  In this study, we introduce a novel approach in quantum field theories to
estimate the action using the artificial neural networks (ANNs). The estimation
is achieved by learning on system configurations governed by the Boltzmann
factor, $e^{-S}$ at different temperatures within the imaginary time formalism
of thermal field theory. We focus on 0+1 dimensional quantum field with
kink/anti-kink configurations to demonstrate the feasibility of the method. The
continuous-mixture autoregressive networks (CANs) enable the construction of
accurate effective actions with tractable probability density estimation. Our
numerical results demonstrate that this methodology not only facilitates the
construction of effective actions at specified temperatures but also adeptly
estimates the action at intermediate temperatures using data from both lower
and higher temperature ensembles. This capability is especially valuable for
the detailed exploration of phase diagrams.
