A Neural Latent Compression of Time-Delay DMD for Nonlinear Ground–Structure Dynamics

This study presents a data-driven framework combined with NN-based compression for system identification and response prediction of nonlinear ground and structural dynamics during earthquakes. The method, formulated for broad applicability across soil and structural systems, is demonstrated using observed ground response data. The framework is able to construct interpretable, physically consistent, and robust models that extract essential dynamic features directly from seismic time series. Time-delay embedded Dynamic Mode Decomposition (DMD) is employed to lift nonlinear earthquake-induced dynamics into a high-dimensional space, where system behavior can be approximated by a linear time-evolution operator. This formulation decomposes complex responses into modal components characterized by distinct oscillation frequencies, amplification–damping properties, and deformation patterns. The resulting DMD operator provides both a means of system identification and a linearized dynamical model approximating nonlinear temporal evolution, offering insight into deformation mechanisms and potential damage. To manage the high-dimensional feature space and generalize across seismic events, the extracted DMD features and operators are mapped onto a low-dimensional latent space using neural-network-based compression (e.g., Variational Autoencoder). In this latent representation, DMD operators can be sampled based on new ground-motion characteristics, enabling response prediction with quantified uncertainties while preserving modal interpretability. The proposed DMD–NN framework provides a unified approach for identifying and predicting nonlinear dynamics in soils and structures, enhancing interpretability and establishing a foundation for resilient, data-driven assessment of earthquake-induced dynamic systems.