  Targeted free energy perturbation uses an invertible mapping to promote
configuration space overlap and the convergence of free energy estimates.
However, developing suitable mappings can be challenging. Wirnsberger et al.
(2020) demonstrated the use of machine learning to train deep neural networks
that map between Boltzmann distributions for different thermodynamic states.
Here, we adapt their approach to free energy differences of a flexible bonded
molecule, deca-alanine, with harmonic biases with different spring centers.
When the neural network is trained until ``early stopping'' - when the loss
value of the test set increases - we calculate accurate free energy differences
between thermodynamic states with spring centers separated by 1 \r{A} and
sometimes 2 \r{A}. For more distant thermodynamic states, the mapping does not
produce structures representative of the target state and the method does not
reproduce reference calculations.
