Learning Galaxy Intrinsic Alignment Correlations

TL;DR

The paper tackles the challenge of modeling galaxy intrinsic alignments (IA), which contaminate weak-lensing signals, by building a deep learning emulator that maps a 7D HOD parameter vector to IA correlation functions $ξ(r)$, $ω(r)$, and $η(r)$ and their aleatoric uncertainties. It uses an encoder–decoder neural network with mean-variance estimation and Monte Carlo dropout, trained on IA-augmented halo catalogs generated with halotools, to produce fast, joint predictions across all three statistics. The results show $ξ(r)$ predictions reaching $\leq 10\%$ accuracy and strong correlation with ground truth (PCC$\approx$0.98 for $ξ$, 0.88 for $ω$, 0.65 for $η$), while $ω(r)$ and $η(r)$ remain noisier but empirically captured with calibrated uncertainties. This emulator dramatically accelerates IA modeling and enables efficient Monte Carlo inference for cosmology, with open-source code planned, thereby facilitating robust weak-lensing analyses and validation against larger simulations.

Abstract

The intrinsic alignments (IA) of galaxies, regarded as a contaminant in weak lensing analyses, represents the correlation of galaxy shapes due to gravitational tidal interactions and galaxy formation processes. As such, understanding IA is paramount for accurate cosmological inferences from weak lensing surveys; however, one limitation to our understanding and mitigation of IA is expensive simulation-based modeling. In this work, we present a deep learning approach to emulate galaxy position-position ($ξ$), position-orientation ($ω$), and orientation-orientation ($η$) correlation function measurements and uncertainties from halo occupation distribution-based mock galaxy catalogs. We find strong Pearson correlation values with the model across all three correlation functions and further predict aleatoric uncertainties through a mean-variance estimation training procedure. $ξ(r)$ predictions are generally accurate to $\leq10\%$. Our model also successfully captures the underlying signal of the noisier correlations $ω(r)$ and $η(r)$, although with a lower average accuracy. We find that the model performance is inhibited by the stochasticity of the data, and will benefit from correlations averaged over multiple data realizations. Our code will be made open source upon journal publication.

Figures (6)

• Figure 1: We generate uniform random values for the four occupation parameters, excluding $\log \mathrm{M_{min}}$. These values are based on a linear relationship with $\log \mathrm{M_{min}}$, serving as a central line. The range for random values extends $4\times\mathrm{RMSE}$ surrounding this line. To clarify the visualization, $\sigma_{\log(\mathrm{M})}$ is displayed separately from other mass variables. Each panel presents published data from Zheng_2007 as a solid line, while the dotted line illustrates the linear fit to $\log \mathrm{M_{min}}$, with the shaded area indicating the range for uniform random value selection for each parameter. Not shown here are the two IA parameters, $\mu_{\rm cen}$ and $\mu_{\rm sat}$, which both vary uniformly on the range $[-1,1]$ with no relation to these five occupation parameters.
• Figure 2: Model Pipeline. A logarithm factor is implied for all masses $M$. The HOD input model parameters are normalized before entering the 7-layer deep fully-connected encoder. The encoder expands the dimensionality of the input until the decoder stage, which features four 1D convolutional layers which learn the individual local correlations present in the output correlation functions, $\xi'$, $\omega'$, and $\eta'$. These are then re-scaled back to their original values. A detailed description of the encoder-decoder architecture is shown in Appendix \ref{['sec:AppendixB']}.
• Figure 3: Top: Plot of median errors with aleatoric and epistemic $1\sigma$ regions of the median predictions for position-position ($\xi(r)$), position-orientation ($\omega(r)$), and orientation-orientation ($\eta(r)$) correlation functions in the scaled domain. The 50% IQR is also shown in green. The results for a random sample of 100 test-set predictions are shown in the background, showcasing the variability of performance. Bottom: Mean fractional errors with aleatoric uncertainties for $\xi(r)$, $\omega(r)$, and $\eta(r)$. Ratios are computed with respect to the running mean using a window size of 3 for $\omega(r)$ and $\eta(r)$ due to their increased noise.
• Figure 4: Good performance examples on test set in rescaled domain. On the left panel one can see the small bias in $\xi(r)$ predictions at high $r$.
• Figure 5: Noisy data examples on test set in rescaled domain. $\xi(r)$ exhibits a small bump at low $r$ which is likely a noisy artifact. $\omega(r)$ and $\eta(r)$ are very noisy, but the model is able to capture the underlying signal as well as overall shape.