In this paper, we demonstrate for the first time how the Integrated Finite Element Neural Network (I-FENN) framework, previously proposed by the authors , can efficiently simulate the entire loading history of non-local gradient damage propagation. To achieve this goal, we first adopt a Temporal Convolutional Network (TCN) as the neural network of choice to capture the history-dependent evolution of the non-local strain in a coarsely meshed domain. The quality of the network predictions governs the computational performance of I-FENN, and therefore we perform an extended investigation aimed at enhancing them. We explore a data-driven vs. physics-informed TCN setup to arrive at an optimum network training, evaluating the network based on a coherent set of relevant performance metrics. We address the crucial issue of training a physics-informed network with input data that span vastly different length scales by proposing a systematic way of input normalization and output un-normalization. We then integrate the trained TCN within the nonlinear iterative FEM solver and apply I-FENN to simulate the damage propagation analysis. I-FENN is always applied in mesh idealizations different from the one used for the TCN training, showcasing the framework’s ability to be used at progressively refined mesh resolutions. We illustrate several cases that I-FENN completes the simulation using either a modified or a full Newton–Raphson scheme, and we showcase its computational savings compared to both the classical monolithic and staggered FEM solvers. We underline that we satisfy very strict convergence criteria for every increment across the entire simulation, providing clear evidence of the robustness and accuracy of I-FENN. All the code and data used in this work will be made publicly available upon publication of the article.

中文翻译：

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I-FENN 与时间卷积网络：加快非局部梯度损伤传播的负载历史分析

在本文中，我们首次演示了作者之前提出的集成有限元神经网络（I-FENN）框架如何有效地模拟非局部梯度损伤传播的整个加载历史。为了实现这一目标，我们首先采用时间卷积网络（TCN）作为选择的神经网络，以捕获粗网格域中非局部应变的历史相关演化。网络预测的质量决定了 I-FENN 的计算性能，因此我们进行了一项旨在增强网络预测的扩展研究。我们探索数据驱动与物理通知的 TCN 设置，以达到最佳的网络训练，并根据一组连贯的相关性能指标评估网络。我们通过提出输入标准化和输出非标准化的系统方法来解决使用跨不同长度尺度的输入数据训练物理信息网络的关键问题。然后，我们将经过训练的 TCN 集成到非线性迭代 FEM 求解器中，并应用 I-FENN 来模拟损伤传播分析。 I-FENN 始终应用于与 TCN 训练所使用的网格理想化不同的网格理想化中，展示了该框架在逐步细化的网格分辨率下使用的能力。我们说明了 I-FENN 使用修改的或完整的牛顿-拉夫森方案完成模拟的几种情况，并展示了与经典的整体式和交错式有限元求解器相比，它节省的计算量。我们强调，整个模拟过程中的每个增量都满足非常严格的收敛标准，为 I-FENN 的稳健性和准确性提供了明确的证据。这项工作中使用的所有代码和数据将在文章发表后公开。