With such justification, one can approach the problem of finding this mapping in a completely different way -not by building approximations to the known exact solution (as done in the wavefunction theory), but by parameterizing an empirical representation of the mapping device, the functional. Most DFAs are built upon mathematical representations of the functional grounded in our physical understanding of what it should look like (based on exact results for model systems), but one can envision finding the mapping without any such help from physics -for example, by brute-force training of a neural network (machine learning). One can, therefore, think of DFT as an empirical method that can be made exact.