TY - JOUR
T1 - Bayesian-EUCLID
T2 - Discovering hyperelastic material laws with uncertainties
AU - Joshi, Akshay
AU - Thakolkaran, Prakash
AU - Zheng, Yiwen
AU - Escande, Maxime
AU - Flaschel, Moritz
AU - De Lorenzis, Laura
AU - Kumar, Siddhant
PY - 2022
Y1 - 2022
N2 - Within the scope of our recent approach for Efficient Unsupervised Constitutive Law Identification and Discovery (EUCLID), we propose an unsupervised Bayesian learning framework for discovery of parsimonious and interpretable constitutive laws with quantifiable uncertainties. As in deterministic EUCLID, we do not resort to stress data, but only to realistically measurable full-field displacement and global reaction force data; as opposed to calibration of an a priori assumed model, we start with a constitutive model ansatz based on a large catalog of candidate functional features; we leverage domain knowledge by including features based on existing, both physics-based and phenomenological, constitutive models. In the new Bayesian-EUCLID approach, we use a hierarchical Bayesian model with sparsity-promoting priors and Monte Carlo sampling to efficiently solve the parsimonious model selection task and discover physically consistent constitutive equations in the form of multivariate multi-modal probabilistic distributions. We demonstrate and validate the ability to accurately and efficiently recover isotropic and anisotropic hyperelastic models like the Neo-Hookean, Isihara, Gent–Thomas, Arruda–Boyce, Ogden, and Holzapfel models in both elastostatics and elastodynamics. The discovered constitutive models are reliable under both epistemic uncertainties — i.e. uncertainties on the true features of the constitutive catalog – and aleatoric uncertainties – which arise from the noise in the displacement field data, and are automatically estimated by the hierarchical Bayesian model.
AB - Within the scope of our recent approach for Efficient Unsupervised Constitutive Law Identification and Discovery (EUCLID), we propose an unsupervised Bayesian learning framework for discovery of parsimonious and interpretable constitutive laws with quantifiable uncertainties. As in deterministic EUCLID, we do not resort to stress data, but only to realistically measurable full-field displacement and global reaction force data; as opposed to calibration of an a priori assumed model, we start with a constitutive model ansatz based on a large catalog of candidate functional features; we leverage domain knowledge by including features based on existing, both physics-based and phenomenological, constitutive models. In the new Bayesian-EUCLID approach, we use a hierarchical Bayesian model with sparsity-promoting priors and Monte Carlo sampling to efficiently solve the parsimonious model selection task and discover physically consistent constitutive equations in the form of multivariate multi-modal probabilistic distributions. We demonstrate and validate the ability to accurately and efficiently recover isotropic and anisotropic hyperelastic models like the Neo-Hookean, Isihara, Gent–Thomas, Arruda–Boyce, Ogden, and Holzapfel models in both elastostatics and elastodynamics. The discovered constitutive models are reliable under both epistemic uncertainties — i.e. uncertainties on the true features of the constitutive catalog – and aleatoric uncertainties – which arise from the noise in the displacement field data, and are automatically estimated by the hierarchical Bayesian model.
KW - Bayesian learning
KW - Constitutive modeling
KW - Data-driven discovery
KW - Hyperelasticity
KW - Uncertainty quantification
KW - Unsupervised learning
UR - http://www.scopus.com/inward/record.url?scp=85133223374&partnerID=8YFLogxK
U2 - 10.1016/j.cma.2022.115225
DO - 10.1016/j.cma.2022.115225
M3 - Article
AN - SCOPUS:85133223374
SN - 0045-7825
VL - 398
JO - Computer Methods in Applied Mechanics and Engineering
JF - Computer Methods in Applied Mechanics and Engineering
M1 - 115225
ER -