Since each 2D map and 3D grid is characterized by a set of 6 parameters, one natural application of CMD is to build emulators, i.e.


where \(\textbf{X}\) can be a summary statistics (e.g. the probability distribution function of the pixels in a 2D map), or can be the entire 2D map or 3D grid. \(\vec{\theta}\) is a vector with the value of the parameters (e.g. \(\vec{\theta}=\{\Omega_{\rm m}, \sigma_8, A_{\rm SN1}, A_{\rm SN2}, A_{\rm AGN1}, A_{\rm AGN2} \}\)) and \(f\) is the function relating the parameters with the data.

The idea is to use neural networks, or other methods, to approximate \(f\). CMD provides a significant amount of data to achieve this task.