There is a growing interest in utilizing machine learning (ML) methods for structural metamodeling due to the substantial computational cost of traditional numerical simulations. The existing data-driven strategies show potential limitations to the model robustness and interpretability as well as the dependency of rich data. To address these challenges, this paper presents a novel physics-informed machine learning (PiML) method, which incorporates scientific principles and physical laws into deep neural networks for modeling seismic responses of nonlinear structures. The basic concept is to constrain the solution space of the ML model within known physical bounds. This is made possible with three main features, namely, model order reduction, a long short-term memory (LSTM) networks, and Newton's second law (e.g., the equation of motion). Model order reduction is essential for handling structural systems with inherent redundancy and enhancing model efficiency. The LSTM network captures temporal dependencies, enabling accurate prediction of time series responses. The equation of motion is manipulated to learn system nonlinearities and confines the solution space within physically interpretable results. These features enable model training with relatively sparse data and offer benefits in terms of accuracy, interpretability, and robustness. Furthermore, a dataset of seismically designed archetype ductile planar steel moment resistant frames under horizontal seismic loading, available in the DesignSafe-CI Database, is considered for evaluation of the proposed method. The resulting metamodel is capable of handling more complex data compared to existing physics-guided LSTM models and outperforms other non-physics data-driven neural networks.

翻译：由于传统数值模拟的巨大计算成本，利用机器学习方法进行结构元建模日益受到关注。现有数据驱动策略在模型鲁棒性、可解释性以及对丰富数据的依赖性方面存在潜在局限。为解决这些挑战，本文提出了一种新型的基于物理信息的机器学习方法，该方法将科学原理和物理定律融入深度神经网络，用于建模非线性结构的地震响应。其基本思想是将机器学习模型的解空间约束在已知的物理界限内。这通过三个主要特性实现：模型降阶、长短期记忆网络和牛顿第二定律（例如运动方程）。模型降阶对于处理具有内在冗余性的结构系统并提升模型效率至关重要。长短期记忆网络捕捉时间依赖性，从而能够准确预测时间序列响应。运动方程被用于学习系统非线性，并将解空间限制在物理可解释的结果范围内。这些特性使得模型能够在相对稀疏的数据下进行训练，并在准确性、可解释性和鲁棒性方面带来优势。此外，本文使用DesignSafe-CI数据库中可用的、在水平地震荷载作用下按抗震设计的典型延性平面钢框架数据集对所提方法进行评估。与现有的物理引导长短期记忆模型相比，所生成的元模型能够处理更复杂的数据，并优于其他非物理数据驱动神经网络。