Learning implicit yield surface models with uncertainty quantification for noisy datasets

Materials often exhibit stochastic mechanical behaviors due to their inherent intrinsic variability. Data acquisition also introduces extrinsic noise into data. To learn yield surface models under uncertainty, we present a method that uses genetic programming based symbolic regression (GPSR) and a multi-objective fitness function (MOSR). Previous works have demonstrated using an implicit fitness metric in GPSR that compares the partial derivatives of proposed models with those of the data, allowing the generation of mechanics-guided, implicit yield surface models. MOSR adds to that a Bayesian fitness metric to simultaneously quantify parameter uncertainty. We test this method on benchmark implicit and physical test problems to demonstrate MOSR’s efficacy in finding implicit model forms on noisy data compared to the conventional implicit fitness metric. The results show that the MOSR algorithm prevents overfitting to noisy data, improves parameter estimates on data even with no noise present, and reduces model complexity, improving overall model interpretability. The MOSR method affords the ability to learn new and improved yield surface models while simultaneously quantifying the uncertainty in model parameters, leading to enhanced model interpretability.