Three many-electron training wave functions via exact diagonalization at different geometries in a Lowdin atomic orbital (SAO) basis of a linear 6-atom hydrogen chain. The values of < n | Ψ ( a ) > show the (exponentially many) wave function amplitudes for each training state. Geometry-agnostic one- and two-body transition density matrices ( Γ i j k l ) and overlaps ( S ) are constructed between all pairs of training states ( b ), which allows for fast variational prediction of the potential energy surfaces at arbitrary test geometries in the many-body basis of these training states ( c ). This allows efficient inference of wave functions at each test geometry, as shown in ( c.1 ), with its associated ground state on the basis of the three training states. Plots in ( c.2 ) show that enlarging the training space from one to three geometries systematically converges the full symmetric stretching mode of this system to the exact diagonalization result, with training data points where explicit electronic structure calculations are performed denoted by crosses. Source data are provided as a Source Data file.
