质量加权算法优化基于傅里叶的物理信息神经网络在粘着接触力学中的应用
Mass weighting algorithm optimizes Fourier-based physics-informed neural network in adhesive contact mechanics
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中文总结 AI 辅助
研究弹性接触力学中物理信息神经网络的谱刚度失衡问题，采用谱预处理策略，通过质量加权函数和低通滤波器，应用于粘着线接触问题，收敛结果与格林函数分子动力学解定量相符。
中文摘要 AI 辅助
用于弹性接触力学的物理信息神经网络（PINNs）存在谱刚度失衡问题，即弹性核随波数线性增长，导致短波长模式主导梯度更新并使宏观变形收敛停滞。我们引入一种谱预处理策略，在反向传播前对傅里叶空间中的位移梯度重新加权，通过质量加权（MW）函数放大低波数分量，同时通过内置低通滤波器抑制亚网格噪声。应用于粘着线接触问题时，质量加权PINN在400次Adam迭代内达到机器零残差损失，而参考基准在高三个数量级的损失处停滞。收敛的位移和接触应力场与格林函数分子动力学（GFMD）解在从拉伸到压缩的压力下的光滑赫兹接触以及粗糙度覆盖几十年波长的粗糙表面上定量一致。该方法直接在均匀实空间网格上运行，不需要显式的格林函数积分或求积规则，并且完全根据最小化标量能量函数来制定。扩展到二维粗糙表面很直接，因为傅里叶弹性能量和谱预处理器都只取决于波数大小。
英文摘要
Physics-informed neural networks (PINNs) for elastic contact mechanics suffer from a spectral stiffness imbalance,that is, the elastic kernel grows linearly with wave number, causing short-wavelength modes to dominate gradient updates and stall convergence of the macroscopic deformation. We introduce a spectral preconditioning strategy that reweights loss gradients with respect to displacements in Fourier space before back-propagation, amplifying low wavenumber components through a mass weighting (MW) function while suppressing sub-grid noise via a built-in low-pass filter. Applied to adhesive line contact problems, the mass weighted PINN reaches machine-zero residual loss within $400$ Adam iterations for specified benchmark, whereas the reference benchmark stalls at three orders of magnitude higher loss. The converged displacement and contact stress fields agree quantitatively with Green's function molecular dynamics (GFMD) solutions for both smooth Hertz contact at pressures spanning tension to compression and rough surfaces with roughness covering several decades of wavelength. The method operates directly on a uniform real-space grid, requires no explicit Green's function integration or quadrature rules, and is formulated entirely in terms of minimising a scalar energy function. Extension to two-dimensional rough surfaces is direct, as both the Fourier elastic energy and the spectral preconditioner depend only on the wave-number magnitude.
发表机构
- Yangzhou University（扬州大学）
- Hefei University of Technology（合肥工业大学）
- University of Chinese Academy of Sciences（中国科学院大学）
机构由 AI 辅助整理，请以论文原文为准。
