Dark Matter profiles of "in silico" galaxies: deep learning inference

TL;DR

The paper demonstrates that a steerable equivariant CNN (EquiCNN) can non-parametrically infer dark matter mass profiles from photometric SDSS-band images and HI data cubes in simulated galaxies from Illustris-TNG, outperforming a standard CNN. By training on 3D mock observations generated with SKIRT and MARTINI for $M_\star$ in $[10^{10},10^{12}] M_\\odot$ and $z=0$, the model recovers the DM mass enclosed in 20 radial bins with an average MSE of $\sim 0.013$, substantially below the training-baseline of $\sim 0.044$, and performs best near $2\times R_{SHM}$. The study includes thorough interpretability analyses, showing the combined importance of photometric and HI kinematic data and revealing that inner galactic regions carry most predictive power. While the results are compelling in the simulated, in silico setting, the authors discuss necessary steps for robust real-world application, including cross-simulation validation, handling domain shifts, and accommodating varied observational conditions. Overall, the work provides a proof-of-concept that adversarial-free, symmetry-aware deep learning can extract detailed DM profiles from multi-wavelength galaxy observations, potentially accelerating DM studies with upcoming surveys like LSST.

Abstract

Machine learning has the potential to improve the reconstruction of the dark matter profile of galaxies with respect to traditional methods, like rotation curves. We demonstrate on the simulation suite Illustris-TNG that a steerable equivariant convolutional neural network (CNN) is able to infer the dark matter profiles within and around individual galaxies from photometric and interferometric data, improving on a standard CNN. Within the in silico environment of the simulations, our architecture is able to capture the dark matter distribution within galaxies without a parametrization of the profile. We perform an interpretability analysis to understand the internal mechanisms of the trained model and the most important data features used to estimate the dark matter profiles. The equivariant CNN recovers the dark matter profile of galaxies within the stellar mass range $[10^{10} - 10^{12} ]$ $M_{\odot}$ with excellent precision and accuracy: the mean squared error is reduced by a factor of ~ 3 from its value under the training distribution, demonstrating that the network has learnt from the data features. While this holds within the controlled 'in silico' environment of the simulation, we argue that few additional steps are needed before this method can be reliably applied to galaxies in the real field observations.

Figures (12)

• Figure 1: Examples of simulated SDSS images of galaxies in the $g$ band produced with SKIRT.
• Figure 2: HI second momentum map produced with MARTINI for the same simulated galaxies as in Fig. \ref{['fig:sdss_examples']}.
• Figure 3: Schematic layout of our equivariant steerable CNN, EquiCNN. Our network has $C=8$ and $H=W=128$, 3 equivariant convolutional blocks, where we call the R2Conv layer, as defined in the library e2cnn, and in sequence a BatchNorm Layer, the ReLU layer, Dropout and MaxPooling. The Convolution block is followed by a GroupPooling, a Flatten layer and 5 Fully-Connected Layers.
• Figure 4: Training and validation loss behaviour for run 1 out 20 of the EquiCNN instances.
• Figure 5: Scatter plot of the logarithm of the EquiCNN estimated mass vs the logarithm of the real mass. Each panel correspond to the mass enclosed at a given radius as specified in the upper left corner. Each dot correspond to a test galaxy and its color represent the $\kappa$ value.