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.

翻译：表面匹配通常会产生显著变形，由于缺乏物理约束，这可能导致结构失效。在此背景下，非线性可变形体的部分表面匹配对于控制工程中的结构变形至关重要。本文提出将配准问题表述为一个最优控制问题，采用人工神经网络，其中未知量是作用于物体的表面力分布，而通过超弹性模型计算所得的变形是该问题的解。优化问题通过伴随方法求解：利用前馈神经网络解决超弹性问题，并通过网络反向传播获得伴随问题。该方法在提供可接受的配准误差的同时，将计算速度提升了多个数量级。