Empirical fits to inclusive electron-carbon scattering data obtained by deep-learning methods

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.