Generative Hyperelasticity with Physics-Informed Probabilistic Diffusion Fields

TL;DR

This paper introduces a probabilistic, generative modeling approach for hyperelastic materials that captures complex behaviors, heterogeneity, and uncertainty using neural ordinary equations and diffusion models, validated on biological tissues.

Contribution

It combines neural ODEs with diffusion models to generate plausible, spatially heterogeneous strain energy functions, incorporating uncertainty in data-driven hyperelasticity modeling.

Findings

Successfully models complex biological tissue behavior.

Generates spatially heterogeneous material properties.

Enhances predictive accuracy with uncertainty quantification.

Abstract

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