  Complex processes ranging from protein folding to nuclear fission often
follow a low-dimension reaction path parameterized in terms of a few collective
variables. In nuclear theory, variables related to the shape of the nuclear
density in a mean-field picture are key to describing the large amplitude
collective motion of the neutrons and protons. Exploring the adiabatic energy
landscape spanned by these degrees of freedom reveals the possible reaction
channels while simulating the dynamics in this reduced space yields their
respective probabilities. Unfortunately, this theoretical framework breaks down
whenever the systems encounters a quantum phase transition with respect to the
collective variables. Here we propose a generative-deep-learning algorithm
capable of building new collective variables highly representative of a nuclear
process while ensuring a differentiable mapping to its Fermionic wave function.
Within this collective space, the nucleus can evolve continuously from one of
its adiabatic quantum phase to the other at the price of crossing a potential
energy barrier. This approach applies to any Fermionic system described by a
single Slater determinant, which encompasses electronic systems described
within the density functional theory.
