A Multi-task Bayesian Optimization framework to identify a Gurson–Tvergaard–Needleman constitutive model for an MS1500 steel in hydrogen environment

In this work, we propose a Multi-task Bayesian Optimization framework for identifying constitutive parameters of material models whose calibration typically requires significant computational effort. While the objective function is formally expressed as a residual between experimental and simulated curves of the specimen, we allow a Multi-task Gaussian Process to directly learn the entire force–displacement response. This richer representation captures more structural information than the scalar objective alone, improving predictive accuracy and efficiency. The surrogate is used iteratively to infer optimal parameter values and to adaptively select new simulation points, balancing exploration of the parameter space with exploitation of current optima. A key advantage of the approach is that the trained surrogate can be reused for new specimens, progressively reducing the number of simulations required for parameter identification. The methodology is demonstrated through a case study on the Gurson–Tvergaard–Needleman damage model, applied to MS1500 steel specimens exposed to hydrogen charging at different concentrations. To ensure that the Multi-task Gaussian Process effectively represents the simulated curves, the force–displacement data were pre-processed to exclude regions minimally influenced by hydrogen for the concentrations investigated, such as the elastic regime. The proposed approach demonstrates its effectiveness by allowing the identification of parameter values through a limited number of iterations. The results confirm the suitability of the GTN model for describing hydrogen embrittlement and suggest that the proposed methodology can be potentially extended not only to different materials, but also to other constitutive models whose parameter identification entails significant computational cost.