MAgNET: A Graph U-Net Architecture for Mesh-Based Simulations

Abstract

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.

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• Self-Attention Graph Pooling
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• Gaussian process regression + deep neural network autoencoder for probabilistic surrogate modeling in nonlinear mechanics of solids
• Deep learning for nano-photonic materials -- The solution to everything!?
• LatticeGraphNet: A two-scale graph neural operator for simulating lattice structures