Solving nonlinear multiscale methods with history-dependent behaviors and fine macroscopic meshes is a well-known challenge. In this work, an unsupervised machine learning-based clustering approach is developed to reduce nonlinear Multilevel Finite Element-FE${}^2$ calculations. In contrast with most available techniques which aim at developing Reduced Order Models (ROM) or AI-based surrogate models for the microscale nonlinear problems, the present technique reduces the problem from the macro scale by creating clusters of macro Gauss points which are assumed to be in close mechanical states. Then, a single micro nonlinear Representative Volume Element (RVE) calculation is performed for each cluster. A linear approximation of the macro stress is used in each cluster. Handling internal variables is carried out by using anelastic macro strains in the clustering vectors in addition to the macro strains components. Finally, some convergence issues related to the use of clusters at the macro scale are addressed through a cluster freezing algorithm. The technique is applied to nonlinear hyperelastic, viscoelastic and elastoplastic composites. In contrast to available ROM or machine-learning -based acceleration techniques, the present method does not require neither preliminary off-line calculations, nor training, nor data base, nor reduced basis at the macro scale, while maintaining typical speed-up factors about 20 as compared to classical FE${}^2$.

解决具有历史相关行为和精细宏观网格的非线性多尺度方法是一个众所周知的挑战。在这项工作中，开发了一种基于无监督机器学习的聚类方法来减少非线性多级有限元有限元${}^2$计算。与大多数旨在为微观非线性问题开发降阶模型（ROM）或基于人工智能的替代模型的可用技术相比，本技术通过创建宏观高斯点簇来从宏观尺度减少问题，假设宏观高斯点簇为处于紧密机械状态。然后，对每个簇执行单​​个微观非线性代表体积元 (RVE) 计算。每个簇中都使用宏观应力的线性近似。除了宏观应变分量之外，还通过在聚类向量中使用非弹性宏观应变来处理内部变量。最后，通过集群冻结算法解决了与宏观尺度上集群使用相关的一些收敛问题。该技术适用于非线性超弹性、粘弹性和弹塑性复合材料。与现有的 ROM 或基于机器学习的加速技术相比，本方法既不需要初步的离线计算，也不需要训练，也不需要数据库，也不需要宏观尺度的简化基础，同时保持典型的加速因子与经典 FE 相比为 20${}^2$。