In crystallography, that is, the science of working out how atoms are arranged in crystalline materials, the usual method is to guess at how the atoms are arranged, then calculate the expected diffraction pattern (the distribution of reflections of X-rays, electrons or neutrons off the crystal), and iteratively adjust the atomic arrangement until it matches the data. But that assumes that the crystal is built up from identical little unit cells that can be stacked up like bricks, so you only have to work with the atoms in one cell (fewer if there is symmetry). But in many cases the cells are not identical. You need to model hundreds, thousands of cells that are all different if you are to capture the real subtleties of the structure, and these might be the most important factors. But you cannot determine the positions of millions upon millions of atoms. The data cannot constrain that many variables. So you try to deduce the rules that are governing how the atoms are arranging themselves in response to each other. (Yes, I did have a point.) To put it another way, if you can accurately determine the variables that give rise to the atomic coordinates then you no longer need to solve all the coordinates individually.
Just thought it might be of interest.

]]>