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We propose a new framework for the analysis of current and futurecosmological surveys, which combines perturbative methods (PT) on large scaleswith conditional simulation-based implicit inference (SBI) on small scales.This enables modeling of a wide range of statistics across all scales usingonly small-volume simulations, drastically reducing computational costs, andavoids the assumption of an explicit small-scale likelihood. As aproof-of-principle for this hybrid simulation-based inference (HySBI) approach,we apply it to dark matter density fields and constrain cosmological parametersusing both the power spectrum and wavelet coefficients, finding promisingresults that significantly outperform classical PT methods. We additionally layout a roadmap for the next steps necessary to implement HySBI on actual surveydata, including consideration of bias, systematics, and customized simulations.Our approach provides a realistic way to scale SBI to future survey volumes,avoiding prohibitive computational costs.

Hybrid SBI or How I Learned to Stop Worrying and Learn the Likelihood