Deep Learning-Based Prediction of Nonlinear Seismic Response of Spherical Shell Structures

To overcome the inherent trade-off between computational efficiency and accuracy in traditional numerical methods, this study develops a series of deep learning models for accurately predicting the nonlinear seismic responses of spherical shell structures. The proposed models are based on four different architectures: bidirectional long short-term memory networks (BiLSTM), bidirectional gated recurrent units (BiGRU), and their attention-enhanced variants (AttLSTM, AttGRU), systematically investigating the influence of different deep learning architectures on structural dynamic response prediction performance. Based on the NGA West2 database, an input dataset incorporating multi-dimensional seismic excitations was constructed, and benchmark dynamic response solutions were generated using a finite element model for the training of deep learning models. Model performance was evaluated using both mean squared error and coefficient of determination metrics, and validated on independent test sets as well as representative earthquake records. Results demonstrate that compared with the finite element method (FEM), the deep learning models achieved a significant improvement in computational efficiency for predicting the nonlinear seismic responses of spherical shell structures. Among them, the BiGRU model, benefiting from its simplified gating mechanism and higher parameter efficiency, exhibited the best performance in predicting seismic responses in the [Formula: see text]- and [Formula: see text]-directions, with its predictions closely matching the FEM benchmark solutions. Additionally, the BiLSTM model, due to its more complex memory unit structure, showed superior directional balance when handling multi-dimensional inputs. Notably, although the attention mechanism enhanced the models’ capability to capture local nonlinear features, under the current conditions of limited dataset size and long-time sequences, its effect on improving the base models was not significant and even exhibited some degree of performance suppression. This study provides a methodological basis for selecting appropriate deep learning models for seismic safety assessments of complex spatial structures and offers in-depth insights into the applicability of different architectures under specific engineering scenarios.