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Dynamical Modelling of Galactic Kinematics using Neural Networks

David A. Simon, Michele Cappellari, Shude Mao, Jiani Chu, Dandan Xu

TL;DR

The paper tackles the gap between traditional dynamical modelling assumptions and real galaxies by using Jeans Anisotropic Modelling (JAM) to generate training data from $Sérsic$ photometry and trains a neural network to predict JAM-consistent kinematics from photometry. Training data are produced under physical constraints such as $β_z \le 0.7 ε_{\rm intr}$ and sampled on a $64\times64$ grid, enabling a CNN+MLP pipeline to map photometry to the JAM $V_{\rm RMS}$ predictions. The resulting model achieves $<1\%$ pixel-level accuracy and $<3\%$ per-galaxy maximum error on $V_{\rm RMS}$ maps, with inference times around $0.3\mathrm{~ms}$ per run, constituting a ~300× speedup over previous JAM-based approaches. This approach demonstrates a viable path toward fast, scalable dynamical modelling and motivates extending training data to relax axisymmetry and velocity-ellipsoid assumptions, thereby improving realism in galactic dynamical analyses.

Abstract

The advent of integral field data has revolutionised the study of galaxy evolution. A key component of this is dynamical modelling methods which have allowed for crucial insights to be made from kinematic data. Despite this importance, most dynamical models make a number of key assumptions which do not hold for real galaxies. These include assumptions about the geometry (axisymmetry or triaxiality), the shape of the velocity ellipsoid, and the shape of the underlying stellar distribution. At the same time, machine learning methods are becoming increasingly powerful, with many applications appearing in astronomy. As a first step towards building new dynamical modelling methods with machine learning, it is important to understand the types of machine learning architectures that are best fit for dynamical modelling. To investigate this, we construct a training set of dynamical models of early-type galaxies using Jeans Anisotropic Modelling (JAM). We then train a neural network on this data using the parameters of JAM and mock photometry as the input. We are able to accurately model JAM galaxies with relatively simple machine learning architectures, leading to a significant speed increase over traditional JAM modelling.

Dynamical Modelling of Galactic Kinematics using Neural Networks

TL;DR

The paper tackles the gap between traditional dynamical modelling assumptions and real galaxies by using Jeans Anisotropic Modelling (JAM) to generate training data from photometry and trains a neural network to predict JAM-consistent kinematics from photometry. Training data are produced under physical constraints such as and sampled on a grid, enabling a CNN+MLP pipeline to map photometry to the JAM predictions. The resulting model achieves pixel-level accuracy and per-galaxy maximum error on maps, with inference times around per run, constituting a ~300× speedup over previous JAM-based approaches. This approach demonstrates a viable path toward fast, scalable dynamical modelling and motivates extending training data to relax axisymmetry and velocity-ellipsoid assumptions, thereby improving realism in galactic dynamical analyses.

Abstract

The advent of integral field data has revolutionised the study of galaxy evolution. A key component of this is dynamical modelling methods which have allowed for crucial insights to be made from kinematic data. Despite this importance, most dynamical models make a number of key assumptions which do not hold for real galaxies. These include assumptions about the geometry (axisymmetry or triaxiality), the shape of the velocity ellipsoid, and the shape of the underlying stellar distribution. At the same time, machine learning methods are becoming increasingly powerful, with many applications appearing in astronomy. As a first step towards building new dynamical modelling methods with machine learning, it is important to understand the types of machine learning architectures that are best fit for dynamical modelling. To investigate this, we construct a training set of dynamical models of early-type galaxies using Jeans Anisotropic Modelling (JAM). We then train a neural network on this data using the parameters of JAM and mock photometry as the input. We are able to accurately model JAM galaxies with relatively simple machine learning architectures, leading to a significant speed increase over traditional JAM modelling.
Paper Structure (9 sections, 3 figures, 1 table)

This paper contains 9 sections, 3 figures, 1 table.

Table of Contents

  1. Introduction
  2. Machine Learning Model
  3. Training Data
  4. Machine Learning Architecture
  5. Training
  6. Performance
  7. Accuracy
  8. Speed
  9. Conclusion

Figures (3)

  • Figure 1: A schematic of our neural network architecture. Note that due to axisymmetry, the output only features data from one quarter of the total field of view.
  • Figure 2: Random sample of test set galaxies and their performance. Top row: Mock photometry used for a test set data point with kinematic parameters $\beta$ and inclination. Center row: True JAM kinematics. Units are normalized. Bottom row: recovered ML prediction from the photometry and kinematic parameters. The maps are virtually indistinguishable by eye.
  • Figure 3: Left panel shows a histogram of the percent error of every pixel for every galaxy in the test set of galaxy kinematics. Almost all of the errors are less than 1 per-cent. Right panel shows a histogram of the maximum error for each galaxy in the test data. Here we see that the max error for almost every galaxy is less than 3 per-cent.