Stress prediction in porous materials and structures is challenging due to the high computational cost associated with direct numerical simulations. Convolutional Neural Network (CNN) based architectures have recently been proposed as surrogates to approximate and extrapolate the solution of such multiscale simulations. These methodologies are usually limited to 2D problems due to the high computational cost of 3D voxel based CNNs. We propose a novel geometric learning approach based on a Graph Neural Network (GNN) that efficiently deals with three-dimensional problems by performing convolutions over 2D surfaces only. Following our previous developments using pixel-based CNN, we train the GNN to automatically add local fine-scale stress corrections to an inexpensively computed coarse stress prediction in the porous structure of interest. Our method is Bayesian and generates densities of stress fields, from which credible intervals may be extracted. As a second scientific contribution, we propose to improve the extrapolation ability of our network by deploying a strategy of online physics-based corrections. Specifically, we condition the posterior predictions of our probabilistic predictions to satisfy partial equilibrium at the microscale, at the inference stage. This is done using an Ensemble Kalman algorithm, to ensure tractability of the Bayesian conditioning operation. We show that this innovative methodology allows us to alleviate the effect of undesirable biases observed in the outputs of the uncorrected GNN, and improves the accuracy of the predictions in general.

翻译：由于与直接数字模拟有关的计算成本高昂,对松散材料和结构的压力作出预测具有挑战性。基于革命神经网络(CNN)的建筑最近被提议作为替代,以替代和推断这种多尺度模拟的近似和外推解决办法。由于基于3D voxel的CNN的计算成本高,这些方法通常限于2D问题。我们提议基于一个图象神经网络(GNN)的新型几何学习方法,它有效地处理三维问题,只进行2D表面的共振。在我们以前使用平流基CNN的发展后,我们训练GNN将本地微规模的压力校正校正调整自动添加到低廉的计算粗略压力预测中。我们的方法是巴伊斯式的,产生压力场的密度,可以从中抽取可靠的间隔。作为第二项科学贡献,我们建议通过采用在线物理校正的校正战略,提高我们的网络的外推能力。具体地说,我们把我们一般的不稳定性预测的后演预测结果附加到在松散结构中部分平衡,在这个阶段,我们用不断调整的基级的精确性的方法,确保我们进行这种调整。