We present an approach to estimate the single-particle energies in double InAs/InP nanowire quantum dots by combining an atomistic tight-binding approach with machine learning. The method works particularly well with a neural network and transfer learning, where we can accurately recover ground state energies with root-mean-square deviation around 1 meV by using only a small training set and capitalizing on earlier, smaller-scale computations. The training set is only a fraction of the multidimensional search space of possible dot sizes and inter-dot spacings. Besides the cases presented in this work, we expect this technique will interest other researchers involved in solving the inverse computational problem of matching spectra to nanostructure morphological properties.