Field-level simulation-based inference of galaxy clustering with convolutional neural networks

We present the first simulation-based inference (SBI) of cosmological parameters from field-level analysis of galaxy clustering. Standard galaxy clustering analyses rely on analyzing summary statistics, such as the power spectrum $P_{\ell }$, with analytic models based on perturbation theory. Consequently, they do not fully exploit the nonlinear and non-Gaussian features of the galaxy distribution. To address these limitations, we use the SimBIG forward modeling framework to perform SBI using normalizing flows. We apply SimBIG to a subset of the Baryon Oscillation Spectroscopic Survey CMASS galaxy sample using a convolutional neural network with stochastic weight averaging to perform massive data compression of the galaxy field. We infer constraints on ${\mathrm{\Omega }}_m={0.267}_{-0.029}^{+0.033}$ and ${\sigma }_8={0.762}_{-0.035}^{+0.036}$. While our constraints on ${\mathrm{\Omega }}_m$ are in line with standard $P_{\ell }$ analyses, ours on ${\sigma }_8$ are $2.65\times$ tighter. Our analysis also provides constraints on the Hubble constant $H_0=64.5\pm 3.8\mathrm{km}/\mathrm{s}/\mathrm{Mpc}$ from galaxy clustering alone. This higher constraining power comes from additional non-Gaussian cosmological information, inaccessible with $P_{\ell }$. We demonstrate the robustness of our analysis by showcasing our ability to infer unbiased cosmological constraints from a series of test simulations that are constructed using different forward models than the one used in our training dataset. This work not only presents competitive cosmological constraints but also introduces novel methods for leveraging additional cosmological information in upcoming galaxy surveys like the Dark Energy Spectroscopic Instrument, Prime Focus Spectrograph, and Euclid.

Figure 1

Schematic illustrating the various elements of the SimBIG forward modeling pipeline. First, we generate synthetic galaxy catalogs that mimic the real BOSS observations. Then, we train a data compression step using our CNN to compress the catalog to its cosmological parameters. Next, we train a neural posterior estimator on the estimating parameters and the true parameters to estimate posteriors over the cosmological parameters. Once our data compression and neural posterior estimator are trained, we apply our pipeline to infer cosmological parameters from the real BOSS observations.

Figure 2

TARP expected coverage probability vs probability level. For an accurate posterior estimator, the line will follow the diagonal, while deviations from the diagonal are indicative of over- or underconfidence. We show the NDE accuracy test, using 5180 of our base simulations that were not used in the training of our CNN.

Figure 3

Validation of our model on the SimBIG mock challenge data: (a) Marginalized two-dimensional posterior distribution of $\{{\mathrm{\Omega }}_m,{\sigma }_8\}$. (b) Likelihoods of $\mathrm{\Lambda }\mathrm{CDM}$ parameters.

Figure 4

Left: posterior distributions for all $\mathrm{\Lambda }\mathrm{CDM}$ cosmological parameters from our CNN-based field-level inference of BOSS observations (orange). For comparison, we include the SimBIG $P_{\ell }$ analysis (gray). The contours represent the 68% and 95% confidence intervals. Our CNN-based field-level inference produces tighter, yet consistent, constraints to the SimBIG $P_{\ell }$ analysis. Right: posterior distributions for ${\mathrm{\Omega }}_m$ and ${\sigma }_8$. For comparison, we include posteriors from the SimBIG $P_{\ell }$ analysis (gray) and the standard PT-based $P_{\ell }$ analysis (black dashed) [8]. Our analysis constrains ${\mathrm{\Omega }}_m$ and ${\sigma }_8$ 1.76 and $1.92\times$ tighter than the SimBIG $P_{\ell }$ analysis. Moreover, our constraints on ${\mathrm{\Omega }}_m$ are in line with the PT-based $P_{\ell }$ analysis, and ours on ${\sigma }_8$ are $2.65\times$ tighter.