用神经算子加速多尺度材料模拟，100倍提速且误差小于6%。
A Neural Operator based Hybrid Microscale Model for Multiscale Simulation of Rate-Dependent Materials
- 用神经算子替代传统微尺度计算，融合物理规律与数据驱动。
- 在粘弹性材料模拟中实现均质应力误差低于6%，速度提升约100倍。
- 适合需要快速高精度多尺度仿真的材料科学家与工程师。
材料行为受跨时间与长度尺度的多种现象影响。为理解微观结构对宏观响应的影响，多尺度建模至关重要。数值方法如$\text{FE}^2$能并发捕捉微宏相互作用，但因需反复求解微尺度问题而计算量巨大。为此，本文引入神经算子预测微尺度物理，构建数据驱动与物理机制融合的混合模型，兼具灵活性与物理一致性。该方法应用于涉及时变固体力学的粘弹性材料问题，仅在微尺度使用内部变量表征状态，其本构关系嵌入模型架构，并依据物理原理计算内部变量。均质应力结果误差小于6%，计算效率提升约100倍。
原文摘要 · Abstract (English)
The behavior of materials is influenced by a wide range of phenomena occurring across various time and length scales. To better understand the impact of microstructure on macroscopic response, multiscale modeling strategies are essential. Numerical methods, such as the $\text{FE}^2$ approach, account for micro-macro interactions to predict the global response in a concurrent manner. However, these methods are computationally intensive due to the repeated evaluations of the microscale. This challenge has led to the integration of deep learning techniques into computational homogenization frameworks to accelerate multiscale simulations. In this work, we employ neural operators to predict the microscale physics, resulting in a hybrid model that combines data-driven and physics-based approaches. This allows for physics-guided learning and provides flexibility for different materials and spatial discretizations. We apply this method to time-dependent solid mechanics problems involving viscoelastic material behavior, where the state is represented by internal variables only at the microscale. The constitutive relations of the microscale are incorporated into the model architecture and the internal variables are computed based on established physical principles. The results for homogenized stresses ($<6\%$ error) show that the approach is computationally efficient ($\sim 100 \times$ faster).
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