  Neural networks used for multi-interaction trajectory reconstruction lack the
ability to estimate the uncertainty in their outputs, which would be useful to
better analyse and understand the systems they model. In this paper we extend
the Factorised Neural Relational Inference model to output both a mean and a
standard deviation for each component of the phase space vector, which together
with an appropriate loss function, can account for uncertainty. A variety of
loss functions are investigated including ideas from convexification and a
Bayesian treatment of the problem. We show that the physical meaning of the
variables is important when considering the uncertainty and demonstrate the
existence of pathological local minima that are difficult to avoid during
training.
