  Quantifying biomechanical properties of the human vasculature could deepen
our understanding of cardiovascular diseases. Standard nonlinear regression in
constitutive modeling requires considerable high-quality data and an explicit
form of the constitutive model as prior knowledge. By contrast, we propose a
novel approach that combines generative deep learning with Bayesian inference
to efficiently infer families of constitutive relationships in data-sparse
regimes. Inspired by the concept of functional priors, we develop a generative
adversarial network (GAN) that incorporates a neural operator as the generator
and a fully-connected neural network as the discriminator. The generator takes
a vector of noise conditioned on measurement data as input and yields the
predicted constitutive relationship, which is scrutinized by the discriminator
in the following step. We demonstrate that this framework can accurately
estimate means and standard deviations of the constitutive relationships of the
murine aorta using data collected either from model-generated synthetic data or
ex vivo experiments for mice with genetic deficiencies. In addition, the
framework learns priors of constitutive models without explicitly knowing their
functional form, providing a new model-agnostic approach to learning hidden
constitutive behaviors from data.
