  This paper introduces a framework designed to accurately predict piecewise
linear mappings of arbitrary meshes via a neural network, enabling training and
evaluating over heterogeneous collections of meshes that do not share a
triangulation, as well as producing highly detail-preserving maps whose
accuracy exceeds current state of the art. The framework is based on reducing
the neural aspect to a prediction of a matrix for a single given point,
conditioned on a global shape descriptor. The field of matrices is then
projected onto the tangent bundle of the given mesh, and used as candidate
jacobians for the predicted map. The map is computed by a standard Poisson
solve, implemented as a differentiable layer with cached pre-factorization for
efficient training. This construction is agnostic to the triangulation of the
input, thereby enabling applications on datasets with varying triangulations.
At the same time, by operating in the intrinsic gradient domain of each
individual mesh, it allows the framework to predict highly-accurate mappings.
We validate these properties by conducting experiments over a broad range of
scenarios, from semantic ones such as morphing, registration, and deformation
transfer, to optimization-based ones, such as emulating elastic deformations
and contact correction, as well as being the first work, to our knowledge, to
tackle the task of learning to compute UV parameterizations of arbitrary
meshes. The results exhibit the high accuracy of the method as well as its
versatility, as it is readily applied to the above scenarios without any
changes to the framework.
