Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Research › peer-review
Polynomial Neural Networks and Taylor Maps for Dynamical Systems Simulation and Learning. / Ivanov, Andrei ; Golovkina, Anna ; Iben, Uwe.
ECAI 2020 - 24th European Conference on Artificial Intelligence, including 10th Conference on Prestigious Applications of Artificial Intelligence, PAIS 2020 - Proceedings. ed. / Giuseppe De Giacomo; Alejandro Catala; Bistra Dilkina; Michela Milano; Senen Barro; Alberto Bugarin; Jerome Lang. IOS Press, 2020. p. 1230-1237 (Frontiers in Artificial Intelligence and Applications; Vol. 325).Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Research › peer-review
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TY - GEN
T1 - Polynomial Neural Networks and Taylor Maps for Dynamical Systems Simulation and Learning
AU - Ivanov, Andrei
AU - Golovkina, Anna
AU - Iben, Uwe
N1 - Conference code: 24
PY - 2020/8/24
Y1 - 2020/8/24
N2 - The paper discusses the connection of Taylor maps and polynomial neural networks (PNN) for numerical solving of the ordinary differential equations (ODEs). Having the system of ODEs, it is possible to calculate weights of PNN that simulates the dynamics of these equations. It is shown that proposed PNN architecture can provide better accuracy with less computational time in comparison with traditional numerical solvers. Moreover, neural network derived from the ODEs can be used for simulation of system dynamics with different initial conditions, but without training procedure. Besides, if the equations are unknown, the weights of the PNN can be fitted in a data-driven way. In the paper, we describe the connection of PNN with differential equations theoretically along with the examples for both dynamics simulation and learning with data.
AB - The paper discusses the connection of Taylor maps and polynomial neural networks (PNN) for numerical solving of the ordinary differential equations (ODEs). Having the system of ODEs, it is possible to calculate weights of PNN that simulates the dynamics of these equations. It is shown that proposed PNN architecture can provide better accuracy with less computational time in comparison with traditional numerical solvers. Moreover, neural network derived from the ODEs can be used for simulation of system dynamics with different initial conditions, but without training procedure. Besides, if the equations are unknown, the weights of the PNN can be fitted in a data-driven way. In the paper, we describe the connection of PNN with differential equations theoretically along with the examples for both dynamics simulation and learning with data.
UR - http://ebooks.iospress.nl/volume/ecai-2020-24th-european-conference-on-artificial-intelligence
UR - http://www.scopus.com/inward/record.url?scp=85091775761&partnerID=8YFLogxK
UR - https://www.mendeley.com/catalogue/829849c1-408a-31f3-b62b-c16814fb67bd/
U2 - 10.3233/FAIA200223
DO - 10.3233/FAIA200223
M3 - Conference contribution
SN - 978-1-64368-100-9
T3 - Frontiers in Artificial Intelligence and Applications
SP - 1230
EP - 1237
BT - ECAI 2020 - 24th European Conference on Artificial Intelligence, including 10th Conference on Prestigious Applications of Artificial Intelligence, PAIS 2020 - Proceedings
A2 - De Giacomo, Giuseppe
A2 - Catala, Alejandro
A2 - Dilkina, Bistra
A2 - Milano, Michela
A2 - Barro, Senen
A2 - Bugarin, Alberto
A2 - Lang, Jerome
PB - IOS Press
Y2 - 29 August 2020 through 8 September 2020
ER -
ID: 62094035