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Discrete Lagrangian Neural Networks with Automatic Symmetry Discovery

Published version
Peer-reviewed

Repository DOI


Type

Article

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Authors

Lishkova, Y 
Scherer, P 
Ridderbusch, S 
Liò, P 

Abstract

By one of the most fundamental principles in physics, a dynamical system will exhibit those motions which extremise an action functional. This leads to the formation of the Euler-Lagrange equations, which serve as a model of how the system will behave in time. If the dynamics exhibit additional symmetries, then the motion fulfils additional conservation laws, such as conservation of energy (time invariance), momentum (translation invariance), or angular momentum (rotational invariance). To learn a system representation, one could learn the discrete Euler-Lagrange equations, or alternatively, learn the discrete Lagrangian function Ld which defines them. Based on ideas from Lie group theory, we introduce a framework to learn a discrete Lagrangian along with its symmetry group from discrete observations of motions and, therefore, identify conserved quantities. The learning process does not restrict the form of the Lagrangian, does not require velocity or momentum observations or predictions and incorporates a cost term which safeguards against unwanted solutions and against potential numerical issues in forward simulations. The learnt discrete quantities are related to their continuous analogues using variational backward error analysis and numerical results demonstrate the improvement such models can have both qualitatively and quantitatively even in the presence of noise.

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Keywords

40 Engineering, 4007 Control Engineering, Mechatronics and Robotics, 4008 Electrical Engineering

Journal Title

IFAC-PapersOnLine

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Journal ISSN

2405-8963
2405-8963

Volume Title

56

Publisher

Elsevier

Version History

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2*
2024-05-28 12:36:39
Published version
2024-04-22 23:32:46
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