Use of machine learning techniques for the matching

Currently, we use a solving method to determine the matching from the end of a grid to move onto another gird. This is the most time consuming part of the population synthesis part.

To improve on this we should consider to use machine learning techniques for this. The problem is a classical machine learning of giving an input vector and getting an output vector. Here the difference is that we are not interested in getting values with physics meaning out but the coordinates in the grid corresponding to physical quantities. In principle the inverse of the current interpolators. From the grids for the training, we have as before both input and output vectors for the training.

Another advantage could be the scaling of including more and more parameters at the same time with small additional computational costs.

What will be important here to take care of:

1. That we always get an output vector with the aim of being the one with the smallest distance on the input vector.
2. That we have the ability to put weights on the different quantities of the input vector.

P.S.: Some more details can be found on Slack