  While there have been many developments in computational probes of both
strongly-correlated molecular systems and machine-learning accelerated
molecular dynamics, there remains a significant gap in capabilities between
them, where it is necessary to describe the accurate electronic structure over
timescales in which atoms move. We describe a practical approach to bridge
these fields by interpolating the correlated many-electron state through
chemical space, whilst avoiding the exponential complexity of these underlying
states. With a small number of accurate correlated wave function calculations
as a training set, we demonstrate provable convergence to near-exact potential
energy surfaces for subsequent dynamics with propagation of a valid many-body
wave function and inference of its variational energy at all points, whilst
retaining a mean-field computational scaling. This represents a profoundly
different paradigm to the direct interpolation of properties through chemical
space in established machine-learning approaches. It benefits from access to
all electronic properties of interest from the same model without relying on
local descriptors, and demonstrates improved performance compared to the direct
training on energies themselves. We combine this with modern
systematically-improvable electronic structure methods to resolve the molecular
dynamics for a number of correlated electron problems, including the proton
dynamics of a Zundel cation trajectory, where we highlight the qualitative
improvement from traditional machine learning or ab initio dynamics on
mean-field surfaces.
