A generalizable framework of solution-guided machine learning with application to nanoindentation of free-standing thin films

Abstract

Despite the significant success of machine learning (ML) in various fields, there remains a critical need to enhance its ability to extrapolate from insufficient data. Here, we propose a generalizable framework called solution-guided machine learning (SGML), which integrates existing solutions as additional features to supplement limited training data. Our application of SGML to nanoindentation of free-standing thin films demonstrates robust performance, including good training convergence, accuracy, and extrapolation. Notably, the SGML models trained on limited data are able to be applied across a wider range of scenarios, e.g., the model trained on relatively moderate indenter sizes applies to relatively small as well as large indenter sizes, and the model trained for graphene successfully extends its applicability to other 2D nanomaterials (e.g., MoS2) and even to microscale thin films (e.g., silicone), highlighting extraordinary extrapolation performance. We discuss also the cooperative relationship between solutions and data, further confirming that the enhanced performance of SGML is attributed to the complementary information supplemented by solutions to data. This work presents a robust method to train more powerful ML models by combining known knowledge with limited data, offering great potential for addressing complex problems that often suffer from data insufficiency.