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.
翻译:材料科学物理系统建模的计算方法大部分来自分析(即物理基础)或数据驱动(即机器学习基础)的起源。为了结合这两种方法的长处,我们推行一种新型机器学习方法,以解决通用Lippmann-Schwinger(L-S)型等式的方程。在这个模式中,一个特定问题被转换成等效L-S方程,并作为一个优化问题得到解决,优化程序与手头问题相适应。作为学习循环解滚的一部分,我们使用一个经常性的脉冲神经网络,为感兴趣的领域迭接地解决治理方程。这一结构利用机器学习方法的通用性和计算效率,但也允许基于物理学的解释。我们展示了我们关于两阶段弹性本地(即oxel-Voxel-level)的预测非常精确的学习方法,因为许多调控方程式可以转换成等效L-S形式,因此,拟议的多级模型应用范围具有多种规模。