  The heterogeneous micromechanical properties of biological tissues have
profound implications across diverse medical and engineering domains. However,
identifying full-field heterogeneous elastic properties of soft materials using
traditional engineering approaches is fundamentally challenging due to
difficulties in estimating local stress fields. Recently, there has been a
growing interest in using data-driven models to learn full-field mechanical
responses such as displacement and strain from experimental or synthetic data.
However, research studies on inferring full-field elastic properties of
materials, a more challenging problem, are scarce, particularly for large
deformation, hyperelastic materials. Here, we propose a physics-informed
machine learning approach to identify the elasticity map in nonlinear, large
deformation hyperelastic materials. We evaluate the prediction accuracies and
computational efficiency of physics-informed neural networks (PINNs) by
inferring the heterogeneous elasticity maps across three materials with
structural complexity that closely resemble real tissue patterns, such as brain
tissue and tricuspid valve tissue. We further applied our improved architecture
to three additional examples of breast cancer tissue and extended our analysis
to three hyperelastic constitutive models: Neo-Hookean, Mooney Rivlin, and
Gent. Our selected network architecture consistently produced highly accurate
estimations of heterogeneous elasticity maps, even when there was up to 10%
noise present in the training data.
