论文标题
机器学习加速Fe $^2 $
A machine learning accelerated FE$^2$ homogenization algorithm for elastic solids
论文作者
论文摘要
用于多尺度建模的Fe $^2 $均质化算法在宏观和微观之间迭代（由代表体积元素表示），直到在宏观载荷的每一个增量中都达到收敛。两个量表之间的信息交换发生在宏观有限元离散化的高斯点。还使用有限元元素解决了微观问题问题，从而使复杂微观结构的算法计算算法昂贵。我们调用机器学习，以建立使用神经网络框架的RVE边界价值问题的输入输出因果关系。这将RVE作为一个黑框，该黑框从宏观科学中获取信息作为输入，并将信息作为输出作为输出，从而消除了对rve级别上固定有限元求解的需求。该框架有可能显着加速Fe $^2 $算法。
The FE$^2$ homogenization algorithm for multiscale modeling iterates between the macroscale and the microscale (represented by a representative volume element) till convergence is achieved at every increment of macroscale loading. The information exchange between the two scales occurs at the gauss points of the macroscale finite element discretization. The microscale problem is also solved using finite elements on-the-fly thus rendering the algorithm computationally expensive for complex microstructures. We invoke machine learning to establish the input-output causality of the RVE boundary value problem using a neural network framework. This renders the RVE as a blackbox which gets the information from the macroscale as an input and gives information back to the macroscale as output, thereby eliminating the need for on-the-fly finite element solves at the RVE level. This framework has the potential to significantly accelerate the FE$^2$ algorithm.
