Measuring Galactic Dark Matter through Unsupervised Machine Learning

Buckley, Matthew R.; Lim, S.; Putney, Eric; Shih, David Q.

doi:10.48550/arxiv.2205.01129

Cited by 2 publications

(2 citation statements)

References 56 publications

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“…The most significant difference between these two approaches, in our view, is that by solving for the potential field, ( ) F x , one can place a positivity constraint on the underlying matter density (∇ 2 Φ 0) and can penalize overly complicated potentials (e.g., through L 2 weight regularization). In the final stages of the preparation of the present manuscript, Buckley et al (2022) published a related technique, which derives accelerations using a similar method to An et al (2021) and then calculates densities using Gauss' theorem.…”

Section: Discussionmentioning

confidence: 99%

Deep Potential: Recovering the Gravitational Potential from a Snapshot of Phase Space

Green

Ting

Kamdar

2023

ApJ

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One of the major goals of the field of Milky Way dynamics is to recover the gravitational potential field. Mapping the potential would allow us to determine the spatial distribution of matter—both baryonic and dark—throughout the galaxy. We present a novel method for determining the gravitational field from a snapshot of the phase-space positions of stars, based only on minimal physical assumptions, which makes use of recently developed tools from the field of deep learning. We first train a normalizing flow on a sample of observed six-dimensional phase-space coordinates of stars, obtaining a smooth, differentiable approximation of the distribution function. Using the collisionless Boltzmann equation, we then find the gravitational potential—represented by a feed-forward neural network—that renders this distribution function stationary. This method, which we term “Deep Potential,” is more flexible than previous parametric methods, which fit restricted classes of analytic models of the distribution function and potential to the data. We demonstrate Deep Potential on mock data sets and demonstrate its robustness under various nonideal conditions. Deep Potential is a promising approach to mapping the density of the Milky Way and other stellar systems, using rich data sets of stellar positions and kinematics now being provided by Gaia and ground-based spectroscopic surveys.

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Section: Discussionmentioning

confidence: 99%

Deep Potential: Recovering the Gravitational Potential from a Snapshot of Phase Space

Green

Ting

Kamdar

2023

ApJ

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“…The most significant difference between these two approaches, in our view, is that by solving for the potential field Φ ( x), one can place a positivity constraint on the underlying matter density (∇ 2 Φ ≥ 0) and can penalize overly complicated potentials (e.g., through L 2 weight regularization). In the final stages of the preparation of the present manuscript, Buckley et al (2022) published a related technique, which derives accelerations using a similar method to An et al ( 2021), and then calculates densities using Gauss' theorem.…”

Section: Discussionmentioning

confidence: 99%

Deep Potential: Recovering the gravitational potential from a snapshot of phase space

Green¹,

Ting²,

Kamdar³

2022

Preprint

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One of the major goals of the field of Milky Way dynamics is to recover the gravitational potential field. Mapping the potential would allow us to determine the spatial distribution of matter -both baryonic and dark -throughout the Galaxy. We present a novel method for determining the gravitational field from a snapshot of the phase-space positions of stars, based only on minimal physical assumptions, which makes use of recently developed tools from the field of deep learning. We first train a normalizing flow on a sample of observed six-dimensional phase-space coordinates of stars, obtaining a smooth, differentiable approximation of the distribution function. Using the Collisionless Boltzmann Equation, we then find the gravitational potential -represented by a feed-forward neural networkthat renders this distribution function stationary. This method, which we term "Deep Potential," is more flexible than previous parametric methods, which fit restricted classes of analytic models of the distribution function and potential to the data. We demonstrate Deep Potential on mock datasets, and demonstrate its robustness under various non-ideal conditions. Deep Potential is a promising approach to mapping the density of the Milky Way and other stellar systems, using rich datasets of stellar positions and kinematics now being provided by Gaia and ground-based spectroscopic surveys.

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Measuring Galactic Dark Matter through Unsupervised Machine Learning

Cited by 2 publications

References 56 publications

Deep Potential: Recovering the Gravitational Potential from a Snapshot of Phase Space

Deep Potential: Recovering the Gravitational Potential from a Snapshot of Phase Space

Deep Potential: Recovering the gravitational potential from a snapshot of phase space

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