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The intrinsic alignments (IA) of galaxies, a key contaminant in weak lensing analyses, arise from correlations in galaxy shapes driven by tidal interactions and galaxy formation processes. Accurate IA modeling is essential for robust cosmological inference, but current approaches rely on perturbative methods that break down on nonlinear scales or on expensive simulations. We introduce IAEmu, a neural network-based emulator that predicts the galaxy position-position ( $\xi$), position-orientation ( $\omega$), and orientation-orientation ( $\eta$) correlation functions and their uncertainties using mock catalogs based on the halo occupation distribution (HOD) framework. Compared to simulations, IAEmu achieves ~3% average error for $\xi$and ~5% for $\omega$, while capturing the stochasticity of $\eta$without overfitting. The emulator provides both aleatoric and epistemic uncertainties, helping identify regions where predictions may be less reliable. We also demonstrate generalization to non-HOD alignment signals by fitting to IllustrisTNG hydrodynamical simulation data. As a fully differentiable neural network, IAEmu enables $ $10,000$$ speed-ups in mapping HOD parameters to correlation functions on GPUs, compared to CPU-based simulations. This acceleration facilitates inverse modeling via gradient-based sampling, making IAEmu a powerful surrogate model for galaxy bias and IA studies with direct applications to Stage IV weak lensing surveys. 

Halotools, originally published in 2017, is a Python package for cosmology and astrophysics designed to generate mock universes using existing catalogs of dark matter halos (Hearin et al., 2017). A theoretical basis of the library is the so-called halo model, which describes the matter distribution of dark matter as gravitationally self-bound clouds of dark matter particles that we call halos. Halotools is designed to take an underlying catalog of dark matter halos and populate them with galaxies using subhalo abundance, or halo occupation distribution (HOD) models, creating catalogs of simulated galaxies for use in research. This release (v0.9) adds functionality to align galaxies, injecting what are known as intrinsic alignments (IA) into these catalogs. As a result, these simulated galaxy catalogs can now be created with realistically complex correlations between galaxies, mimicking some effects seen in more expensive hydrodynamic simulations. 

We extend current models of the halo occupation distribution (HOD) to include a flexible, empirical framework for the forward modeling of the intrinsic alignment (IA) of galaxies. A primary goal of this work is to produce mock galaxy catalogs for the purpose of validating existing models and methods for the mitigation of IA in weak lensing measurements. This technique can also be used to produce new, simulation-based predictions for IA and galaxy clustering. Our model is probabilistically formulated, and rests upon the assumption that the orientations of galaxies exhibit a correlation with their host dark matter (sub)halo orientation or with their position within the halo. We examine the necessary components and phenomenology of such a model by considering the alignments between (sub)halos in a cosmological dark matter only simulation. We then validate this model for a realistic galaxy population in a set of simulations in the Illustris-TNG suite. We create an HOD mock with Illustris-like correlations using our method, constraining the associated IA model parameters, with the between our model’s correlations and those of Illustris matching as closely as 1.4 and 1.1 for orientation–position and orientation–orientation correlation functions, respectively. By modeling the misalignment between galaxies and their host halo, we show that the 3-dimensional two-point position and orientation correlation functions of simulated (sub)halos and galaxies can be accurately reproduced from quasi-linear scales down to . We also find evidence for environmental influence on IA within a halo. Our publicly-available software provides a key component enabling efficient determination of Bayesian posteriors on IA model parameters using observational measurements of galaxy-orientation correlation functions in the highly nonlinear regime.