Machine learning framework for determination of elastic modulus without contact model fitting

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Many contact models have been proposed for determining the elastic modulus of materials based on AFM force measurement. However, contact model fitting could be a challenging task since the elastic modulus usually varies depending on the tip parameters (i.e., radius and half-opening angle) which are difficult to determine in practice. Therefore, this study proposes a supervised machine learning (SML) regression framework for determining the elastic modulus without the need to either select an appropriate contact model or perform contact model fitting. In the proposed approach, the SML regressor learns the relationship between the force-displacement (FZ) features and the elastic modulus, and then predicts the elastic modulus of unseen samples directly from their FZ features. The predictive power of the proposed framework is demonstrated using both homogeneous materials (polydimethylsiloxane, polymethyl methacrylate, and polyvinyl alcohol), and heterogeneous materials (Staphylococcus aureus bacteria and methylammonium lead iodide). It is shown that the Gaussian process regression (GPR) model achieves a higher prediction accuracy than the multiple linear regression (MLR), random forest (RF), and support vector regression (SVR) models for both groups of materials. Particularly, GPR achieves a testing coefficient of determination value of up to 91.55% for homogeneous materials, and 82.73% for heterogeneous materials. Overall, the results confirm that the proposed SML regression framework is capable of determining the elastic modulus of both homogeneous and heterogeneous materials without the need for both contact model fitting and knowledge of tip shape.