Empirical fits to inclusive electron-carbon scattering data obtained by
  deep-learning methods
Beata E. Kowal Krzysztof M. Graczyk Artur M. Ankowski Rwik Dharmapal Banerjee Hemant Prasad Jan T. Sobczyk
Employing the neural network framework, we obtain empirical fits to the
electron-scattering cross section for carbon over a broad kinematic region,
extending from the quasielastic peak, through resonance excitation, to the
onset of deep-inelastic scattering. We consider two different methods of
obtaining such model-independent parametrizations and the corresponding
uncertainties: based on the NNPDF approach [J. High Energy Phys. 2002, 062],
and on the Monte Carlo dropout. In our analysis, the $\chi^2$ function defines
the loss function, including point-to-point uncertainties and considering the
systematic normalization uncertainties for each independent set of
measurements. Our statistical approaches lead to fits of comparable quality and
similar uncertainties of the order of $7\%$ and $12\%$ for the first and the
second approaches, respectively. To test these models, we compare their
predictions to a~test dataset, excluded from the training process, a~dataset
lying beyond the covered kinematic region, and theoretical predictions obtained
within the spectral function approach. The predictions of both models agree
with experimental measurements and the theoretical predictions. However, the
first statistical approach shows better interpolation and extrapolation
abilities than the one based on the dropout algorithm.