Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Research › peer-review
Reconstruction of Ordinary Differential Equations from Irregularly Distributed Time-Series Data. / Golovkina, A.G. ; Kozynchenko, V.A. ; Kulabukhova, N.V. .
Proceedings of the 9th International Conference "Distributed Computing and Grid Technologies in Science and Education" (GRID'2021), Dubna, Russia, July 5-9, 2021 . ed. / Vladimir Korenkov; Andrey Nechaevskiy; Tatiana Zaikina. Vol. 3041 RWTH Aahen University, 2021. p. 342-347 (CEUR Workshop Proceedings; Vol. 3041).Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Research › peer-review
}
TY - GEN
T1 - Reconstruction of Ordinary Differential Equations from Irregularly Distributed Time-Series Data
AU - Golovkina, A.G.
AU - Kozynchenko, V.A.
AU - Kulabukhova, N.V.
N1 - Conference code: 9
PY - 2021/12/13
Y1 - 2021/12/13
N2 - The present paper aims to develop a reconstruction method for the right side of a system of ODEs in polynomial form from sparse and irregularly distributed time-series data. This method doesn’t require any additional knowledge about the system and has several steps. The scarcity of the data through the trajectory length is compensated by the artificially generated points using approximating trigonometrical polynomials. Then, we get uniformly spread data points with the step conditioned by the desired accuracy of derivatives approximation in ODEs. This let to further use conventional reconstruction algorithms described in the literature. We test the proposed method on time series data generated from known ODE models in a two-dimensional system. We quantify the accuracy of the reconstruction for the system of ODEs as a function of the amount of data used by the method. Further, we solve the reconstructed system of ODEs and compare the solution to the original time series data. The method developed and validated here can now be applied to large data sets for physical and biological systems for which there is no known system of ODEs.
AB - The present paper aims to develop a reconstruction method for the right side of a system of ODEs in polynomial form from sparse and irregularly distributed time-series data. This method doesn’t require any additional knowledge about the system and has several steps. The scarcity of the data through the trajectory length is compensated by the artificially generated points using approximating trigonometrical polynomials. Then, we get uniformly spread data points with the step conditioned by the desired accuracy of derivatives approximation in ODEs. This let to further use conventional reconstruction algorithms described in the literature. We test the proposed method on time series data generated from known ODE models in a two-dimensional system. We quantify the accuracy of the reconstruction for the system of ODEs as a function of the amount of data used by the method. Further, we solve the reconstructed system of ODEs and compare the solution to the original time series data. The method developed and validated here can now be applied to large data sets for physical and biological systems for which there is no known system of ODEs.
UR - http://ceur-ws.org/Vol-3041/342-347-paper-63.pdf
M3 - Conference contribution
VL - 3041
T3 - CEUR Workshop Proceedings
SP - 342
EP - 347
BT - Proceedings of the 9th International Conference "Distributed Computing and Grid Technologies in Science and Education" (GRID'2021), Dubna, Russia, July 5-9, 2021
A2 - Korenkov, Vladimir
A2 - Nechaevskiy, Andrey
A2 - Zaikina, Tatiana
PB - RWTH Aahen University
T2 - 9th International Conference "Distributed Computing and Grid Technologies in Science and Education", GRID 2021
Y2 - 5 July 2021 through 9 July 2021
ER -
ID: 87925616