Uncovering differential equations from data with hidden variables

Agustín Somacal, Yamila Barrera, Leonardo Boechi, Matthieu Jonckheere, Vincent Lefieux, Dominique Picard, and Ezequiel Smucler
Phys. Rev. E 105, 054209 – Published 20 May 2022

Abstract

SINDy is a method for learning system of differential equations from data by solving a sparse linear regression optimization problem [Brunton, Proctor, and Kutz, Proc. Natl. Acad. Sci. USA 113, 3932 (2016)]. In this article, we propose an extension of the SINDy method that learns systems of differential equations in cases where some of the variables are not observed. Our extension is based on regressing a higher order time derivative of a target variable onto a dictionary of functions that includes lower order time derivatives of the target variable. We evaluate our method by measuring the prediction accuracy of the learned dynamical systems on synthetic data and on a real data set of temperature time series provided by the Réseau de Transport d'Électricité. Our method provides high quality short-term forecasts and it is orders of magnitude faster than competing methods for learning differential equations with latent variables.

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  • Received 3 June 2021
  • Accepted 12 April 2022

DOI:https://doi.org/10.1103/PhysRevE.105.054209

©2022 American Physical Society

Physics Subject Headings (PhySH)

Nonlinear Dynamics

Authors & Affiliations

Agustín Somacal* and Yamila Barrera

  • Aristas S.R.L., Dorrego 1940, Torre A, 2do Piso, dpto. N (1425), Ciudad Autónoma de Buenos Aires, Argentina

Leonardo Boechi and Matthieu Jonckheere§

  • Instituto de Calculo-CONICET, Intendente Güiraldes 2160, Ciudad Universitaria, Pabellón II, 2do. piso, (C1428EGA), Buenos Aires, Argentina

Vincent Lefieux

  • Réseau de Transport d'Electricité (RTE), 92060 Paris, France

Dominique Picard

  • Université de Paris, LPSM, UFR Mathematiques Batiment Sophie Germain, 75013 Paris, France

Ezequiel Smucler#

  • Universidad Torcuato Di Tella, Av. Figueroa Alcorta 7350 (C1428BCW) Sáenz Valiente 1010 (C1428BIJ) Ciudad de Buenos Aires, Argentina and Aristas S.R.L., Dorrego 1940, Torre A, 2do Piso, dpto. N (1425), Ciudad Autónoma de Buenos Aires, Argentina

  • *a.somacal@aristas.com.ar
  • y.barrera@aristas.com.ar
  • lboechi@ic.fcen.uba.ar
  • §mjonckhe@dm.uba.ar
  • vincent.lefieux@rte-france.com
  • picard@math.univ-paris-diderot.fr
  • #e.smucler@aristas.com.ar

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Issue

Vol. 105, Iss. 5 — May 2022

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