Learning Trajectories of Hamiltonian Systems with Neural Networks

Katsiaryna Haitsiukevich; Alexander Ilin

doi:10.1007/978-3-031-15919-0_47

Learning Trajectories of Hamiltonian Systems with Neural Networks

Katsiaryna Haitsiukevich, Alexander Ilin

Research output: Chapter in Book/Report/Conference proceeding › Conference article in proceedings › Scientific › peer-review

1 Citation (Scopus)

53 Downloads (Pure)

Abstract

Modeling of conservative systems with neural networks is an area of active research. A popular approach is to use Hamiltonian neural networks (HNNs) which rely on the assumptions that a conservative system is described with Hamilton's equations of motion. Many recent works focus on improving the integration schemes used when training HNNs. In this work, we propose to enhance HNNs with an estimation of a continuous-time trajectory of the modeled system using an additional neural network, called a deep hidden physics model in the literature. We demonstrate that the proposed integration scheme works well for HNNs, especially with low sampling rates, noisy and irregular observations.

Original language	English
Title of host publication	Artificial Neural Networks and Machine Learning – ICANN 2022
Editors	Elias Pimenidis, Mehmet Aydin, Plamen Angelov, Chrisina Jayne, Antonios Papaleonidas
Place of Publication	Bristol, UK
Publisher	Springer
Pages	562–573
Number of pages	12
ISBN (Electronic)	978-3-031-15919-0
ISBN (Print)	978-3-031-15918-3
DOIs	https://doi.org/10.1007/978-3-031-15919-0_47
Publication status	Published - 7 Sept 2022
MoE publication type	A4 Conference publication
Event	International Conference on Artificial Neural Networks - University of the West of England (UWE Bristol), Bristol, United Kingdom Duration: 6 Sept 2022 → 9 Sept 2022 https://e-nns.org/icann2022/

Publication series

Name	Lecture Notes in Computer Science
Publisher	Springer
Volume	13529
ISSN (Print)	0302-9743

Conference

Conference	International Conference on Artificial Neural Networks
Abbreviated title	ICANN
Country/Territory	United Kingdom
City	Bristol
Period	06/09/2022 → 09/09/2022
Internet address	https://e-nns.org/icann2022/

Keywords

Conservative systems
Deep Hidden Physics Models
Dynamical systems
Hamiltonian Neural Networks
Physics-Informed Neural Networks

Access to Document

10.1007/978-3-031-15919-0_47

SCI_Haitsiukevich_etal_ICANN_2022Accepted author manuscript, 379 KB

Cite this

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title = "Learning Trajectories of Hamiltonian Systems with Neural Networks",

abstract = "Modeling of conservative systems with neural networks is an area of active research. A popular approach is to use Hamiltonian neural networks (HNNs) which rely on the assumptions that a conservative system is described with Hamilton's equations of motion. Many recent works focus on improving the integration schemes used when training HNNs. In this work, we propose to enhance HNNs with an estimation of a continuous-time trajectory of the modeled system using an additional neural network, called a deep hidden physics model in the literature. We demonstrate that the proposed integration scheme works well for HNNs, especially with low sampling rates, noisy and irregular observations.",

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author = "Katsiaryna Haitsiukevich and Alexander Ilin",

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booktitle = "Artificial Neural Networks and Machine Learning – ICANN 2022",

address = "Germany",

note = "International Conference on Artificial Neural Networks, ICANN ; Conference date: 06-09-2022 Through 09-09-2022",

url = "https://e-nns.org/icann2022/",

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Haitsiukevich, K & Ilin, A 2022, Learning Trajectories of Hamiltonian Systems with Neural Networks. in E Pimenidis, M Aydin, P Angelov, C Jayne & A Papaleonidas (eds), Artificial Neural Networks and Machine Learning – ICANN 2022. Lecture Notes in Computer Science, vol. 13529, Springer, Bristol, UK, pp. 562–573, International Conference on Artificial Neural Networks, Bristol, United Kingdom, 06/09/2022. https://doi.org/10.1007/978-3-031-15919-0_47

Learning Trajectories of Hamiltonian Systems with Neural Networks. / Haitsiukevich, Katsiaryna; Ilin, Alexander.
Artificial Neural Networks and Machine Learning – ICANN 2022. ed. / Elias Pimenidis; Mehmet Aydin; Plamen Angelov; Chrisina Jayne; Antonios Papaleonidas. Bristol, UK: Springer, 2022. p. 562–573 (Lecture Notes in Computer Science; Vol. 13529).

Research output: Chapter in Book/Report/Conference proceeding › Conference article in proceedings › Scientific › peer-review

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Learning Trajectories of Hamiltonian Systems with Neural Networks

Abstract

Publication series

Conference

Keywords

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-: Finnish Center for Artificial Intelligence

Science-IT

Cite this

Learning Trajectories of Hamiltonian Systems with Neural Networks

Abstract

Publication series

Conference

Keywords

Access to Document

Other files and links

Fingerprint

Projects

-: Finnish Center for Artificial Intelligence

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Science-IT

Cite this