TY - GEN

T1 - Reconstruction and Identification of Dynamical Systems Based on Taylor Maps

AU - Golovkina, Anna

AU - Kozynchenko, Vladimir

AU - Kulabukhova, Nataliia

N1 - Conference code: 21

PY - 2021/9/10

Y1 - 2021/9/10

N2 - In the process of conducting various physical experiments, a certain set of data is accumulated. Processing and interpreting the simulation results is a fundamental task for analyzing the behaviour of the model, predicting its future actions, and managing the entire system. This paper provides an overview of the currently existing approaches to identification of dynamic systems models: white, gray and black boxes. Special attention is paid to methods based on neural networks. The article suggests a combined approach that allows both preserving a physical consistency of the model and using modern methods for learning from data. A polynomial neural network of a special architecture, approximating the general solution of the system of ordinary differential equations (ODEs) in the form of Taylor map is considered. This model can work in the case of a small amount of initial data, which is a problem when exploiting traditional machine learning methods, and neural networks in particular. The paper presents a new learning approach for PNN based on two steps: reconstructing an ODEs system based on a single trajectory, and identifying a general solution to initialize the weights of a neural network. Neural network representation allows using traditional learning algorithms for additional fine-turning the weights in line with new measured data. A toy example of a nonlinear deflector demonstrates the power and generalization ability of the proposed algorithm.

AB - In the process of conducting various physical experiments, a certain set of data is accumulated. Processing and interpreting the simulation results is a fundamental task for analyzing the behaviour of the model, predicting its future actions, and managing the entire system. This paper provides an overview of the currently existing approaches to identification of dynamic systems models: white, gray and black boxes. Special attention is paid to methods based on neural networks. The article suggests a combined approach that allows both preserving a physical consistency of the model and using modern methods for learning from data. A polynomial neural network of a special architecture, approximating the general solution of the system of ordinary differential equations (ODEs) in the form of Taylor map is considered. This model can work in the case of a small amount of initial data, which is a problem when exploiting traditional machine learning methods, and neural networks in particular. The paper presents a new learning approach for PNN based on two steps: reconstructing an ODEs system based on a single trajectory, and identifying a general solution to initialize the weights of a neural network. Neural network representation allows using traditional learning algorithms for additional fine-turning the weights in line with new measured data. A toy example of a nonlinear deflector demonstrates the power and generalization ability of the proposed algorithm.

KW - Polynomial neural networks

KW - Taylor mapping

KW - System identification

KW - Lie transformation

KW - dynamic systems

KW - Dynamic systems

UR - http://www.scopus.com/inward/record.url?scp=85115712845&partnerID=8YFLogxK

UR - https://www.mendeley.com/catalogue/4eab48c5-ccee-3d90-bc3a-a125616ec5fd/

U2 - 10.1007/978-3-030-87010-2_26

DO - 10.1007/978-3-030-87010-2_26

M3 - Conference contribution

SN - 978-3-030-87009-6

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 360

EP - 369

BT - Computational Science and Its Applications – ICCSA 2021 - 21st International Conference, Proceedings

A2 - Gervasi, Osvaldo

A2 - Murgante, Beniamino

A2 - Misra, Sanjay

A2 - Garau, Chiara

A2 - Blečić, Ivan

A2 - Taniar, David

A2 - Apduhan, Bernady O.

A2 - Rocha, Ana Maria

A2 - Tarantino, Eufemia

A2 - Torre, Carmelo Maria

PB - Springer Nature

Y2 - 13 September 2021 through 16 September 2021

ER -