  We present a comparison of methods for uncertainty quantification (UQ) in
deep learning algorithms in the context of a simple physical system. Three of
the most common uncertainty quantification methods - Bayesian Neural Networks
(BNN), Concrete Dropout (CD), and Deep Ensembles (DE) - are compared to the
standard analytic error propagation. We discuss this comparison in terms
endemic to both machine learning ("epistemic" and "aleatoric") and the physical
sciences ("statistical" and "systematic"). The comparisons are presented in
terms of simulated experimental measurements of a single pendulum - a
prototypical physical system for studying measurement and analysis techniques.
Our results highlight some pitfalls that may occur when using these UQ methods.
For example, when the variation of noise in the training set is small, all
methods predicted the same relative uncertainty independently of the inputs.
This issue is particularly hard to avoid in BNN. On the other hand, when the
test set contains samples far from the training distribution, we found that no
methods sufficiently increased the uncertainties associated to their
predictions. This problem was particularly clear for CD. In light of these
results, we make some recommendations for usage and interpretation of UQ
methods.
