Lagrangian neural networks for nonholonomic mechanics
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Abstract (arXiv)
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.
Key facts. Cited by 2 papers in the map (data through 14 Oct 2026). Builds on 7 of its 28 references that are in the map. First posted on arXiv 31 Oct 2024.
Builds on
7 of 28 references.
References · 7
- 2019Hamiltonian Neural Networkscited by 712
- 2020Lagrangian Neural Networkscited by 398
- 2019Deep Lagrangian Networks: Using Physics as Model Prior for Deep Learningcited by 212
- 2019Hamiltonian Generative Networkscited by 137
- 2020Simplifying Hamiltonian and Lagrangian Neural Networks via Explicit Constraintscited by 105
- 2020Benchmarking Energy-Conserving Neural Networks for Learning Dynamics from Datacited by 40
- 2020Hamiltonian neural networks for solving equations of motioncited by 33
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Citing papers per year: 2026: 2.
2 papers.