Bayesian optimization to infer parameters in viscoelasticity

Inferring viscoelasticity parameters is a key challenge that often leads to nonunique solutions when fitting rheological data. In this context, we utilize Bayesian optimization for parameter inference within curve-fitting processes. To fit a viscoelastic model to rheological data, the Bayesian optimization maps via a surrogate model the parameter values to a given error function. It then exploits the mapped space to identify parameter combinations that minimize the error. We compare the results of Bayesian optimization with traditional fitting routines and find that, while the Bayesian method requires a similar number of iterations to achieve a fit for a viscoelastic model, it does incur a higher computational cost. In sum, despite higher cost, Bayesian optimization provides a white-box framework that explicitly models the error landscape via the surrogate mean and uncertainty, using an acquisition function to target informative regions and enhance supervised parameter estimation in linear viscoelasticity.