CrossBlend physics-informed LSTM for nonlinear structural response prediction within a cyber-physical framework

This study develops and evaluates physics-informed deep learning models for predicting nonlinear seismic structural responses within a cyber-physical framework. Four variants of Physics-Informed Long Short-Term Memory (PhyLSTM) models are proposed: baseline windowed and full-sequence PhyLSTM models and their CrossBlend counterparts. The CrossBlend mechanism implements a learnable dual-path displacement blending mechanism within the PhyLSTM framework, in which a sequence-level and floor-wise gating parameter adaptively combines direct displacement prediction with a velocity-integrated displacement pathway, while embedding dynamic equilibrium equation residuals as physics-based constraints to enhance long-sequence stability and mitigate cumulative displacement prediction drift. The models are trained and validated using finite element (FE) simulation data from three structural configurations with varying levels of nonlinearity, and evaluated against experimental datasets through two single-stage strategies, namely baseline cyber-domain training and weighted training, and three two-stage strategies, namely fine-tuning, partial-freeze tuning, and teacher-student training. The CrossBlend-PhyLSTM models outperform the baseline PhyLSTM models in displacement prediction accuracy, achieving mean correlation coefficients of 0.96–0.98 compared to 0.85–0.88 for the baseline models under the most nonlinear structural configuration. A controlled ablation analysis further confirms that the proposed CrossBlend models provides the strongest overall displacement prediction performance compared with the direct-only, integrated-only, and fixed-blending alternatives. Two-stage fine-tuning emerges as the most effective cross-domain adaptation approach, substantially improving prediction accuracy across all structural configurations compared with baseline cyber-domain training. These results establish the CrossBlend-PhyLSTM models as reliable structure-specific surrogate predictors for real-time structural response evaluation and digital twin applications.