Generative Hyperelasticity with Physics-Informed Probabilistic Diffusion
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Vahidullah Tac Manuel K Rausch Ilias Bilionis Francisco Sahli Costabal Adrian Buganza Tepole
Many natural materials exhibit highly complex, nonlinear, anisotropic, and
heterogeneous mechanical properties. Recently, it has been demonstrated that
data-driven strain energy functions possess the flexibility to capture the
behavior of these complex materials with high accuracy while satisfying
physics-based constraints. However, most of these approaches disregard the
uncertainty in the estimates and the spatial heterogeneity of these materials.
In this work, we leverage recent advances in generative models to address these
issues. We use as building block neural ordinary equations (NODE) that -- by
construction -- create polyconvex strain energy functions, a key property of
realistic hyperelastic material models. We combine this approach with
probabilistic diffusion models to generate new samples of strain energy
functions. This technique allows us to sample a vector of Gaussian white noise
and translate it to NODE parameters thereby representing plausible strain
energy functions. We extend our approach to spatially correlated diffusion
resulting in heterogeneous material properties for arbitrary geometries. We
extensively test our method with synthetic and experimental data on biological
tissues and run finite element simulations with various degrees of spatial
heterogeneity. We believe this approach is a major step forward including
uncertainty in predictive, data-driven models of hyperelasticity