Quadrature rule based discovery of dynamics by data-driven denoising

Yiqi Gu, Michael K. Ng*

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review


In this paper, we study the discovery of unknown dynamical systems with observed noisy data of the dynamics by neural networks. It is well-known that the performance of the neural network approach is degraded when observed data is noisy, even if the noise level is small. The main contribution of this paper is to propose a new network-based formulation for the dynamics discovery using numerical quadrature rules and to employ a self-supervision network to denoise observed data from the underlying dynamics. Our experimental results show that the performance of the proposed approach is better than that of existing dynamical discovery methods.

Original languageEnglish
Article number112102
Number of pages16
JournalJournal of Computational Physics
Early online date11 Apr 2023
Publication statusPublished - 1 Aug 2023

Scopus Subject Areas

  • Numerical Analysis
  • Modelling and Simulation
  • Physics and Astronomy (miscellaneous)
  • Physics and Astronomy(all)
  • Computer Science Applications
  • Computational Mathematics
  • Applied Mathematics

User-Defined Keywords

  • Deep learning
  • Denoising
  • Dynamical system
  • Neural network
  • Quadrature rule


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