  Personalization of cardiac models involves the optimization of organ tissue
properties that vary spatially over the non-Euclidean geometry model of the
heart. To represent the high-dimensional (HD) unknown of tissue properties,
most existing works rely on a low-dimensional (LD) partitioning of the
geometrical model. While this exploits the geometry of the heart, it is of
limited expressiveness to allow partitioning that is small enough for effective
optimization. Recently, a variational auto-encoder (VAE) was utilized as a more
expressive generative model to embed the HD optimization into the LD latent
space. Its Euclidean nature, however, neglects the rich geometrical information
in the heart. In this paper, we present a novel graph convolutional VAE to
allow generative modeling of non-Euclidean data, and utilize it to embed
Bayesian optimization of large graphs into a small latent space. This approach
bridges the gap of previous works by introducing an expressive generative model
that is able to incorporate the knowledge of spatial proximity and hierarchical
compositionality of the underlying geometry. It further allows transferring of
the learned features across different geometries, which was not possible with a
regular VAE. We demonstrate these benefits of the presented method in synthetic
and real data experiments of estimating tissue excitability in a cardiac
electrophysiological model.
