficiency, and greater robustness. Thus, DANN provides a physics-informed, data-efficient, and scalable approach for addressing complex problems in solid mechanics.