On-the-fly construction of surrogate constitutive models for concurrent multiscale mechanical analysis through probabilistic machine learning

• An active learning framework is proposed for accelerating concurrent multiscale (FE2) analysis. Gaussian Process (GP) surrogates are constructed online without the need offline sampling. Data collected from a small number of full-order anchor models weakly associated with macroscopic integration points. Greedy sampling based on predictive variance GP used to minimize full model computations. Concurrent finite element analysis (FE 2 ) powerful approach high-fidelity modeling materials which suitable constitutive not available. However, extreme computational effort computing nested micromodel at every point makes FE prohibitive most practical applications. Constructing surrogate able efficiently compute microscopic response therefore promising in enabling modeling. This work presents reduction adaptively constructing statistical learning. The micromodels replaced by machine Processes (GP). data collection bypassed training coming set fully-solved that undergo same strain history as their Bayesian formalism inherent provides natural tool uncertainty estimation through new observations or inclusion triggered. manifold few micromechanical evaluations possible enhancing gradient information and solution scheme made robust greedy selection embedded within conventional loop nonlinear sensitivity parameters studied tapered bar example plasticity further demonstrated elastoplastic plate multiple cutouts crack growth mixed-mode bending. Although handle non-monotonic paths its current form, found be reducing cost , significant efficiency gains being obtained resorting training.