Inferring Time-Dependent Distribution Functions from Kinematic Snapshots

TL;DR

This paper introduces a neural network-based method to infer the evolving phase space distribution of collisionless systems from a single snapshot, leveraging Koopman operator theory and demonstrated on quantum and astrophysical models.

Contribution

It presents a novel approach combining Koopman spectral analysis with CNNs to reconstruct time-dependent distributions from static data, applicable to complex dynamical systems.

Findings

Successfully applied to quantum harmonic oscillator

Reproduces phase space spiral structures in astrophysical models

Demonstrates potential for analyzing Gaia data

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.