Saved in:
Bibliographic Details
Main Authors: Wolf, Luca, Buck, Tobias, Schaefer, Bjoern Malte
Format: Preprint
Published: 2025
Subjects:
Online Access:https://arxiv.org/abs/2510.06367
Tags: Add Tag
No Tags, Be the first to tag this record!
Table of 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.