Granular materials are complex systems whose macroscopic mechanics are governed by particles at the grain-scale. The need to understand their grain-scale behavior has motivated significant experimental and modeling efforts. Bridging the grain-scale with the continuum scale is important in order to develop constitutive theories based on grain-scale behavior, as well as for interpreting the results of grain-scale models and experiments from a macroscopic context. In this work, we present a new data-driven framework based on convolutional neural networks to bridge the grain-scale and continuum scale in granular materials. We use this framework to obtain a micromechanical model of stress and demonstrate that spatial correlations at the grain-scale are critical for bridging length scales. Our results suggest that it is possible to learn data-driven relationships between the grain-scale and macroscale even if we have limited knowledge about the physical state of a granular system. We also observed that it is possible to train a model to predict macroscopic stress using only a subset of the contact data for each time step. This points to the discovery of a new pattern in granular systems, whereby any spatially correlated subset of contact data is sufficient to model macroscopic stress, regardless of how much force they may be carrying. Finally, we demonstrated that our framework is robust with potential for generalizability in time.

颗粒材料是复杂的系统，其宏观力学受晶粒度上的颗粒支配。了解它们的晶粒尺度行为的需要激发了巨大的实验和建模工作。为了发展基于晶粒度行为的本构理论，以及从宏观环境解释晶粒度模型和实验的结果，将晶粒度与连续度尺度相联系是重要的。在这项工作中，我们提出了一个基于卷积神经网络的新数据驱动框架，以桥接颗粒材料中的晶粒度和连续度。我们使用这个框架来获得应力的微机械模型，并证明在晶粒尺度上的空间相关性对于桥接长度尺度是至关重要的。我们的结果表明，即使我们对颗粒系统的物理状态知之甚少，也有可能学习晶粒度和宏观度之间的数据驱动关系。我们还观察到，有可能训练模型以预测每个时间步仅使用一部分接触数据的宏观应力。这表明在粒状系统中发现了一种新的模式，因此，接触数据的任何与空间相关的子集都足以对宏观应力进行建模，无论它们可能承受多少力。最后，我们证明了我们的框架是强大的，具有及时推广的潜力。我们还观察到，有可能训练模型以预测每个时间步仅使用一部分接触数据的宏观应力。这表明在粒状系统中发现了一种新的模式，因此，接触数据的任何与空间相关的子集都足以对宏观应力进行建模，无论它们可能承受多少力。最后，我们证明了我们的框架是强大的，具有及时推广的潜力。我们还观察到，有可能训练模型以预测每个时间步仅使用一部分接触数据的宏观应力。这表明在粒状系统中发现了一种新的模式，因此，接触数据的任何与空间相关的子集都足以对宏观应力进行建模，无论它们可能承受多少力。最后，我们证明了我们的框架是强大的，具有及时推广的潜力。