Mitigating Model Misspecification in Simulation-Based Inference for Galaxy Clustering

Abstract: Simulation-based inference (SBI) has become an important tool in cosmology for extracting additional information from observational data using simulations. However, all cosmological simulations are approximations of the actual universe, and SBI methods can be sensitive to model misspecification - particularly when the observational data lie outside the support of the training distribution. We present a method to improve the robustness of cosmological analyses under such conditions. Our approach first identifies and discards components of the summary statistics that exhibit inconsistency across related simulators, then learns a transformation that brings the observation back within the support of the training distribution. We apply our method in the context of a recent SimBIG SBI galaxy clustering analysis using the wavelet scattering transform (WST) summary statistic. The original analysis struggled to produce robust constraints for certain subsets of WST coefficients, where the observational data appeared out-of-distribution (OOD) relative to the training data. We show that our method enables robust cosmological inference and resolves OOD issues, while preserving most of the constraining power. In particular, the improved SimBIG WST analysis yields $\Lambda$CDM constraints of $\Omega_m = 0.32^{+0.02}_{-0.02}$ and $\sigma_8 = 0.80^{+0.02}_{-0.02}$, which are respectively $1.4\times$ and $3.1\times$ tighter than those from a standard perturbation-theory-based power spectrum analysis, confirming the significant information gain of WST summary statistics. The proposed method is easily applicable to other cosmological SBI contexts and represents a step toward more robust SBI pipelines.