  Using the Horizon-AGN hydrodynamical simulation and self-organising maps
(SOMs), we show how to compress the complex data structure of a cosmological
simulation into a 2-d grid which is much easier to analyse. We first verify the
tight correlation between the observed 0.3$\!-\!5\mu$m broad-band colours of
Horizon-AGN galaxies and their high-resolution spectra. The correlation is
found to extend to physical properties such as redshift, stellar mass, and star
formation rate (SFR). This direct mapping from colour to physical parameter
space is shown to work also after including photometric uncertainties that
mimic the COSMOS survey. We then label the SOM grid with a simulated
calibration sample and estimate redshift and SFR for COSMOS-like galaxies up to
$z\sim3$. In comparison to state-of-the-art techniques based on synthetic
templates, our method is comparable in performance but less biased at
estimating redshifts, and significantly better at predicting SFRs. In
particular our "data-driven" approach, in contrast to model libraries,
intrinsically allows for the complexity of galaxy formation and can handle
sample biases. We advocate that obtaining the calibration for this method
should be one of the goals of next-generation galaxy surveys.
