Gaussian process-transformer diffusion model for seabed plastic strain field prediction under tidal loading

Traditional liquefaction criteria based on pore water pressure ratio fail to characterize cumulative plastic deformation prior to liquefaction onset. This study presents a Gaussian process-transformer (GT) diffusion model enabling end-to-end mapping from tidal loading to seabed plastic volumetric strain increments. The GT model embeds cyclic loading history into Gaussian Process covariance structures through a stress path dynamic factor matrix, capturing memory effects absent in conventional methods. Physics constraints are enforced via multi-task learning with cross-attention mechanisms for seamless physics-deep learning integration. Primary validation at Crissy Field achieves R2 = 0.94, outperforming Modified Cam Clay models by 47%–61%. Cross-domain validation using Tokyo Bay CPT data from the 2011 Tohoku earthquake (Mw 9.1) confirms frequency-independence (R2 = 0.82–0.95). Validation at Sheringham Shoal (101 CPT soundings) establishes generalizability across seabed types. The research reveals a 60° phase lag, identifying mid-flood and early ebb as critical risk phases. Uncertainty quantification achieves expected calibration error = 0.0337 and prediction interval coverage probability = 98.7%. The GT framework enables continuous-field real-time liquefaction risk monitoring for offshore infrastructure.