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.