In many cutting-edge applications, high-fidelity computational models prove to be too slow for practical use and are therefore replaced by much faster surrogate models. Recently, deep learning techniques have increasingly been utilized to accelerate such predictions. To enable learning on large-dimensional and complex data, specific neural network architectures have been developed, including convolutional and graph neural networks. In this work, we present a novel encoder-decoder geometric deep learning framework called MAgNET, which extends the well-known convolutional neural networks to accommodate arbitrary graph-structured data. MAgNET consists of innovative Multichannel Aggregation (MAg) layers and graph pooling/unpooling layers, forming a graph U-Net architecture that is analogous to convolutional U-Nets. We demonstrate the predictive capabilities of MAgNET in surrogate modeling for non-linear finite element simulations in the mechanics of solids.

翻译：在许多前沿应用中，高保真计算模型因实际应用时速度过慢而被更快速的替代模型取代。近年来，深度学习技术越来越多地被用于加速此类预测。为支持对高维复杂数据的学习，研究者开发了特定神经网络架构，包括卷积神经网络和图神经网络。本文提出一种名为MAgNET的新型编码器-解码器几何深度学习框架，该框架将经典的卷积神经网络扩展至任意图结构数据。MAgNET由创新的多通道聚合（MAg）层和图池化/反池化层组成，构成与卷积U-Net类似的图U-Net架构。我们通过固体力学中的非线性有限元仿真替代建模，展示了MAgNET的预测能力。