Finding the optimal parameterization for fitting a given sequence of data points with a parametric curve is a challenging problem that is equivalent to solving a highly non-linear system of equations. In this work, we propose the use of a residual neural network to approximate the function that assigns to a sequence of data points a suitable parameterization for fitting a polynomial curve of a fixed degree. Our model takes as an input a small fixed number of data points and the generalization to arbitrary data sequences is obtained by performing multiple evaluations. We show that the approach compares favorably to classical methods in a number of numerical experiments that include the parameterization of polynomial as well as non-polynomial data.

寻找最佳参数化以使给定数据点序列与参数曲线拟合是一个具有挑战性的问题，它等效于求解高度非线性的方程组。在这项工作中，我们建议使用残差神经网络来近似将分配给数据点序列的函数进行适当的参数化，以拟合固定度的多项式曲线的函数。我们的模型将少量固定数量的数据点作为输入，并且通过执行多次评估可以获得对任意数据序列的概括。我们显示，该方法在包括数值多项式和非多项式数据的参数化在内的许多数值实验中均优于经典方法。