A novel Bayesian strategy for the identification of spatially-varying parameters and model validation in inverse problems: an application to elastography

The present paper proposes a novel Bayesian, computational strategy in the context of model-based inverse problems in elastostatics. On one hand we attempt to provide probabilistic estimates of the material properties and their spatial variability that account for the various sources of uncertainty. On the other hand we attempt to address the question of model fidelity in relation to the experimental reality and particularly in the context of the material constitutive law adopted. This is especially important in biomedical settings when the inferred material properties will be used to make decisions/diagnoses. We propose an expanded parametrization that enables the quantification of model discrepancies in addition to the constitutive parameters. We propose scalable computational strategies for carrying out inference and learning tasks and demonstrate their effectiveness in numerical examples with noiseless and noisy synthetic data.