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

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Title: Numerically stable neural network for simulating Kardar-Parisi-Zhang growth in the presence of uncorrelated and correlated noises.
Authors: Song, Tianshu1,2 (AUTHOR), Xia, Hui1 (AUTHOR) hxia@cumt.edu.cn
Source: Computer Physics Communications. Oct2025, Vol. 315, pN.PAG-N.PAG. 1p.
Subjects: Computer simulation, Exponents, Equations, Noise, Motivation (Psychology)
Abstract: 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 proposed neural network could effectively estimate the scaling exponents eliminating numerical divergence in both (1+1)- and (2+1)-dimensions. • A neural network method for solving KPZ equation is proposed. • Stable numerical simulations are achieved to avoid numerical divergence. • Scaling exponents are obtained for KPZ growth driven by various noises. [ABSTRACT FROM AUTHOR]
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Database: Engineering Source
Description
Abstract: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 proposed neural network could effectively estimate the scaling exponents eliminating numerical divergence in both (1+1)- and (2+1)-dimensions. • A neural network method for solving KPZ equation is proposed. • Stable numerical simulations are achieved to avoid numerical divergence. • Scaling exponents are obtained for KPZ growth driven by various noises. [ABSTRACT FROM AUTHOR]
ISSN:00104655
DOI:10.1016/j.cpc.2025.109682