  The effect of noise in the input data for learning potential energy surfaces
(PESs) based on neural networks for chemical applications is assessed. Noise in
energies and forces can result from aleatoric and epistemic errors in the
quantum chemical reference calculations. Statistical (aleatoric) noise arises
for example due to the need to set convergence thresholds in the self
consistent field (SCF) iterations whereas systematic (epistemic) noise is due
to, {\it inter
  alia}, particular choices of basis sets in the calculations. The two
molecules considered here as proxies are H$_{2}$CO and HONO which are examples
for single- and multi-reference problems, respectively, for geometries around
the minimum energy structure. For H$_2$CO it is found that adding noise to
energies with magnitudes representative of single-point calculations does not
deteriorate the quality of the final PESs whereas increasing the noise level
commensurate with electronic structure calculations for more complicated, e.g.
metal-containing, systems is expected to have a more notable effect. However,
the effect of noise on the forces is more noticeable. On the other hand, for
HONO which requires a multi-reference treatment, a clear correlation between
model quality and the degree of multi-reference character as measured by the
$T_1$ amplitude is found. It is concluded that for chemically "simple" cases
the effect of aleatoric and epistemic noise is manageable without evident
deterioration of the trained model - although the quality of the forces is
important. However, considerably more care needs to be exercised for situations
in which multi-reference effects are present.
