  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.
