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In this work, optimisation-based techniques for solving inverse problems are examined and explored, specifically addressing the challenges posed by expensive-to-evaluate black-box functions within the domain of material modelling. Our primary objectives are twofold: First, we conduct a thorough critical comparison of various cutting-edge optimisation algorithms by leveraging target responses derived from analytical, numerical, and experimental solutions with varying input space dimensionality. The performance of these methods is further evaluated in accurately calibrating material parameters for complex constitutive models, such as a finite strain visco-elastic visco-plastic model for amorphous polymers and a crystal plasticity model with martensitic transformation. Second, we present an innovative composite Bayesian Optimisation strategy tailored for finite element responses, enhancing the quality of surrogate models within the optimisation framework. Our numerical results demonstrate the superior performance of this technique over other methods, requiring only a fraction of the function evaluations. Recognising the sensitivity of the approach to the number of samples in the reference curve, we propose a response reduction algorithm to mitigate the computational cost associated with this strategy, thereby further optimising the overall efficiency of the method. The proposed approach offers an accurate, efficient, and unsupervised calibration of material parameters, reducing the need for time-consuming trial-and-error methods in parameter identification.
Coelho et al. (Fri,) studied this question.