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.

该研究论文介绍了一种将科学原理和物理定律融入深度神经网络的新型物理信息机器学习（PiML）方法，用于建模非线性结构的地震响应，并通过模型降阶、长短期记忆网络（LSTM）和牛顿第二定律等特性，使模型具有相对稀疏数据的训练能力，同时提高了模型的准确性、可解释性和鲁棒性。