  A machine learning technique is used to fit multiplicity distributions in
high-energy proton-proton collisions and applied to make predictions for
collisions at higher energies. The method is tested with Monte Carlo event
generator events. Charged-particle multiplicity and transverse-momentum
distributions within different pseudorapidity intervals in proton-proton
collisions were simulated using the PYTHIA event generator for center of mass
energies $\sqrt{s}$= 0.9, 2.36, 2.76, 5, 7, 8, 13 TeV for model training and
validation and at 10, 20, 27, 50, 100 and 150 TeV for model predictions.
Comparisons are made in order to ensure the model reproduces the relation input
variables and output distributions for the charged particle multiplicity and
transverse-momentum. The multiplicity and transverse-momentum distributions are
described and predicted very well, not only in the case of the trained but also
in the untrained energy values. The study proposes a way to predict
multiplicity distributions at a new energy by extrapolating the information
inherent in the lower energy data. Using real data instead of Monte Carlo, as
measured at the LHC, the technique has the potential to project the
multiplicity distributions for different intervals at very high collision
energies, e.g. 27 TeV or 100 TeV for the upgraded HE-LHC and FCC-hh
respectively, using only data collected at the LHC, i.e. at center of mass
energies from 0.9 up to 13 TeV.
