AI 中文总结
该研究针对复合材料多尺度建模的尺度差距问题，提出神经嵌入图模型（NEGM），实现了无需复杂接口的自洽分层上采样，可高效预测含强非线性等特性的复合材料物理响应。
AI 中文摘要
计算物理建模中长期存在的挑战是微结构与宏观结构构件的特征长度尺度存在巨大差异。多尺度建模已被广泛采用，通过耦合针对不同尺度定制的方法来缩小这一差距。然而，传统方法如渐近均匀化（自底向上）和子建模（自顶向下）往往需要严格的数学前提或复杂的接口程序。为解决这些局限，我们提出一种完全可扩展的神经嵌入图模型（NEGM），为高度异质复合材料的逐步上采样提供统一框架。具体而言，NEGM将所有与微结构和材料相关的复杂性编码到组成神经网络模块中，这些模块随后被组织成超图以模拟逐渐增大的域。大量数值基准表明，NEGM可可靠预测表现出强材料非线性、任意边界条件和不规则几何形状的二维及三维复合材料的物理响应。关键的是，由于NEGM仅依赖神经网络的训练和推理，它提供了尺度不变的公式，这使得NEGM可迭代应用以从微尺度上采样到任意大的尺度，规避了不同建模框架间复杂接口协议的需求。我们在一个大型马赛克复合域上验证了这种逐步上采样策略，结果表明只要组成模块达到足够高的预测精度，累积误差就能得到有效控制。我们的发现表明，人工神经网络不仅如之前所证明的那样提高了直接单尺度模拟的效率，还为简化多尺度建模提供了一条清晰且优雅的途径。
英文摘要
A persistent challenge in computational physical modeling is the substantial disparity between the characteristic length scales of microstructures and macroscopic structural components. Multiscale modeling has been widely adopted to bridge this gap by coupling methodologies tailored to different scales. However, conventional approaches, such as asymptotic homogenization (bottom-up) and submodeling (top-down), often entail rigorous mathematical prerequisites or intricate interfacing procedures. To address these limitations, we introduce a fully scalable neural-embedded graphical model (NEGM) that provides a unified framework for the progressive upscaling of highly heterogeneous composite materials. Specifically, NEGM encodes all microstructure- and material-related complexities into constituent neural network blocks, which are then organized into a hypergraph to simulate progressively larger domains. Extensive numerical benchmarks demonstrate that NEGM reliably predicts the physical responses of 2D and 3D composites exhibiting strong material nonlinearity, arbitrary boundary conditions, and irregular geometries. Crucially, because NEGM relies solely on neural network training and inference, it offers a scale-invariant formulation. This enables iterative application of NEGM to upscale from the microscale to arbitrarily large scales, circumventing the need for complex interfacing protocols between disparate modeling frameworks. We validate this progressive upscaling strategy on a large mosaic composite domain, showing that the accumulated error can be effectively contained provided the constituent blocks achieve sufficiently high prediction accuracy. Our findings suggest that artificial neural networks not only enhance the efficiency of direct single-scale simulations, as previously demonstrated, but also provide a clean and elegant pathway toward streamlined multiscale modeling.
