Enhancing phase transition calculations with fitting and neural network

A bstract The computation of bounce action in a phase transition involves solving partial differential equations and may introduce numerical uncertainties. Deriving characteristic temperatures and transition parameters often involves differentiating or integrating the action, which can amplify residual numerical fluctuations. In this work, we fit the action curve as a function of temperature to mitigate the uncertainties inherent in the calculation of the phase transition parameters. We find that, after extracting a factor, the sixth-order polynomial yields an excellent fit for the action in the high temperature approximated potential. In a realistic model, the singlet extension of the Standard Model, this method performs satisfactorily across most of the parameter space after trimming the fitting data. It not only enhances the accuracy of phase transition calculations but also systematically reduces computation time and facilitates error estimation, particularly in models involving multiple scalar fields. Based on this approach, we discussed the possibility of using multiple neural networks to predict the action curve from model parameters.