Parameterization for polynomial curve approximation via residual deep neural networks

Felix Scholz, Bert Jüttler

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

Abstract

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.

Original languageEnglish
Article number101977
JournalComputer Aided Geometric Design
Volume85
DOIs
Publication statusPublished - 2021 Feb
Externally publishedYes

Keywords

  • Curve fitting
  • Deep learning
  • Parameterization

ASJC Scopus subject areas

  • Modelling and Simulation
  • Automotive Engineering
  • Aerospace Engineering
  • Computer Graphics and Computer-Aided Design

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