  Convolutional neural networks (ConvNets) have demonstrated an exceptional
capacity to discern visual patterns from digital images and signals.
Unfortunately, such powerful ConvNets do not generalize well to
arbitrary-shaped manifolds, where data representation does not fit into a
tensor-like grid. Hence, many fields of science and engineering, where data
points possess some manifold structure, cannot enjoy the full benefits of the
recent advances in ConvNets. The aneurysm wall stress estimation problem
introduced in this paper is one of many such problems. The problem is
well-known to be of a paramount clinical importance, but yet, traditional
ConvNets cannot be applied due to the manifold structure of the data, neither
does the state-of-the-art geometric ConvNets perform well. Motivated by this,
we propose a new geometric ConvNet method named ZerNet, which builds upon our
novel mathematical generalization of convolution and pooling operations on
manifolds. Our study shows that the ZerNet outperforms the other
state-of-the-art geometric ConvNets in terms of accuracy.
