  Surface matching usually provides significant deformations that can lead to
structural failure due to the lack of physical policy. In this context, partial
surface matching of non-linear deformable bodies is crucial in engineering to
govern structure deformations. In this article, we propose to formulate the
registration problem as an optimal control problem using an artificial neural
network where the unknown is the surface force distribution that applies to the
object and the resulting deformation computed using a hyper-elastic model. The
optimization problem is solved using an adjoint method where the hyper-elastic
problem is solved using the feed-forward neural network and the adjoint problem
is obtained through the backpropagation of the network. Our process improves
the computation speed by multiple orders of magnitude while providing
acceptable registration errors.
