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Predictions for the two-photon exchange (TPE) correction to unpolarized $ep$elastic cross section, obtained within two different approaches, are confrontedand discussed in detail. In the first one the TPE correction is extracted fromexperimental data by applying the Bayesian neural network (BNN) statisticalframework. In the other the TPE is given by box diagrams, with the nucleon andthe $P_{33}$ resonance as the hadronic intermediate states. Two different formfactor parametrizations for both the proton and the $P_{33}$ resonance aretaken into consideration. Proton form factors are obtained from the global fitof the full model (with the TPE correction) to the unpolarized cross sectiondata. Predictions of both methods agree well in the intermediate $Q^2$ range,$(1,3)$ GeV$^2$. Above $Q^2=3$ GeV$^2$ the agreement is on $2\sigma$ level.Below $Q^2=1$ GeV$^2$ the consistency between both approaches is broken. Thevalues of the proton radius extracted within both models are given. In bothcases predictions for VEPP-3 experiment have been obtained and confronted withthe preliminary experimental results.

Comparison of Neural Network and Hadronic Model Predictions of Two-Photon Exchange Effect