Machine Learning-Based Surrogate Modelling for Efficient Inverse Analysis of Micro-Indentation Response to Determine Material Parameters.

Inverse analysis from indentation experiments has been a challenging problem due to the nonlinear relationship between indentation response and material parameters. In this work, a data-driven method is proposed that integrates an artificial neural network (ANN) and evolutionary optimization for the reliable and efficient inverse parameter identification. A large dataset is generated by simulating the indentation process based on different combinations of material parameters in a systematic way. Then, by using the simulated data, a set of ANN models is trained that can efficiently predict the indentation responses, i.e., the displacement-time curve, the indentation force, and the surface profile, as a function of material parameters. These trained models exhibit the potential to replace the computationally expensive numerical simulations for the identification of material parameters by inverse analysis. In this way, the surrogate models make the numerical evaluation of the loss function, which is minimized during the inverse analysis, orders of magnitude faster. This enables the use of the powerful genetic algorithm for the minimization of the loss function, which would be impossible without numerically efficient surrogate models, as this algorithm requires many iterations to produce robust results. In this work, we systematically investigate which mathematical loss function leads to robust and unique results in determining the material parameters through inverse analysis of indentation results. The results show that such an inverse analysis can be successfully performed for simulation data. In forthcoming work, this method will be generalized to experimental indentation data, which will allow the characterization of the mechanical behaviour of materials by micro- or nano-indentation tests.