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

IF 3.4 2区物理与天体物理 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Computer Physics Communications Pub Date : 2025-05-30 DOI:10.1016/j.cpc.2025.109682

Tianshu Song , Hui Xia

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引用次数: 0

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.

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非相关和相关噪声下模拟karda - paris - zhang生长的数值稳定神经网络

数值模拟是研究非线性kadar - paris - zhang （KPZ）方程动态尺度特性的重要工具。然而，固有的非线性特性常常导致传统的强耦合模拟方法在数值上出现偏差。为了保持数值的稳定性，以往的研究要么利用属于KPZ普适类的离散增长模型，要么通过设计特定算子对原有的非线性项进行修正。然而，最近的研究表明，这些策略可能会导致异常的结果。基于上述事实，我们提出了一种基于卷积神经网络的方法来模拟不相关和相关噪声驱动的KPZ方程，旨在克服数值发散的挑战，并获得可靠的缩放指数。我们首先训练神经网络以数据驱动的方式表示KPZ方程的行列式项。然后，我们对不同类型的时间和空间相关噪声的KPZ方程进行了模拟。实验结果表明，我们提出的神经网络可以有效地估计缩放指数，消除(1+1)-和(2+1)-维度上的数值发散。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Computer Physics Communications 物理-计算机：跨学科应用

CiteScore

12.10

自引率

3.20%

发文量

287

审稿时长

5.3 months

期刊介绍： The focus of CPC is on contemporary computational methods and techniques and their implementation, the effectiveness of which will normally be evidenced by the author(s) within the context of a substantive problem in physics. Within this setting CPC publishes two types of paper. Computer Programs in Physics (CPiP) These papers describe significant computer programs to be archived in the CPC Program Library which is held in the Mendeley Data repository. The submitted software must be covered by an approved open source licence. Papers and associated computer programs that address a problem of contemporary interest in physics that cannot be solved by current software are particularly encouraged. Computational Physics Papers (CP) These are research papers in, but are not limited to, the following themes across computational physics and related disciplines. mathematical and numerical methods and algorithms; computational models including those associated with the design, control and analysis of experiments; and algebraic computation. Each will normally include software implementation and performance details. The software implementation should, ideally, be available via GitHub, Zenodo or an institutional repository.In addition, research papers on the impact of advanced computer architecture and special purpose computers on computing in the physical sciences and software topics related to, and of importance in, the physical sciences may be considered.