Inferring Time-Dependent Distribution Functions from Kinematic Snapshots

Abstract

We propose a method for constructing the time-dependent phase space distribution function (DF) of a collisionless system from an isolated kinematic snapshot. In general, the problem of mapping a single snapshot to a time-dependent function is intractable. Here we assume a finite series representation of the DF, constructed from the spectrum of the system's Koopman operator. This reduces the original problem to one of mapping a kinematic snapshot to a discrete spectrum rather than to a time-dependent function. We implement this mapping with a convolutional neural network (CNN). The method is demonstrated on two example models: the quantum simple harmonic oscillator, and a self-gravitating isothermal plane. The latter system exhibits phase space spiral structure similar to that observed in Gaia Data Release 2.

arXiv comment14 pages, 11 figures

References in corpus (23)

• SciPy 1.0--Fundamental Algorithms for Scientific Computing in Python
• Array Programming with NumPy
• On Dynamic Mode Decomposition: Theory and Applications
• Deep learning for universal linear embeddings of nonlinear dynamics
• A dynamically young and perturbed Milky Way disk
• Gaia Data Release 2: Mapping the Milky Way disc kinematics
• Footprints of the Sagittarius dwarf galaxy in the $Gaia$ data set
• The GALAH survey and Gaia DR2: dissecting the stellar disc's phase space by age, action, chemistry and location
• Made-to-measure N-body systems
• Transient spirals as superposed instabilities
• Bending and Breathing Modes of the Galactic Disk
• The origin of the Gaia phase-plane spiral
• Emergence of the Gaia Phase Space Spirals from Bending Waves
• Dynamics for Galactic Archaeology
• Spontaneous generation of bending waves in isolated Milky Way-like discs
• Dissecting the Phase Space Snail Shell
• Did Sgr cause the vertical waves in the solar neighbourhood?
• Vertical Oscillations of Fluid and Stellar Disks
• Multi-Resolution Dynamic Mode Decomposition
• Eigenfunctions of Galactic Phase Space Spirals from Dynamic Mode Decomposition
• Spiral instabilities: Linear and nonlinear effects
• Dynamical inference from a kinematic snapshot: The force law in the Solar System
• Deep Potential: Recovering the gravitational potential from a snapshot of phase space

Cited by in corpus (1)

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