aiqbench analysis
This research extends Hamiltonian and Lagrangian Neural Networks to dissipative systems with explicit time dependence, demonstrating their ability to learn underlying physical laws in damped oscillators. The study provides critical insights into how these models handle energy non-conservation, a key advancement for physics-informed machine learning applications.
Lagrangian and Hamiltonian Neural Networks With a Dissipative System
arXiv:2609.31988v1 Announce Type: new Abstract: We investigate the applicability of Lagrangian and Hamiltonian Neural Network models to a dissipative system that has explicit time dependence in its Lagrangian, Hamiltonian, and total energy. To do so we consider these neural network models for simulated systems of a harmonic one-dimensional, one-component oscillator with damping, as well as without damping for comparison. We find that both the Lagrangian and Hamiltonian approaches are able to predict the empirical physical behavior of the damped oscillator systems and to effectively ``learn'' to varying degrees the underlying Lagrangians and Hamiltonians, as has previously been shown to be the case with undamped oscillator systems. These investigations elucidate important properties of Lagrangian and Hamiltonian mechanics, including properties that are not manifest when considering systems without explicit time dependence.
Abstract:We investigate the applicability of Lagrangian and Hamiltonian Neural Network models to a dissipative system that has explicit time dependence in its Lagrangian, Hamiltonian, and total energy. To do so we consider these neural network models for simulated systems of a harmonic one-dimensional, one-component oscillator with damping, as well as without damping for comparison. We find that both the Lagrangian and Hamiltonian approaches are able to predict the empirical physical behavior of the damped oscillator systems and to effectively ``learn'' to varying degrees the underlying Lagrangians and Hamiltonians, as has previously been shown to be the case with undamped oscillator systems. These investigations elucidate important properties of Lagrangian and Hamiltonian mechanics, including properties that are not manifest when considering systems without explicit time dependence.
14 Pages, 7 Figures, 2 Tables, in review. Comments welcome
Machine Learning (cs.LG); Classical Physics (physics.class-ph)
arXiv:2609.31988 [cs.LG]
(or arXiv:2609.31988v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2609.31988 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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Full text under the publisher's open licence · 231 words
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