  Numerical simulations are essential tools for exploring the dynamic scaling
properties of the nonlinear Kadar-Parisi-Zhang (KPZ) equation. Yet the inherent
nonlinearity frequently causes numerical divergence within the strong-coupling
regime using conventional simulation methods. To sustain the numerical
stability, previous works either utilized discrete growth models belonging to
the KPZ universality class or modified the original nonlinear term by the
designed specified operators. However, recent studies revealed that these
strategies could cause abnormal results. Motivated by the above-mentioned
facts, we propose a convolutional neural network-based method to simulate the
KPZ equation driven by uncorrelated and correlated noises, aiming to overcome
the challenge of numerical divergence, and obtaining reliable scaling
exponents. We first train the neural network to represent the determinant terms
of the KPZ equation in a data-driven manner. Then, we perform simulations for
the KPZ equation with various types of temporally and spatially correlated
noises. The experimental results demonstrate that our neural network could
effectively estimate the scaling exponents eliminating numerical divergence.
