β-decay half-life is one of the fundamental physical properties of unstable nuclei and plays an important role in nuclear physics and astrophysics.

This study aimed to provide accurate nuclear β-decay half-life predictions and reasonable uncertainties associated with the predictions.

Nuclear β-decay half-lives were studied based on the Bayesian neural network (BNN) approach. Three types of neural networks with x = (Z, N), x = (Z, N, Q_β), and x = (Z, N, δ, Q_β) were constructed as inputs to explore the influence of the input on the prediction. The posterior distributions were sampled using the Markov chain Monte Carlo algorithm. The mathematical expectations and standard deviations of the neural network predictions on the posterior distributions were used as the predicted values and errors of the BNN approach.

The learning accuracy can be significantly improved by incorporating the β-decay energy and physical quantity related to the nuclear pair effect into the neural network input layer and then using the logarithm of β-decay half-life as the network output. For nuclei with half-lives of less than 1 s, the prediction accuracy is approximately 0.2 orders of magnitude, which is similar to that afforded by the BNN method by learning the differences between the logarithms of the experimental half-lives and theoretical results.

The Bayesian neural network can accurately predict β-decay half-lives. When extrapolated to the unknown nuclear region, the predicted β-decay half-lives agree with the results of other theoretical models within errors, especially for nuclei with Z ? 50.