论文标题
非本地模型的数据驱动学习：从高保真模拟到本构定律
Data-driven learning of nonlocal models: from high-fidelity simulations to constitutive laws
论文作者
论文摘要
我们表明，机器学习可以提高一维复合材料中应力波的模拟准确性。我们提出了一种数据驱动的技术，以学习应力波传播模型的非本地本构定律。该方法是一种基于优化的技术，其中非局部内核函数通过伯恩斯坦多项式近似。内核，包括其函数形式和参数，因此被得出，因此当在非局部求解器中使用时，它会生成与高效率数据紧密匹配的解决方案。因此，最佳内核充当了均质的非局部连续模型，该模型可以准确地重现一个较小，更详细的模型，该模型可以包含多种材料。我们将此技术应用于具有周期性微观结构的异质棒中的波传播。几个一维数值测试说明了我们算法的准确性。证明最佳内核可以重现与用作培训数据的问题大不相同的应用中的复合材料的高保真数据。
We show that machine learning can improve the accuracy of simulations of stress waves in one-dimensional composite materials. We propose a data-driven technique to learn nonlocal constitutive laws for stress wave propagation models. The method is an optimization-based technique in which the nonlocal kernel function is approximated via Bernstein polynomials. The kernel, including both its functional form and parameters, is derived so that when used in a nonlocal solver, it generates solutions that closely match high-fidelity data. The optimal kernel therefore acts as a homogenized nonlocal continuum model that accurately reproduces wave motion in a smaller-scale, more detailed model that can include multiple materials. We apply this technique to wave propagation within a heterogeneous bar with a periodic microstructure. Several one-dimensional numerical tests illustrate the accuracy of our algorithm. The optimal kernel is demonstrated to reproduce high-fidelity data for a composite material in applications that are substantially different from the problems used as training data.
