Numerical site-response predictions often deviate from observations, yet correcting these discrepancies is difficult because records are limited in both sensor coverage and number of events. This study proposes the Transfer-Enabled Forced Latent Autoencoder for Response Equations (FLARE-T) to improve these predictions by learning and calibrating low-dimensional latent dynamics that connect the base acceleration input to acceleration outputs at multiple depths. FLARE-T learns a low-dimensional response manifold and input-driven dynamics from dense finite-element simulations. It then trains a sparse encoder to map simulated sensor responses into the learned coordinates and uses limited records to calibrate the dynamics within them. A short response window initializes each prediction, while the complete base motion drives the response. The framework was evaluated using a layered-soil centrifuge test and the Lotung field vertical array. Test-set results show that FLARE-T improved multi-depth acceleration histories and 5%-damped pseudoacceleration response spectra relative to the original finite-element models, reducing errors at every evaluated sensor for motions of different intensities and, at Lotung, for both horizontal components. Two Lotung source models with different constitutive parameters achieved comparable test-set accuracy, indicating reduced dependence on precise prior calibration. FLARE-T therefore provides a data-efficient means of combining dense numerical response information with limited field records to improve future site-response predictions.
Governing equations provide compact descriptions of physical systems, yet the variables in which they are simple are often hidden in high-dimensional measurements. This challenge is sharper for forced systems, whose responses depend on both intrinsic dynamics and time-dependent inputs. Here we introduce FLARE, a forced latent autoencoder for response equations that learns compact response coordinates, identifies sparse input-dependent latent dynamics and decodes equation rollouts to full responses. By estimating latent dimension from data and separating state estimation from external forcing, FLARE enables forecasts to be initialized from past responses and driven by prescribed future inputs. Across known dynamical systems, application-scale forced responses and visual observations, FLARE recovers compact forced dynamics and predicts long-horizon high-dimensional responses under inputs not used for training. By turning learned coordinates into a dynamical interface, FLARE extends equation discovery to systems whose effective states are hidden within complex observations, providing a route for interpretable modelling and prediction of high-dimensional responses in forced dynamical systems.
The shock response spectrum (SRS) is widely used to characterize the response of single-degree-of-freedom (SDOF) systems to transient accelerations. Because the mapping from acceleration time history to SRS is nonlinear and many-to-one, reconstructing time-domain signals from a target spectrum is inherently ill-posed. Conventional approaches address this problem through iterative optimization, typically representing signals as sums of exponentially decayed sinusoids, but these methods are computationally expensive and constrained by predefined basis functions. We propose a conditional variational autoencoder (CVAE) that learns a data-driven inverse mapping from SRS to acceleration time series. Once trained, the model generates signals consistent with prescribed target spectra without requiring iterative optimization. Experiments demonstrate improved spectral fidelity relative to classical techniques, strong generalization to unseen spectra, and inference speeds three to six orders of magnitude faster. These results establish deep generative modeling as a scalable and efficient approach for inverse SRS reconstruction.
In this paper we build upon a previous study in which we demonstrated, using XGBoost and earthquake catalogue data from Japan and Chile, that a set of 60 seismic statistical features (SSFs) had much greater predictive value than a set of 428 generic time series features from the tsfresh package. We here extend this previous work in two key ways, focusing on data from Japan as a large dataset is necessary in order to allow for the training of a deep learning (autoencoder) model. First, we move from whole-region prediction (considering, for each candidate event, the likelihood of an event M ≥ 5.0 anywhere in the region in the next 15 days) to localised predictions in which both the region of feature computation and the region of prediction are restricted to a circle of radius 24 km around the candidate event, and we show that performance remains excellent, similar to our previous whole-region study for the same area. Second, we here couple this proven set of SSFs, based on one-dimensional (catalogue) data, with a novel feature based on magnitude-stratified two-dimensional seismic maps, obtained by training a VQ-VAE model to reproduce such maps as output and identifying a measure of its error in doing so with anomalies in magnitude distribution reflecting a localised build-up of crustal stress. We show that while localised prediction based only on a set of SSFs can be effective, with test AUC values as high as those obtained in the case of Japan in our previous whole-region study, the inclusion of the new natively-spatial VQ-VAE-derived feature, top-ranked by SHAP analysis, both improves prediction and points toward a new approach that might allow computationally time-demanding traditional seismic features to be entirely set aside.