Journal of Computational Science, volume 53, pages 101345
Partial differential equations discovery with EPDE framework: Application for real and synthetic data [Formula presented]
Publication type: Journal Article
Publication date: 2021-07-01
Journal:
Journal of Computational Science
Quartile SCImago
Q1
Quartile WOS
Q2
Impact factor: 3.3
ISSN: 18777503
Theoretical Computer Science
General Computer Science
Modeling and Simulation
Abstract
• Framework for partial differential discovery is described. • Evolutionary algorithm works with sparse regression to achieve concise PDE model. • Neural network vs. finite-difference approach considered. Data-driven methods provide model creation tools for systems where the application of conventional analytical methods is restrained. The proposed method involves the data-driven derivation of a partial differential equation (PDE) for process dynamics, helping process simulation and study. The paper describes the methods that are used within the EPDE (Evolutionary Partial Differential Equations) partial differential equation discovery framework [1] . The framework involves a combination of evolutionary algorithms and sparse regression. Such an approach is versatile compared to other commonly used data-driven partial differential derivation methods by making fewer assumptions about the resulting equation. This paper highlights the algorithm features that allow data processing with noise, which is similar to the algorithm's real-world applications. This paper is an extended version of the ICCS-2020 conference paper [2] .
Citations by journals
|
1
2
|
|
|
Procedia Computer Science
|
Procedia Computer Science
2 publications, 11.76%
|
|
Processes
|
Processes
2 publications, 11.76%
|
|
Communications in Computer and Information Science
|
Communications in Computer and Information Science
1 publication, 5.88%
|
|
Fractal and Fractional
|
Fractal and Fractional
1 publication, 5.88%
|
|
Mathematics
|
Mathematics
1 publication, 5.88%
|
|
Mechanical Systems and Signal Processing
|
Mechanical Systems and Signal Processing
1 publication, 5.88%
|
|
Journal of Computational Science
|
Journal of Computational Science
1 publication, 5.88%
|
|
Lecture Notes in Networks and Systems
|
Lecture Notes in Networks and Systems
1 publication, 5.88%
|
|
Moscow University Physics Bulletin (English Translation of Vestnik Moskovskogo Universiteta, Fizika)
|
Moscow University Physics Bulletin (English Translation of Vestnik Moskovskogo Universiteta, Fizika)
1 publication, 5.88%
|
|
Chaos, Solitons and Fractals
|
Chaos, Solitons and Fractals
1 publication, 5.88%
|
|
Physical Review Research
|
Physical Review Research
1 publication, 5.88%
|
|
Doklady Mathematics
|
Doklady Mathematics
1 publication, 5.88%
|
|
1
2
|
Citations by publishers
|
1
2
3
4
5
|
|
|
Elsevier
|
Elsevier
5 publications, 29.41%
|
|
Multidisciplinary Digital Publishing Institute (MDPI)
|
Multidisciplinary Digital Publishing Institute (MDPI)
4 publications, 23.53%
|
|
Springer Nature
|
Springer Nature
2 publications, 11.76%
|
|
Pleiades Publishing
|
Pleiades Publishing
2 publications, 11.76%
|
|
IEEE
|
IEEE
1 publication, 5.88%
|
|
American Physical Society (APS)
|
American Physical Society (APS)
1 publication, 5.88%
|
|
1
2
3
4
5
|
- We do not take into account publications that without a DOI.
- Statistics recalculated only for publications connected to researchers, organizations and labs registered on the platform.
- Statistics recalculated weekly.
