Differentiable Stochastic Halo Occupation Distribution with Galaxy Intrinsic Alignments

TL;DR

We introduce diffHOD-IA, a fully differentiable halo occupation distribution model with galaxy intrinsic alignments, enabling end-to-end gradient-based inference for weak lensing analyses.

Contribution

The paper presents a novel differentiable implementation of HOD with IA, extending galaxy modeling to include orientation-dependent statistics and enabling gradient-based inference.

Findings

Excellent agreement with halotools-IA in simulations.

Verified gradient accuracy via finite differences.

Applied in Hamiltonian Monte Carlo for IA parameter recovery.

Abstract

We present diffHOD-IA, a fully differentiable implementation of a halo occupation distribution (HOD) model that incorporates galaxy intrinsic alignments (IA). Motivated by the diffHOD framework, we create a new implementation that extends differentiable galaxy population modeling to include orientation-dependent statistics crucial for weak gravitational lensing analyses. Our implementation combines this HOD formulation with an IA model, enabling end-to-end automatic differentiation from HOD and IA parameters through to the galaxy field. We additionally extend this framework to differentiably model two-point correlation functions, including galaxy clustering and IA statistics. We validate diffHOD-IA against the reference halotools-IA implementation using the Bolshoi-Planck simulation, demonstrating excellent agreement across both one-point and two-point statistics. We verify the accuracy of gradients computed via automatic differentiation by comparison with finite-difference estimates for both HOD and IA parameters. We present science use cases leveraging gradients in the simulations to recover the IA parameters of a galaxy field representative of the TNG300 simulation. Finally, we apply diffHOD-IA in a Hamiltonian Monte Carlo analysis and compare its performance with halotools-IA and a neural-network-based emulator, IAEmu. Unlike emulator-based approaches for statistics, diffHOD-IA provides differentiability at the galaxy catalog level, enabling integration into field-level inference pipelines and extension to arbitrary summary statistics for next-generation weak-lensing analyses. Our code is publicly available.