  Single crystal inelastic neutron scattering data contain rich information
about the structure and dynamics of a material. Yet the challenge of matching
sophisticated theoretical models with large data volumes is compounded by
computational complexity and the ill-posed nature of the inverse scattering
problem. Here we utilize a novel machine-learning-assisted framework featuring
multiple neural network architectures to address this via high-dimensional
modeling and numerical methods. A comprehensive data set of diffraction and
inelastic neutron scattering measured on the Kitaev material $\alpha-$RuCl$_3$
is processed to extract its Hamiltonian. Semiclassical Landau-Lifshitz dynamics
and Monte-Carlo simulations were employed to explore the parameter space of an
extended Kitaev-Heisenberg Hamiltonian. A machine-learning-assisted iterative
algorithm was developed to map the uncertainty manifold to match experimental
data; a non-linear autoencoder used to undertake information compression; and
Radial Basis networks utilized as fast surrogates for diffraction and dynamics
simulations to predict potential spin Hamiltonians with uncertainty. Exact
diagonalization calculations were employed to assess the impact of quantum
fluctuations on the selected parameters around the best prediction.
