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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]
Copyright of Computer Physics Communications is the property of Elsevier B.V. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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DbLabel: Engineering Source
An: 187025391
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  Data: 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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  Data: <i>Copyright of Computer Physics Communications is the property of Elsevier B.V. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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      – Type: doi
        Value: 10.1016/j.cpc.2025.109682
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      – Code: eng
        Text: English
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        PageCount: 1
        StartPage: N.PAG
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      – SubjectFull: Computer simulation
        Type: general
      – SubjectFull: Exponents
        Type: general
      – SubjectFull: Equations
        Type: general
      – SubjectFull: Noise
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      – SubjectFull: Motivation (Psychology)
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      – TitleFull: Numerically stable neural network for simulating Kardar-Parisi-Zhang growth in the presence of uncorrelated and correlated noises.
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            – D: 01
              M: 10
              Text: Oct2025
              Type: published
              Y: 2025
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              Value: 315
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