Constants of Motion for Conserved and Non-conserved Dynamics
This paper begins with a dynamical model that was obtained by applying a machine learning technique (FJet) to time-series data; this dynamical model is then analyzed with Lie symmetry techniques to obtain constants of motion. This analysis is performed on both the conserved and non-conserved cases of the 1D and 2D harmonic oscillators. For the 1D oscillator, constants are found in the cases where the system is underdamped, overdamped, and critically damped. The novel existence of such a constant for a non-conserved model is interpreted as a manifestation of the conservation of energy of the {\em total} system (i.e., oscillator plus dissipative environment). For the 2D oscillator, constants are found for the isotropic and anisotropic cases, including when the frequencies are incommensurate; it is also generalized to arbitrary dimensions. In addition, a constant is identified which generalizes angular momentum for all ratios of the frequencies. The approach presented here can produce {\em multiple} constants of motion from a {\em single}, generic data set.
Code (0)
등록된 구현이 없습니다.
Tasks
Time SeriesSimilar Papers 제목 키워드 기반
Constants of motion network
The beauty of physics is that there is usually a conserved quantity in an always-changing system, known as the constant of motion. Finding the constant of motion is important in understanding the dynamics of the system, …
Discovering conservation laws from data for control
Conserved quantities, i.e. constants of motion, are critical for characterizing many dynamical systems in science and engineering. These quantities are related to underlying symmetries and they provide fundamental knowle…
Symmetry Control Neural Networks
This paper continues the quest for designing the optimal physics bias for neural networks predicting the dynamics of systems when the underlying dynamics shall be inferred from the data directly. The description of physi…
Discovering Symmetry Invariants and Conserved Quantities by Interpreting Siamese Neural Networks
In this paper, we introduce interpretable Siamese Neural Networks (SNN) for similarity detection to the field of theoretical physics. More precisely, we apply SNNs to events in special relativity, the transformation of e…
Improving Simulations with Symmetry Control Neural Networks
The dynamics of physical systems is often constrained to lower dimensional sub-spaces due to the presence of conserved quantities. Here we propose a method to learn and exploit such symmetry constraints building upon Ham…