The astrophysical $S$ factor for the radiative capture reaction ${}^3\mathrm{He}(\alpha ,\gamma ){}^7\mathrm{Be}$ plays a crucial role in big bang nucleosynthesis as well as stellar hydrogen burning. Its precise value is important in the context of primordial elemental abundances and the solar neutrino fluxes. In the present work we carry out a data-driven analysis of the $S$ factor using a Bayesian neural network. Unlike conventional neural networks, the Bayesian formulation produces a posterior distribution of $S$ factor curves consistent with experimental data and their uncertainties. From this distribution we extract the zero-energy astrophysical $S$ factor $S_{34}\left(0\right)=0.{544}_{-0.021}^{+0.022}\mathrm{keV}\mathrm{b}$. The posterior ensemble is further used to obtain reaction rates over the temperature range $T=0.005–4$ GK. The results are in agreement with existing calculations. This work provides an alternative framework for low-energy $S$ factor determination and uncertainty quantification in nuclear astrophysics.

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• Big bang nucleosynthesis
• H & He induced nuclear reactions
• Nuclear astrophysics
• Nuclear reaction rates
• Radiative capture
• S-factor
• Bayesian methods