Unsupervised discovery of constitutive laws

Abstract: The speaker and her group recently proposed a new approach for data-driven automated discovery of constitutive laws. The approach is unsupervised, i.e., it requires no stress data but only displacement and global force data, which are realistically available through mechanical testing and digital image correlation techniques; it delivers interpretable models, i.e., models that are embodied by parsimonious mathematical expressions discovered through sparse regression of a large catalogue of candidate functions; it is one-shot, i.e., discovery only needs one experiment — but can use more if available. The problem of unsupervised discovery is solved by enforcing equilibrium constraints in the bulk and at the loaded boundary of the domain. Sparsity of the solution is achieved by Lp regularization combined with thresholding, which calls for a non-linear optimization scheme. The ensuing fully automated algorithm leverages physics-based constraints for the automatic determination of the penalty parameter in the regularization term. We focus on isotropic hyperelasticity and, using numerically generated data including artificial noise, we demonstrate the ability of the approach to accurately discover five hyperelastic models of different complexity. We also show that, if a “true” feature is missing in the function library, the proposed approach is able to surrogate it in such a way that the actual response is still accurately predicted. We finally outline the first steps in the direction of extending the approach to more complex types of constitutive laws.

computational engineering, finance, and sciencemathematical softwarenumerical analysiscomputational physics

Audience: researchers in the topic

Australian Seminar on Computational Mathematics

Series comments: This seminar includes talks in computational mathematics with an Australian time zone friendly schedule. If you want to receive email alerts announcing new talks, you can subscribe to the mailing list in the seminar webpage www.mocao.org/cm-webinar or just add the seminar calendar to yours with the links below