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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2411.00110 |
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| _version_ | 1866918105077252096 |
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| author | Diaz, Viviana Alejandra Salomone, Leandro Martin Zuccalli, Marcela |
| author_facet | Diaz, Viviana Alejandra Salomone, Leandro Martin Zuccalli, Marcela |
| contents | Lagrangian Neural Networks (LNNs) are a powerful tool for addressing physical systems, particularly those governed by conservation laws. LNNs can parametrize the Lagrangian of a system to predict trajectories with nearly conserved energy. These techniques have proven effective in unconstrained systems as well as those with holonomic constraints. In this work, we adapt LNN techniques to mechanical systems with nonholonomic constraints. We test our approach on some well-known examples with nonholonomic constraints, showing that incorporating these restrictions into the neural network's learning improves not only trajectory estimation accuracy but also ensures adherence to constraints and exhibits better energy behavior compared to the unconstrained counterpart. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_00110 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Lagrangian neural networks for nonholonomic mechanics Diaz, Viviana Alejandra Salomone, Leandro Martin Zuccalli, Marcela Machine Learning Disordered Systems and Neural Networks Emerging Technologies Neural and Evolutionary Computing 70F25, 68T07, 70H03 J.2.0; I.2.6; C.2.0 Lagrangian Neural Networks (LNNs) are a powerful tool for addressing physical systems, particularly those governed by conservation laws. LNNs can parametrize the Lagrangian of a system to predict trajectories with nearly conserved energy. These techniques have proven effective in unconstrained systems as well as those with holonomic constraints. In this work, we adapt LNN techniques to mechanical systems with nonholonomic constraints. We test our approach on some well-known examples with nonholonomic constraints, showing that incorporating these restrictions into the neural network's learning improves not only trajectory estimation accuracy but also ensures adherence to constraints and exhibits better energy behavior compared to the unconstrained counterpart. |
| title | Lagrangian neural networks for nonholonomic mechanics |
| topic | Machine Learning Disordered Systems and Neural Networks Emerging Technologies Neural and Evolutionary Computing 70F25, 68T07, 70H03 J.2.0; I.2.6; C.2.0 |
| url | https://arxiv.org/abs/2411.00110 |