aiqbench analysis
This study compares how different machine learning architectures—specifically Deep Sets, MLPs, KANs, and GNNs—extract cosmological parameters from galaxy catalogs with varying inductive biases. The results demonstrate that graph neural networks significantly outperform set-based models by effectively encoding spatial relations, achieving lower error rates in inferring the matter density parameter $\Omega_m$. For AI researchers in scientific domains, this highlights the critical importance of architectural choice and input observables when designing models for complex physical inference tasks.
Inductive Biases in Field-Level Cosmological Inference from Galaxy Catalogs
arXiv:2609.09504v1 Announce Type: cross Abstract: We perform field-level likelihood-free inference of the matter density parameter $\Omega_m$ from simulated galaxy catalogs using machine learning models with differing inductive biases. Using hydrodynamic simulations from CAMELS, we examine how observable choice and architecture govern cosmological information extraction. We consider galaxy positions and line-of-sight peculiar velocities, separately and jointly, and compare permutation-invariant Deep Sets, implemented with either multilayer perceptrons (MLPs) or Kolmogorov-Arnold Networks (KANs), to graph neural networks (GNNs), which explicitly encode spatial relations. We test in-distribution and out-of-distribution (OOD) performance across simulations with different subgrid galaxy-formation prescriptions. Deep Sets infer $\Omega_m$ from velocities alone with mean relative errors of approximately $18\%$ in-distribution and $\sim25\%$ OOD, with KANs and MLPs achieving comparable performance. In contrast, the same set-based approach does not yield useful $\sigma_8$ predictions in either in-distribution or cross-suite tests. Adding positions does not improve Deep Sets, while GNNs infer $\Omega_m$ with mean relative errors of about $10\%$ in-distribution and $10$--$17\%$ OOD. These results indicate that peculiar velocities provide the dominant source of $\Omega_m$ information for set-based models in this setting, while spatial information is most effectively used by architectures that explicitly encode galaxy-galaxy relations. Because the velocity inputs are exact simulated peculiar velocities, applications to survey data will require validation under realistic velocity-measurement noise, selection effects, and survey geometry.
Abstract:We perform field-level likelihood-free inference of the matter density parameter $\Omega_m$ from simulated galaxy catalogs using machine learning models with differing inductive biases. Using hydrodynamic simulations from CAMELS, we examine how observable choice and architecture govern cosmological information extraction. We consider galaxy positions and line-of-sight peculiar velocities, separately and jointly, and compare permutation-invariant Deep Sets, implemented with either multilayer perceptrons (MLPs) or Kolmogorov-Arnold Networks (KANs), to graph neural networks (GNNs), which explicitly encode spatial relations. We test in-distribution and out-of-distribution (OOD) performance across simulations with different subgrid galaxy-formation prescriptions. Deep Sets infer $\Omega_m$ from velocities alone with mean relative errors of approximately $18\%$ in-distribution and $\sim25\%$ OOD, with KANs and MLPs achieving comparable performance. In contrast, the same set-based approach does not yield useful $\sigma_8$ predictions in either in-distribution or cross-suite tests. Adding positions does not improve Deep Sets, while GNNs infer $\Omega_m$ with mean relative errors of about $10\%$ in-distribution and $10$--$17\%$ OOD. These results indicate that peculiar velocities provide the dominant source of $\Omega_m$ information for set-based models in this setting, while spatial information is most effectively used by architectures that explicitly encode galaxy-galaxy relations. Because the velocity inputs are exact simulated peculiar velocities, applications to survey data will require validation under realistic velocity-measurement noise, selection effects, and survey geometry.
23 pages, 8 figures, 5 tables. Accepted for publication in The Astrophysical Journal
Cosmology and Nongalactic Astrophysics (astro-ph.CO); Machine Learning (cs.LG)
arXiv:2609.09504 [astro-ph.CO]
(or arXiv:2609.09504v1 [astro-ph.CO] for this version)
https://doi.org/10.48550/arXiv.2609.09504 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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