Technically, even the SHM-DL approach remains a challenge regarding the computing power needed to numerically produce the spectra (training data) from the SHMs. Hence, (i) a reduction of the required training data size by better knowledge of the underlying physics is desirable as well as (ii) a reduction of computational costs by ultra-efficient quantum propagation in time to obtain the spectra . (iii) Furthermore, the computed spectra as training data must be balanced. For the time being this is done by simply discarding spectra from the training set which are too close to each other. However, this implies a large waste of computing time. To reduce this waste several advances are desirable: Firstly, use of an optimal metric to determine the Euclidean "distance" between two spectra. Here, recently the Wasserstein metric has become popular , or approximations to it which are computationally cheaper. A more elegant, physics-oriented advance would be to find an approximate inversion of the SHM-tospectrum map, or any other way which allows us to shift the balancing of the spectra to suitable choices of the SHMs.