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Numerical simulations are essential tools for exploring the dynamic scalingproperties of the nonlinear Kadar-Parisi-Zhang (KPZ) equation. Yet the inherentnonlinearity frequently causes numerical divergence within the strong-couplingregime using conventional simulation methods. To sustain the numericalstability, previous works either utilized discrete growth models belonging tothe KPZ universality class or modified the original nonlinear term by thedesigned specified operators. However, recent studies revealed that thesestrategies could cause abnormal results. Motivated by the above-mentionedfacts, we propose a convolutional neural network-based method to simulate theKPZ equation driven by uncorrelated and correlated noises, aiming to overcomethe challenge of numerical divergence, and obtaining reliable scalingexponents. We first train the neural network to represent the determinant termsof the KPZ equation in a data-driven manner. Then, we perform simulations forthe KPZ equation with various types of temporally and spatially correlatednoises. The experimental results demonstrate that our neural network couldeffectively estimate the scaling exponents eliminating numerical divergence.

Numerically stable neural network for simulating Kardar-Parisi-Zhang growth in the presence of uncorrelated and correlated noises