Lagrangian neural ODEs: Measuring the existence of a Lagrangian with Helmholtz metrics
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866914145613381632 |
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| author | Wolf, Luca Buck, Tobias Schaefer, Bjoern Malte |
| author_facet | Wolf, Luca Buck, Tobias Schaefer, Bjoern Malte |
| contents | Neural ODEs are a widely used, powerful machine learning technique in particular for physics. However, not every solution is physical in that it is an Euler-Lagrange equation. We present Helmholtz metrics to quantify this resemblance for a given ODE and demonstrate their capabilities on several fundamental systems with noise. We combine them with a second order neural ODE to form a Lagrangian neural ODE, which allows to learn Euler-Lagrange equations in a direct fashion and with zero additional inference cost. We demonstrate that, using only positional data, they can distinguish Lagrangian and non-Lagrangian systems and improve the neural ODE solutions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_06367 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Lagrangian neural ODEs: Measuring the existence of a Lagrangian with Helmholtz metrics Wolf, Luca Buck, Tobias Schaefer, Bjoern Malte Machine Learning Dynamical Systems Computational Physics Data Analysis, Statistics and Probability Neural ODEs are a widely used, powerful machine learning technique in particular for physics. However, not every solution is physical in that it is an Euler-Lagrange equation. We present Helmholtz metrics to quantify this resemblance for a given ODE and demonstrate their capabilities on several fundamental systems with noise. We combine them with a second order neural ODE to form a Lagrangian neural ODE, which allows to learn Euler-Lagrange equations in a direct fashion and with zero additional inference cost. We demonstrate that, using only positional data, they can distinguish Lagrangian and non-Lagrangian systems and improve the neural ODE solutions. |
| title | Lagrangian neural ODEs: Measuring the existence of a Lagrangian with Helmholtz metrics |
| topic | Machine Learning Dynamical Systems Computational Physics Data Analysis, Statistics and Probability |
| url | https://arxiv.org/abs/2510.06367 |