{"yearsCitations":{"type":"bar","data":{"show":true,"labels":[2021,2022,2023,2024],"ids":[0,0,0,0],"codes":[0,0,0,0],"imageUrls":["","","",""],"datasets":[{"label":"Citations number","data":[2,4,8,3],"backgroundColor":["#3B82F6","#3B82F6","#3B82F6","#3B82F6"],"percentage":["11.76","23.53","47.06","17.65"],"barThickness":null}]},"options":{"indexAxis":"x","maintainAspectRatio":true,"scales":{"y":{"ticks":{"precision":0,"autoSkip":false,"font":{"family":"Montserrat"},"color":"#000000"}},"x":{"ticks":{"stepSize":1,"precision":0,"font":{"family":"Montserrat"},"color":"#000000"}}},"plugins":{"legend":{"position":"top","labels":{"font":{"family":"Montserrat"},"color":"#000000"}},"title":{"display":true,"text":"Citations per year","font":{"size":24,"family":"Montserrat","weight":600},"color":"#000000"}}}},"journals":{"type":"bar","data":{"show":true,"labels":["Procedia Computer Science","Processes","Communications in Computer and Information Science","Fractal and Fractional","Mathematics","Mechanical Systems and Signal Processing","Journal of Computational Science","Lecture Notes in Networks and Systems","Moscow University Physics Bulletin (English Translation of Vestnik Moskovskogo Universiteta, Fizika)","Chaos, Solitons and Fractals","Physical Review Research","Doklady Mathematics"],"ids":[14281,19796,9768,28802,9290,25162,21058,17269,3806,5975,26813,12175],"codes":[0,0,0,0,0,0,0,0,0,0,0,0],"imageUrls":["\/storage\/images\/resized\/GDnYOu1UpMMfMMRV6Aqle4H0YLLsraeD9IP9qScG_medium.webp","\/storage\/images\/resized\/MjH1ITP7lMYGxeqUZfkt2BnVLgjkk413jwBV97XX_medium.webp","\/storage\/images\/resized\/voXLqlsvTwv5p3iMQ8Dhs95nqB4AXOG7Taj7G4ra_medium.webp","\/storage\/images\/resized\/MjH1ITP7lMYGxeqUZfkt2BnVLgjkk413jwBV97XX_medium.webp","\/storage\/images\/resized\/MjH1ITP7lMYGxeqUZfkt2BnVLgjkk413jwBV97XX_medium.webp","\/storage\/images\/resized\/GDnYOu1UpMMfMMRV6Aqle4H0YLLsraeD9IP9qScG_medium.webp","\/storage\/images\/resized\/GDnYOu1UpMMfMMRV6Aqle4H0YLLsraeD9IP9qScG_medium.webp","\/storage\/images\/resized\/voXLqlsvTwv5p3iMQ8Dhs95nqB4AXOG7Taj7G4ra_medium.webp","\/storage\/images\/resized\/oZgeErrVFhuDksyqFURLvYS1wtVSBWczh001igGo_medium.webp","\/storage\/images\/resized\/GDnYOu1UpMMfMMRV6Aqle4H0YLLsraeD9IP9qScG_medium.webp","\/storage\/images\/resized\/nrK64iXHTzj43wMrfN1ZoUQ0vanswGzWPN45K3jA_medium.webp","\/storage\/images\/resized\/oZgeErrVFhuDksyqFURLvYS1wtVSBWczh001igGo_medium.webp"],"datasets":[{"label":"","data":[2,2,1,1,1,1,1,1,1,1,1,1],"backgroundColor":["#3B82F6","#3B82F6","#3B82F6","#3B82F6","#3B82F6","#3B82F6","#3B82F6","#3B82F6","#3B82F6","#3B82F6","#3B82F6","#3B82F6"],"percentage":[11.76,11.76,5.88,5.88,5.88,5.88,5.88,5.88,5.88,5.88,5.88,5.88],"barThickness":13}]},"options":{"indexAxis":"y","maintainAspectRatio":false,"scales":{"y":{"ticks":{"precision":0,"autoSkip":false,"font":{"family":"Montserrat"},"color":"#000000"}},"x":{"ticks":{"stepSize":null,"precision":0,"font":{"family":"Montserrat"},"color":"#000000"}}},"plugins":{"legend":{"position":"top","labels":{"font":{"family":"Montserrat"},"color":"#000000"}},"title":{"display":true,"text":"Journals","font":{"size":24,"family":"Montserrat","weight":600},"color":"#000000"}}}},"publishers":{"type":"bar","data":{"show":true,"labels":["Elsevier","Multidisciplinary