  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.
