Bayesian-EUCLID: Discovering hyperelastic material laws with uncertainties

Within the scope of our recent approach for Efficient Unsupervised Constitutive Law Identification and Discovery (EUCLID), we propose an unsupervised Bayesian learning framework discovery parsimonious interpretable constitutive laws with quantifiable uncertainties. As in deterministic EUCLID, do not resort to stress data, but only realistically measurable full-field displacement global reaction force data; as opposed calibration a priori assumed model, start model ansatz based on large catalog candidate functional features; leverage domain knowledge by including features existing, both physics-based phenomenological, models. In new Bayesian-EUCLID approach, use hierarchical sparsity-promoting priors Monte Carlo sampling efficiently solve selection task discover physically consistent equations form multivariate multi-modal probabilistic distributions. We demonstrate validate ability accurately recover isotropic anisotropic hyperelastic models like Neo-Hookean, Isihara, Gent–Thomas, Arruda–Boyce, Ogden, Holzapfel elastostatics elastodynamics. The discovered are reliable under epistemic uncertainties — i.e. true – aleatoric which arise from noise field automatically estimated model.