Inferring Galactic Parameters from Chemical Abundances with Simulation-Based Inference

TL;DR

This work introduces simulation-based inference (SBI) as a scalable alternative to Hamiltonian Monte Carlo for constraining galactic parameters from stellar chemical abundances. By coupling CHEMPY-based GCE, a neural emulator, and a Neural Posterior Estimator, the authors achieve orders-of-magnitude speedups while maintaining high accuracy for the IMF high-mass slope $\alpha_{\rm IMF}$ and SN Ia normalization $\log_{10}(N_{\rm Ia})$, even across yield-table misspecifications and in data from simulated Milky Way-like galaxies. The method scales to thousands of stars, enabling robust, population-level inferences that are currently impractical with traditional MCMC approaches. While acknowledging simplifying assumptions (e.g., independent star formation environments), the study demonstrates SBI’s potential to revolutionize galactic archaeology and to leverage next-generation spectroscopic survey data for deeper insights into chemical evolution and star formation histories.

Abstract

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 the 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 $\sim75,600\times$ speed-up compared to HMC, reducing inference runtime from $\gtrsim42$ hours to mere seconds for thousands of stars. Inference on $1,000$ stars yields precise estimates for the IMF slope ($α_{\rm IMF} = -2.298 \pm 0.002$) and SN Ia normalization ($\log_{10}(N_{\rm Ia}) = -2.885 \pm 0.003$), 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. (shortened...)

Figures (15)

• Figure 1: SBI flow chart. From a set of priors we simulate a sample of stellar abundances using CHEMPYRybizki_2017Philcox_2019 which we use to train a neural network emulator to speed up the data generation process. Using the neural network emulator we produce training data to train the Neural Density Estimator. With this we infer the posterior distribution of the model parameters from a single star. Repeating that for $N_{\rm stars}$ from the same galaxy gives an accurate fit of the IMF slope and Type Ia supernovae normalization.
• Figure 2: Cumulative absolute percentage error of the NN emulator for the CHEMPY simulator. The orange histogram shows the cumulative distribution of percentage errors with the vertical dashed line indicating the median and the vertical dotted lines indicating the first and third quartile. The box plot on the top of the plot extends from the first quartile to the third quartile of the data, with a line at the median. The whiskers extend from the box to the farthest data point lying within $1.5\times$ the inter-quartile range from the box. The NN predicts abundances with an absolute percentage error far below typical observational errors.
• Figure 3: Absolute percentage error of the neural posterior density estimate for a single star. Different colored histograms show the full error distribution for all 6 parameters of interest with the median values highlighted by the vertical dashed lines. The box plots show again the first and third quantiles with the median represented by a vertical line and the whiskers extending from the box to the farthest data point lying within $1.5\times$ the inter-quartile range from the box. The global parameters of main interest for this work are shown by the light blue and red histogram.
• Figure 4: Corner plot of the posteriors for all six parameters for a single star from the validation set. The gray contours show a kde-estimate of the posterior from our SBI inference and the red dot and lines show the ground truth parameter values. Gray histograms on the diagonal show a kde estimate of the marginals.
• Figure 5: Accuracy of inferred global galactic parameters $\alpha_{IMF}$ and $\log_{10}(N_{Ia})$ as a function of number of observed stars. We compare our SBI results (blue line) to the inferred values using HMC (red line) as done by Philcox_2019 and the ground truth values (black dashed line) for various test cases as described in Sec. For the SBI analysis we show $1\sigma$ and $2\sigma$ contours while HMC results only show $1\sigma$ statistical uncertainties as reported in Tab. 3 of Philcox_2019 (blue/red shaded regions). See Sec. \ref{['subsec:chempy_tng']} for a full description.