While the blind brute-force (e.g., via ML) discovery of the density-energy mapping is, in principle, possible, it has important limitations compared to physically motivated DFAs. First, without any constrains due to physics, such brute-force search is going to be computationally wasteful. Second, having discovered the mapping between energy and density, one still has no recipe for computing energy derivatives with respect to various perturbations (i.e., properties), unless properties (or various energy derivatives) were included in the training. In contrast, using a physically motivated form of the functional opens access to properties (although the quality is not guaranteed, as illustrated by the developments of magnetic DFAs ).