Abstract: I will present ongoing work about inference with generative cosmological models. I assume that only a small number of parameters are of interest, but that the process generating the data is very general: a noisy non-linear dynamical system with millions of hidden variables.

The main challenge is then the intractability of the likelihood, and therefore, the computational cost. The proposed strategy combines probabilistic modelling of the discrepancy between simulated and observed data with optimisation to facilitate likelihood-free inference. As a consequence, the number of required simulations is reduced by several orders of magnitude.

I will discuss prospects to reanalyse existing large-scale structure data sets, including thorough forward-modelling of all relevant physical and observational effects.