  The nonequilibrium relaxation (NER) method, which has been used to
investigate equilibrium systems via their nonequilibrium behavior, has been
widely applied to various models to estimate critical temperatures and critical
exponents. Although the estimation of critical temperatures has become more
reliable and reproducible, that of critical exponents raises concerns about the
method's reliability. Therefore, we propose a more reliable and reproducible
approach using Gaussian process regression. In addition, the present approach
introduces statistical errors through the bootstrap method by combining them
using the extrapolation method. Our estimation for the two-dimensional Ising
model yielded $\beta = 0.12504(6)$, $\gamma = 1.7505(10)$, and $\nu =
1.0003(6)$, consistent with the exact values. The value $z = 2.1669(9)$ is
reliable because of the high accuracy of these exponents. We also obtained the
critical exponents for the three-dimensional Ising model and found that they
are close to those reported in a previous study. Thus, for systems undergoing
second-order transitions, our approach improves the accuracy, reliability, and
reproducibility of the NER analysis. Because the proposed approach requires the
relaxation of some observables from Monte Carlo simulations, its simplicity
imparts it with significant potential.
