In many cutting-edge applications, high-fidelity computational models prove too slow to be practical and are thus replaced by much faster surrogate models. Recently, deep learning techniques have become increasingly important in accelerating such predictions. However, they tend to falter when faced with larger and more complex problems. Therefore, this work introduces MAgNET: Multi-channel Aggregation Network, a novel geometric deep learning framework designed to operate on large-dimensional data of arbitrary structure (graph data). MAgNET is built upon the MAg (Multichannel Aggregation) operation, which generalizes the concept of multi-channel local operations in convolutional neural networks to arbitrary non-grid inputs. The MAg layers are interleaved with the proposed novel graph pooling/unpooling operations to form a graph U-Net architecture that is robust and can handle arbitrary complex meshes, efficiently performing supervised learning on large-dimensional graph-structured data. We demonstrate the predictive capabilities of MAgNET for several non-linear finite element simulations and provide open-source datasets and codes to facilitate future research.

翻译：在诸多前沿应用中，高保真计算模型因过于缓慢而难以实用，因此常被更快速的代理模型所取代。近年来，深度学习技术在加速此类预测中变得日益重要，然而在处理更大规模、更复杂的问题时，其性能往往下降。为此，本文提出MAgNET：多通道聚合网络——一种新型几何深度学习框架，旨在处理任意结构的高维数据（图数据）。MAgNET基于MAg（多通道聚合）操作构建，该操作将卷积神经网络中多通道局部操作的概念推广至任意非网格化输入。MAg层与本文提出的新型图池化/反池化操作交错排列，构成鲁棒且能处理任意复杂网格的图U-Net架构，从而高效地对高维图结构数据进行监督学习。我们展示了MAgNET在若干非线性有限元模拟中的预测能力，并提供了开源数据集与代码以促进未来研究。