论文标题
深度神经网络，用于打结B-Spline近似
A Deep Neural Network for Knot Placement in B-spline Approximation
论文作者
论文摘要
自动确定结数和位置是B型近似中的一个基本且具有挑战性的问题。在本文中，将结的放置抽象为从初始结到最佳结的映射。我们创新地引入了深层神经网络求解器，以近似映射。神经网络由几个子网组成。每个子网都设计为在固定结数的情况下近似最佳结位置。将所有子网组合在一起，以在某些给定的公差内找到最佳结（包括结数和结位置）。由于强大的近似能力以及在深度学习中发展的成熟宏观，因此提出的方法可以有效，有效地找到最佳的结数和结位置。证明了几个数值示例以显示我们方法的优越性。
Automatically determining knot number and positions is a fundamental and challenging problem in B-spline approximation. In this paper, the knot placement is abstracted as a mapping from initial knots to the optimal knots. We innovatively introduce a deep neural network solver to approximate the mapping. The neural network is composed of several subnetworks. Each subnetwork is designed to approximate the optimal knot positions in the case of fixed knot number. All the subnetworks are stacked together to find the optimal knots (including knot number and knot positions) within some given tolerance. Owing to the powerful approximation capabilities, as well as mature algorithms developed in deep learning, the proposed method can effectively and efficiently find the optimal knot number and knot positions. Several numerical examples are demonstrated to show the superiority of our method.
