Deep learning surrogate models are being increasingly used in accelerating scientific simulations as a replacement for costly conventional numerical techniques. However, their use remains a significant challenge when dealing with real-world complex examples. In this work, we demonstrate three types of neural network architectures for efficient learning of highly non-linear deformations of solid bodies. The first two architectures are based on the recently proposed CNN U-NET and MAgNET (graph U-NET) frameworks which have shown promising performance for learning on mesh-based data. The third architecture is Perceiver IO, a very recent architecture that belongs to the family of attention-based neural networks--a class that has revolutionised diverse engineering fields and is still unexplored in computational mechanics. We study and compare the performance of all three networks on two benchmark examples, and show their capabilities to accurately predict the non-linear mechanical responses of soft bodies.

翻译：深度学习替代模型正日益被用于加速科学模拟，以替代成本高昂的传统数值方法。然而，在处理实际复杂案例时，其应用仍面临重大挑战。本研究展示了三种适用于高效学习固体高度非线性变形的神经网络架构。前两种架构分别基于近期提出的CNN U-NET和MAgNET（图U-NET）框架，这两种框架在处理网格数据的学习任务中已展现出优异性能。第三种架构为Perceiver IO——一种极为新近的架构，属于注意力机制神经网络家族。该网络类型已在多个工程领域引发革命，但在计算力学领域仍属未开发范畴。我们通过两个基准案例研究并比较了三种网络的性能，展示了它们准确预测软体非线性力学响应的能力。