This paper introduces an innovative physics-informed deep learning framework for metamodeling of nonlinear structural systems with scarce data. The basic concept is to incorporate physics knowledge (e.g., laws of physics, scientific principles) into deep long short-term memory (LSTM) networks, which boosts the learning within a feasible solution space. The physics constraints are embedded in the loss function to enforce the model training which can accurately capture latent system nonlinearity even with very limited available training datasets. Specifically for dynamic structures, physical laws of equation of motion, state dependency and hysteretic constitutive relationship are considered to construct the physics loss. In particular, two physics-informed multi-LSTM network architectures are proposed for structural metamodeling. The satisfactory performance of the proposed framework is successfully demonstrated through two illustrative examples (e.g., nonlinear structures subjected to ground motion excitation). It turns out that the embedded physics can alleviate overfitting issues, reduce the need of big training datasets, and improve the robustness of the trained model for more reliable prediction. As a result, the physics-informed deep learning paradigm outperforms classical non-physics-guided data-driven neural networks.

中文翻译：

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用于非线性结构元建模的基于物理的多 LSTM 网络

本文介绍了一种创新的基于物理的深度学习框架，用于对具有稀缺数据的非线性结构系统进行元建模。基本概念是将物理知识（例如，物理定律、科学原理）整合到深度长短期记忆 (LSTM) 网络中，从而在可行的解决方案空间内促进学习。物理约束嵌入在损失函数中以强制执行模型训练，即使可用的训练数据集非常有限，也可以准确捕获潜在的系统非线性。特别是对于动态结构，考虑运动方程的物理定律、状态依赖和滞后本构关系来构建物理损失。特别是，提出了两种基于物理的多 LSTM 网络架构用于结构元建模。通过两个说明性示例（例如，受到地面运动激励的非线性结构）成功地证明了所提出框架的令人满意的性能。事实证明，嵌入式物理可以缓解过拟合问题，减少对大型训练数据集的需求，并提高训练模型的鲁棒性，以实现更可靠的预测。因此，基于物理的深度学习范式优于经典的非物理引导的数据驱动神经网络。并提高训练模型的鲁棒性，以实现更可靠的预测。因此，基于物理的深度学习范式优于经典的非物理引导的数据驱动神经网络。并提高训练模型的鲁棒性，以实现更可靠的预测。因此，基于物理的深度学习范式优于经典的非物理引导的数据驱动神经网络。