  We propose an effective approach to rapid estimation of the energy spectrum
of quantum systems with the use of machine learning (ML) algorithm. In the ML
approach (back propagation), the wavefunction data known from experiments is
interpreted as the attributes class (input data), while the spectrum of quantum
numbers establishes the label class (output data). To evaluate this approach,
we employ two exactly solvable models with the random modulated wavefunction
amplitude. The random factor allows modeling the incompleteness of information
about the state of quantum system. The trial wave functions fed into the neural
network, with the goal of making prediction about the spectrum of quantum
numbers. We found that in such configuration, the training process occurs with
rapid convergence if the number of analyzed quantum states is not too large.
The two qubits entanglement is studied as well. The accuracy of the test
prediction (after training) reached 98 percent. Considered ML approach opens up
important perspectives to plane the quantum measurements and optimal monitoring
of complex quantum objects.
