Decoupled Spatiotemporal Learning for Multi-Location Beam Response Reconstruction from Sparse Deflection Measurements
Abstract
Reconstructing continuous deflection and stress fields from sparse deflection measurements is challenging because the two responses have different spatial distributions and stress depends on deflection curvature. Limited experimental data further constrain model training and cross-domain adaptation. We present a decoupled spatiotemporal physics-informed neural network (DS-PINN) for reconstructing low-frequency elastic responses. The method combines latent temporal integration, dual-response spatial representation and simulation-to-experiment adaptation. Rather than representing the full spatiotemporal field with a single coordinate network, DS-PINN evolves latent coordinates through a Newmark-β integration operator. A shared sinusoidal representation network (SIREN) backbone extracts continuous spatial features, and two response-specific regression heads produce separate bases for deflection and stress. The model was pretrained on 1800 simulated records and fine-tuned on 16 measured records, while 200 simulated and 5 measured records were used for validation. Only three deflection channels were supplied as inputs. Across four independent 55 s test records, DS-PINN achieved Pearson correlation coefficients of 0.9323 for deflection and 0.9093 for stress. The corresponding normalized root-mean-square error (NRMSE) values were 7.94% and 7.59%. Spatial NRMSE values remained below 6% at all 11 evaluation locations. Compared with the closest end-to-end baseline, a temporal convolutional network, DS-PINN reduced deflection and stress NRMSE by approximately 45.0% and 45.9%, respectively. Ablation tests identified distinct roles for Newmark-based latent dynamics, temporal adaptation, magnitude correction, and spatial-basis consistency. These results support a simulation-assisted approach to multi-location virtual sensing of low-frequency beam responses from sparse deflection measurements and limited experimental data.