There is growing interest in using machine learning (ML) methods for structural metamodeling due to the substantial computational cost of traditional simulations. Purely data-driven strategies often face limitations in model robustness, interpretability, and dependency on extensive data. To address these challenges, this paper introduces a novel physics-informed machine learning (PiML) method that integrates scientific principles and physical laws into deep neural networks to model seismic responses of nonlinear structures. The approach constrains the ML model's solution space within known physical bounds through three main features: dimensionality reduction via combined model order reduction and wavelet analysis, long short-term memory (LSTM) networks, and Newton's second law. Dimensionality reduction addresses structural systems' redundancy and boosts efficiency while extracting essential features through wavelet analysis. LSTM networks capture temporal dependencies for accurate time-series predictions. Manipulating the equation of motion helps learn system nonlinearities and confines solutions within physically interpretable results. These attributes allow for model training with sparse data, enhancing accuracy, interpretability, and robustness. Furthermore, a dataset of archetype steel moment resistant frames under seismic loading, available in the DesignSafe-CI Database [1], is considered for evaluation. The resulting metamodel handles complex data better than existing physics-guided LSTM models and outperforms other non-physics data-driven networks.

翻译：由于传统模拟计算成本高昂，利用机器学习方法构建结构元模型日益受到关注。纯数据驱动策略往往面临模型鲁棒性、可解释性不足以及依赖海量数据等问题。为应对这些挑战，本文提出了一种新型基于物理信息的机器学习方法，将科学原理与物理定律融入深度神经网络，以模拟非线性结构的地震响应。该方法通过三大核心特征将机器学习模型的解空间约束在已知物理边界内：结合模型降阶与小波分析的降维技术、长短期记忆网络及牛顿第二定律。降维技术通过小波分析提取关键特征，降低结构系统冗余性并提升效率；LSTM网络捕获时序依赖关系以实现精准时间序列预测；对运动方程的操控有助于学习系统非线性并确保解具有物理可解释性。这些特性使得模型仅需稀疏数据即可训练，同时提升精度、可解释性与鲁棒性。此外，本研究采用DesignSafe-CI数据库[1]中地震荷载作用下标准钢框架结构数据集进行评估。结果表明，与现有物理引导型LSTM模型及其他非物理数据驱动网络相比，该元模型能更有效处理复杂数据。