Inferring Galactic parameters from chemical abundances with simulation-based inference

Galactic chemical abundances provide crucial insights into fundamental galactic parameters, such as the high-mass slope of the initial mass function (IMF) and the normalization of Type Ia supernova (SN,Ia) rates. Constraining these parameters is essential for advancing our understanding of stellar feedback, metal enrichment, and galaxy formation processes. However, traditional Bayesian inference techniques, such as Hamiltonian Monte Carlo (HMC), are computationally prohibitive when applied to large datasets of modern stellar surveys. We leverage simulation-based-inference (SBI) as a scalable, robust, and efficient method for constraining galactic parameters from stellar chemical abundances and demonstrate its advantages over HMC in terms of speed, scalability, and robustness against model misspecifications. We combine a Galactic chemical evolution (GCE) model CHEMPY with a neural network emulator and a neural posterior estimator (NPE) to train our SBI pipeline. Mock datasets are generated using CHEMPY including scenarios with mismatched nucleosynthetic yields, with additional tests conducted on data from a simulated Milky Way-like galaxy. SBI results are benchmarked against HMC-based inference, focusing on computational performance, accuracy, and resilience to systematic discrepancies. SBI achieves a ∼75,600 speed-up compared to HMC, reducing inference runtime from ≳42 hours to mere seconds for thousands of stars. Inference on $1,000$ stars yields precise estimates for the IMF slope (α_ ̊m IMF = -2.299 ± 0.002) and SN,Ia normalization (log_ (N_ ̊m Ia ) = -2.887 ± 0.003), deviating less than 0.05% from the ground truth. SBI also demonstrates similar robustness to model misspecification than HMC, recovering accurate parameters even with alternate yield tables or data from a cosmological simulation. SBI represents a paradigm shift in GCE studies, enabling efficient and precise analysis of massive stellar datasets. By outperforming HMC in speed, scalability, and robustness, SBI is poised to become a cornerstone methodology for future spectroscopic surveys facilitating deeper insights into the chemical and dynamical evolution of galaxies.