Classification of Magnetohydrodynamic Simulations using Wavelet Scattering Transforms

Abstract

The complex interplay of magnetohydrodynamics, gravity, and supersonic turbulence in the interstellar medium (ISM) introduces non-Gaussian structure that can complicate comparison between theory and observation. We show that the Wavelet Scattering Transform (WST), in combination with linear discriminant analysis (LDA), is sensitive to non-Gaussian structure in 2D ISM dust maps. WST-LDA classifies magnetohydrodynamic (MHD) turbulence simulations with up to a 97% true positive rate in our testbed of 8 simulations with varying sonic and Alfvénic Mach numbers. We present a sideby-side comparison with two other methods for non-Gaussian characterization, the Reduced Wavelet Scattering Transform (RWST) and the 3-Point Correlation Function (3PCF). We also demonstrate the 3D-WST-LDA and apply it to classification of density fields in position-position-velocity (PPV) space, where density correlations can be studied using velocity coherence as a proxy. WST-LDA is robust to common observational artifacts, such as striping and missing data, while also sensitive enough to extract the net magnetic field direction for sub-Alfvénic turbulent density fields. We include a brief analysis of the effect of point spread functions and image pixelization on 2D-WST-LDA applied to density fields, which informs the future goal of applying WST-LDA to 2D or 3D all-sky dust maps to extract hydrodynamic parameters of interest.

Equivariant Wavelets: Fast Rotation and Translation Invariant Wavelet Scattering Transforms

“…To support this, we repeated the experiment using a Lanczos interpolation, which better approximates an exact sinc interpolation, for both image resizing and rotation (Figure 5, bottom). Improving the interpolation leads to a qualitatively 18 Repeating the EqWS+LDA entries in the table using Lanczos interpolation for both image resizing and rotation leads to order ∼ 0.1% increased mean classification accuracy and no significant change in the stability result between columns. 19 Of course, an algorithm that does not depend on the images, having an accuracy of 10%, can be perfectly invariant to rotations of the test images.…”

“…As a final comparison, we apply LDA only to the set of coefficients containing S0 , S iso 1 (j 1 ), and S iso,1 2 (j 1 , j 2 ), the constant terms which we refer to in Figure 13 as R-RWST. 29 The accuracy here is not directly comparable to the results obtained for RWST on MHD simulations in [18]. While we use the cumulative sum along the line-of-sight images from the same dataset, the images are standard scaled (set to have mean zero and standard deviation one) here instead of max-min [0, 1] scaled as in [18].…”

“…All three cases have an accuracy of approximately 92.1 and differ by less than 0.1% (which is within 2σ for the error shown). 18 This level of equality is not present in even state-of-theart spherical CNNs, a subset of which are listed in the table for comparison. The best equality and overall accuracy was achieved by [46], showing a 0.4% decrease in accuracy between NR/NR and NR/R, which was a major improvement over the original spherical CNN paper [54] showing a 2.19% decrease.…”

“…To do this, we use the original definition of the wavelet scattering coefficients (p = 1) on which RWST is defined, and compare this to the ISO sum over indices of those same coefficients. 27 We consider a dataset of eight classes of magnetohydrodynamic (MHD) simulations characterized by two different dimensionless numbers on which RWST was previously benchmarked and which is of interest to the astrophysics community [18]. The ISO reduction (75%) outperforms RWST (69%) at the classification task while using Morlet wavelets which are not exactly rotationally invariant.…”

“…This includes computed EqWS coefficients, code for preprocessing each dataset, and code to reproduce all EqWS coefficients. A more ML friendly version of the MHD dataset introduced in [18] is available here. Also included are JUPYTER notebooks containing code to reproduce all figures in the text, some minimal working examples, and how to run these computations on a cluster.…”