Learning discrete Lagrangians for variational PDEs from data and detection of travelling waves
C. Offen, S. Ober-Blöbaum, in: F. Nielsen, F. Barbaresco (Eds.), Geometric Science of Information, Springer, Cham., 2023, pp. 569–579.
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Nielsen, F;
Barbaresco, F
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Abstract
The article shows how to learn models of dynamical systems from data which are governed by an unknown variational PDE. Rather than employing reduction techniques, we learn a discrete field theory governed by a discrete Lagrangian density $L_d$ that is modelled as a neural network. Careful regularisation of the loss function for training $L_d$ is necessary to obtain a field theory that is suitable for numerical computations: we derive a regularisation term which optimises the solvability of the discrete Euler--Lagrange equations. Secondly, we develop a method to find solutions to machine learned discrete field theories which constitute travelling waves of the underlying continuous PDE.
Publishing Year
Proceedings Title
Geometric Science of Information
forms.conference.field.series_title_volume.label
Lecture Notes in Computer Science (LNCS)
Volume
14071
Page
569-579
Conference
GSI'23 6th International Conference on Geometric Science of Information
Conference Location
Saint-Malo, Palais du Grand Large, France
Conference Date
2023-08-30 – 2023-09-01
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Cite this
Offen C, Ober-Blöbaum S. Learning discrete Lagrangians for variational PDEs from data and detection of travelling waves. In: Nielsen F, Barbaresco F, eds. Geometric Science of Information. Vol 14071. Lecture Notes in Computer Science (LNCS). Springer, Cham.; 2023:569-579. doi:10.1007/978-3-031-38271-0_57
Offen, C., & Ober-Blöbaum, S. (2023). Learning discrete Lagrangians for variational PDEs from data and detection of travelling waves. In F. Nielsen & F. Barbaresco (Eds.), Geometric Science of Information (Vol. 14071, pp. 569–579). Springer, Cham. https://doi.org/10.1007/978-3-031-38271-0_57
@inproceedings{Offen_Ober-Blöbaum_2023, series={Lecture Notes in Computer Science (LNCS)}, title={Learning discrete Lagrangians for variational PDEs from data and detection of travelling waves}, volume={14071}, DOI={10.1007/978-3-031-38271-0_57}, booktitle={Geometric Science of Information}, publisher={Springer, Cham.}, author={Offen, Christian and Ober-Blöbaum, Sina}, editor={Nielsen, F and Barbaresco, F}, year={2023}, pages={569–579}, collection={Lecture Notes in Computer Science (LNCS)} }
Offen, Christian, and Sina Ober-Blöbaum. “Learning Discrete Lagrangians for Variational PDEs from Data and Detection of Travelling Waves.” In Geometric Science of Information, edited by F Nielsen and F Barbaresco, 14071:569–79. Lecture Notes in Computer Science (LNCS). Springer, Cham., 2023. https://doi.org/10.1007/978-3-031-38271-0_57.
C. Offen and S. Ober-Blöbaum, “Learning discrete Lagrangians for variational PDEs from data and detection of travelling waves,” in Geometric Science of Information, Saint-Malo, Palais du Grand Large, France, 2023, vol. 14071, pp. 569–579, doi: 10.1007/978-3-031-38271-0_57.
Offen, Christian, and Sina Ober-Blöbaum. “Learning Discrete Lagrangians for Variational PDEs from Data and Detection of Travelling Waves.” Geometric Science of Information, edited by F Nielsen and F Barbaresco, vol. 14071, Springer, Cham., 2023, pp. 569–79, doi:10.1007/978-3-031-38271-0_57.
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LDensityLearning.pdf
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Learning discrete Lagrangians for variational PDEs from data and detection of travelling waves
Description
The article shows how to learn models of dynamical systems
from data which are governed by an unknown variational PDE. Rather
than employing reduction techniques, we learn a discrete field theory
governed by a discrete Lagrangian density Ld that is modelled as a neural network. Careful regularisation of the loss function for training Ld is
necessary to obtain a field theory that is suitable for numerical computations: we derive a regularisation term which optimises the solvability of
the discrete Euler–Lagrange equations. Secondly, we develop a method to
find solutions to machine learned discrete field theories which constitute
travelling waves of the underlying continuous PDE.
Access Level
Open Access
Last Uploaded
2023-08-02T12:04:17Z
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