  $\alpha$-RuCl3 is a magnetic insulator exhibiting quantum spin liquid phases
possibly found in the Kitaev honeycomb model. Much of the effort towards
determining Hamiltonian parameters has focused on low magnetic field ordered
phases. We study this problem in the high magnetic field limit where mean-field
theory is better justified. We do so by machine-learning model parameters from
over 200,000 low dimensional data points by combining available magnetization,
torque, and torsion data sets. Our machine, an artificial neural
network-mean-field theory (ANN-MFT) encoder, maps thermodynamic conditions
(temperature and field vector) to model parameters via a fully connected
time-reversal covariant (equivariant) neural network and then predicts
observable values using mean-field theory. To train the machine, we use PyTorch
to enable backpropagation through mean-field theory with a pure PyTorch
implementation of the Newton-Raphson method. The results at $20$ K and $34.5$ T
are consistent with other parameter inference studies in the literature at low
magnetic field but strikingly have magnitudes that scale with temperature from
1.3 K up to 80 K in the $34.5-60$ T range. We conclude that the data presents
physics beyond the scope of the mean-field theory and that strong interactions
dominate the physics of $\alpha$-RuCl$_3$ up to field strengths of at least 60
Tesla.
