Bayesian calibration and sensitivity analysis of crystal plasticity models using Gaussian process surrogates

Crystal plasticity (CP) models enable accurate predictions of microstructural deformation in metals but can be computationally expensive, limiting their use in conjunction with robust global optimisation and sensitivity analysis routines. We present a framework that combines Gaussian process (GP) surrogate modelling with Bayesian inference and Sobol’ sensitivity analysis to overcome this computational barrier. The GP surrogates were trained to replicate the full stress–strain response for single crystal tungsten and copper using a physics-based and phenomenological model, respectively. This approach achieved high fidelity with only 300 training samples, with a RMSRE < 0.0357 for the tungsten surrogate and RMSRE < 0.0116 for the copper surrogate. Markov Chain Monte Carlo (MCMC) sampling was used to estimate the posterior parameter distribution by constructing a likelihood function which minimised the error between the surrogate predictions and experimental measurements from literature, readily capturing the deformation response for the [100] and [111] crystal orientations up to 0.15 true strain for copper, and 0.05 for tungsten. The Sobol’ indices revealed a strong strain-dependent parameter influence, identifying redundancies in the parameter space which may allow for parameter reduction.