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 (DIC) techniques. In contrast to supervised learning based on stress labels, the problem of unsupervised discovery is solved by leveraging physical laws such as conservation of linear momentum in the bulk and at the loaded boundary of a test specimen. EUCLID enables discovering physically consistent models embodied by either:
parsimonious and interpretable mathematical expressions discovered through sparse regression of a large catalogue of candidate functions, or
ensemble of physics-informed neural networks with higher generalization capability at the cost of analytical interpretability.
We demonstrated several benchmarks on the discovery of hyperelastic and elastoplastic constitutive models without using any or limited stress data. Together with several collaborators across communities, we are currently exploring different applications of EUCLID — from soft biological tissues to metamaterials.