Natalia speaks about forward modelling in the context of Lyman α absorption lines of quasar spectra. Forward modelling essentially takes the initial conditions from your early universe model and evolves them forward to give the full observational prediction of all measurable things, for those specific initial conditions.

This is different to, e.g., having a “summary statistic” of this full set of initial conditions and/or observations that you extract to constrain your model. An example of a summary statistic might be a bispectrum in the late universe. The bispectrum captures some of the information lost from the power spectrum due to non-linearity, but not all. Whereas, in principle, if the forward modelling is done precisely enough no information is lost.

Of course “done precisely enough” is the crucial phrase and forward modelling needs to balance precision with speed. The more common summary statistics methods are usually much, much faster than forward modelling.

So, Natalia presents a new method for evolving non-linearities faster, one that in particular does a much better job at capturing under-densities than the typical particle-mesh codes. She also shows that this forward modelling technique is able to extract, statistically, information about the 3D regions between absorption lines because it uses the full set of (correlated) initial conditions as its set of model parameters.

Natalia: https://nataliaporqueres.wixsite.com/home
Paper: https://arxiv.org/abs/2005.12928