  We address the use of neural networks (NNs) in classifying the environmental
parameters of single-qubit dephasing channels. In particular, we investigate
the performance of linear perceptrons and of two non-linear NN architectures.
At variance with time-series-based approaches, our goal is to learn a
discretized probability distribution over the parameters using tomographic data
at just two random instants of time. We consider dephasing channels originating
either from classical 1/f{\alpha} noise or from the interaction with a bath of
quantum oscillators. The parameters to be classified are the color {\alpha} of
the classical noise or the Ohmicity parameter s of the quantum environment. In
both cases, we found that NNs are able to exactly classify parameters into 16
classes using noiseless data (a linear NN is enough for the color, whereas a
single-layer NN is needed for the Ohmicity). In the presence of noisy data
(e.g. coming from noisy tomographic measurements), the network is able to
classify the color of the 1/f{\alpha} noise into 16 classes with about 70%
accuracy, whereas classification of Ohmicity turns out to be challenging. We
also consider a more coarse-grained task, and train the network to discriminate
between two macro-classes corresponding to {\alpha} \lessgtr 1 and s \lessgtr
1, obtaining up to 96% and 79% accuracy using single-layer NNs.
