Nonlinear mechanical systems can exhibit non-uniqueness of the displacement field in response to a force field, which is related to the non-convexity of strain energy. This work proposes a Neural Network-based surrogate model capable of capturing this phenomenon while introducing an energy in a latent space of small dimension, that preserves the topology of the strain energy; this feature is a novelty with respect to the state of the art. It is exemplified on two mechanical systems of simple geometry, but challenging strong nonlinearities. The proposed architecture offers an additional advantage over existing ones: it can be used to infer both displacements from forces, or forces from displacements, without being trained in both ways.

中文翻译：

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基于潜在能量的 NN：一种可解释的神经网络架构，用于固体力学中非线性静力学的模型阶降阶


非线性机械系统在力场的作用下可以表现出位移场的非唯一性，这与应变能的非凸性有关。这项工作提出了一种基于神经网络的代理模型，该模型能够捕获这种现象，同时在小维潜在空间中引入能量，从而保留应变能的拓扑结构;此功能相对于最先进的技术来说是新颖的。它以两个几何结构简单但具有挑战性的强非线性的机械系统为例。与现有架构相比，所提出的架构提供了额外的优势：它可用于推断力的位移或位移的力，而无需以两种方式进行训练。