面向超大型复合材料精准高效力学建模的通用傅里叶神经群算子求解器
A General-purpose Solver of Fourier Neural Swarm Operator Towards Accurate and Efficient Mechanical Modeling of Ultra Large Composite Materials
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中文总结 AI 辅助
该研究提出两尺度神经群框架，将傅里叶神经算子组装成群并结合粗网格有限元与施瓦茨迭代，实现超大型复合材料高效精准力学建模，成本大幅降低且可扩展性卓越。
中文摘要 AI 辅助
具有复杂微结构的复合介质力学性能可定制性强，但高效且精准的建模仍具挑战性。传统均匀化方法常过度简化微结构效应，而多尺度方法通常需要在空间和时间尺度间进行高成本耦合。为解决这些局限，我们提出一种用于异质复合材料大规模力学建模的两尺度神经群框架。在局部尺度，采用水平集表示法将代表性微结构特征的力学特性编码为基础傅里叶神经算子（FNO）；在全局尺度，根据微结构组分的空间分布，将这些预训练的FNO组装成FNO群。采用粗网格有限元模型提供全局物理指导，同时使用施瓦茨迭代同步相邻FNO并确保共享界面的一致性。通过对具有不同微结构配置的SiC-Al复合材料进行非线性模拟来验证所提框架。与非线性有限元分析相比，FNO群方法达到了相当的精度，同时计算成本降低了数个数量级。对于包含超过10亿个节点的极端双属性SiC-Al复合材料，所提方法在约1小时内即可预测力学响应，展现出卓越的可扩展性。此外，该框架自然适配任意狄利克雷边界条件和复杂域几何。所提神经群策略为大规模力学模拟提供了一种稳健且可扩展的范式，调和了异质材料建模中长期存在的计算效率与物理保真度之间的权衡。
英文摘要
Composite media with complex microstructures exhibit highly tailorable mechanical properties but remain challenging to model efficiently and accurately. Conventional homogenization often oversimplifies microstructural effects, whereas multiscale approaches typically require costly coupling across spatial and temporal scales. To address these limitations, we propose a two-scale neural-swarm framework for large-scale mechanical modeling of heterogeneous composites. At the local scale, the mechanical characteristics of representative microstructural features are encoded into building-block Fourier neural operators (FNOs) using level-set representations. At the global scale, these pretrained FNOs are assembled into an FNO swarm according to the spatial distribution of microstructural constituents. A coarse-mesh finite element model is employed to provide global physical guidance, while Schwarz iteration is used to synchronize neighboring FNOs and enforce consistency across shared interfaces. The proposed framework is validated through nonlinear simulations of SiC-Al composites with diverse microstructural configurations. Compared with nonlinear finite element analysis, the FNO-swarm method achieves comparable accuracy while reducing computational cost by orders of magnitude. For an extreme dual-property SiC-Al composite containing more than a billion nodal points, the proposed approach predicts the mechanical response within approximately one hour, demonstrating exceptional scalability. Furthermore, the framework naturally accommodates arbitrary Dirichlet boundary conditions and complex domain geometries. The proposed neural-swarm strategy provides a robust and scalable paradigm for large-scale mechanics simulations, reconciling the longstanding trade-off between computational efficiency and physical fidelity in heterogeneous materials modeling.