Digital Publishing Institute (MDPI)","Springer Nature","Pleiades Publishing","IEEE","American Physical Society (APS)"],"ids":[17,202,8,101,6953,1539],"codes":[0,0,0,0,0,0],"imageUrls":["\/storage\/images\/resized\/GDnYOu1UpMMfMMRV6Aqle4H0YLLsraeD9IP9qScG_medium.webp","\/storage\/images\/resized\/MjH1ITP7lMYGxeqUZfkt2BnVLgjkk413jwBV97XX_medium.webp","\/storage\/images\/resized\/voXLqlsvTwv5p3iMQ8Dhs95nqB4AXOG7Taj7G4ra_medium.webp","\/storage\/images\/resized\/oZgeErrVFhuDksyqFURLvYS1wtVSBWczh001igGo_medium.webp","\/storage\/images\/resized\/6scCJegesojp2jubwY3uKCzTAmgsaH2GIFlg6Hfk_medium.webp","\/storage\/images\/resized\/nrK64iXHTzj43wMrfN1ZoUQ0vanswGzWPN45K3jA_medium.webp"],"datasets":[{"label":"","data":[5,4,2,2,1,1],"backgroundColor":["#3B82F6","#3B82F6","#3B82F6","#3B82F6","#3B82F6","#3B82F6"],"percentage":[29.41,23.53,11.76,11.76,5.88,5.88],"barThickness":13}]},"options":{"indexAxis":"y","maintainAspectRatio":false,"scales":{"y":{"ticks":{"precision":0,"autoSkip":false,"font":{"family":"Montserrat"},"color":"#000000"}},"x":{"ticks":{"stepSize":null,"precision":0,"font":{"family":"Montserrat"},"color":"#000000"}}},"plugins":{"legend":{"position":"top","labels":{"font":{"family":"Montserrat"},"color":"#000000"}},"title":{"display":true,"text":"Publishers","font":{"size":24,"family":"Montserrat","weight":600},"color":"#000000"}}}}}
Metrics
Cite this
GOST |
RIS |
BibTex
Cite this
GOST
Copy
Maslyaev M. et al. Partial differential equations discovery with EPDE framework: Application for real and synthetic data [Formula presented] // Journal of Computational Science. 2021. Vol. 53. p. 101345.
GOST all authors (up to 50)
Copy
Maslyaev M., Hvatov A., Kalyuzhnaya A. V., Kalyuzhnaya A. Partial differential equations discovery with EPDE framework: Application for real and synthetic data [Formula presented] // Journal of Computational Science. 2021. Vol. 53. p. 101345.
Cite this
RIS
Copy
TY - JOUR
DO - 10.1016/j.jocs.2021.101345
UR - https://doi.org/10.1016%2Fj.jocs.2021.101345
TI - Partial differential equations discovery with EPDE framework: Application for real and synthetic data [Formula presented]
T2 - Journal of Computational Science
AU - Maslyaev, Mikhail
AU - Hvatov, Alexander
AU - Kalyuzhnaya, Anna V
AU - Kalyuzhnaya, Anna
PY - 2021
DA - 2021/07/01 00:00:00
PB - Elsevier
SP - 101345
VL - 53
SN - 1877-7503
ER -
Cite this
BibTex
Copy
@article{2021_Maslyaev,
author = {Mikhail Maslyaev and Alexander Hvatov and Anna V Kalyuzhnaya and Anna Kalyuzhnaya},
title = {Partial differential equations discovery with EPDE framework: Application for real and synthetic data [Formula presented]},
journal = {Journal of Computational Science},
year = {2021},
volume = {53},
publisher = {Elsevier},
month = {jul},
url = {https://doi.org/10.1016%2Fj.jocs.2021.101345},
pages = {101345},
doi = {10.1016/j.jocs.2021.101345}
}