Recurrent localization networks applied to the Lippmann-Schwinger equation
Recurrent localization networks applied to the Lippmann-Schwinger equation
复制标题
应用于 Lippmann-Schwinger 方程的循环定位网络
DOI：
10.1016/j.commatsci.2021.110356
复制
发表时间：
2021
影响因子：
3.3
通讯作者：
Kalidindi, Surya R.
中科院分区：
文献类型：
--
作者：
Kelly, Conlain;Kalidindi, Surya R.
材料科学中用于建模物理系统的大部分计算方法来源于分析（即，基于物理的）或数据驱动的（即，基于机器学习的）起源。为了联合收割机这两种方法的优点，我们提出了一种新的机器学习方法求解广义Lippmann-Schwinger（L-S）型方程。在这个范例中，一个给定的问题被转换成一个等价的L-S方程，并解决了作为一个优化问题，其中的优化过程是校准的问题在手。作为基于学习的循环展开的一部分，我们使用递归卷积神经网络来迭代求解感兴趣领域的控制方程。这种架构利用了机器学习方法的通用性和计算效率，但也允许基于物理的解释。我们在两相弹性定位问题上展示了我们的学习方法，其中它在局部（即，体素级）弹性应变。由于大量的控制方程可以转换成一个等效的L-S形式，所提出的架构具有潜在的应用范围内的多尺度材料现象。
The bulk of computational approaches for modeling physical systems in materials science derive from either analytical (i.e., physics based) or data-driven (i.e., machine-learning based) origins. In order to combine the strengths of these two approaches, we advance a novel machine learning approach for solving equations of the generalized Lippmann-Schwinger (L-S) type. In this paradigm, a given problem is converted into an equivalent L-S equation and solved as an optimization problem, where the optimization procedure is calibrated to the problem at hand. As part of a learning-based loop unrolling, we use a recurrent convolutional neural network to iteratively solve the governing equations for a field of interest. This architecture leverages the generalizability and computational efficiency of machine learning approaches, but also permits a physics-based interpretation. We demonstrate our learning approach on the two-phase elastic localization problem, where it achieves excellent accuracy on the predictions of the local (i.e., voxel-level) elastic strains. Since numerous governing equations can be converted into an equivalent L-S form, the proposed architecture has potential applications across a range of multiscale materials phenomena.