A physics-guided machine learning model for cantilever and anchored sheet pile walls

Back-analysis of soil parameters requires thousands of forward solves, which is costly and occasionally non-convergent when each is a nonlinear finite-difference computation. This study develops a multi-tier physics-guided surrogate that returns the complete Winkler response of cantilever (A0) and single-anchored (A1) sheet pile walls. A finite-difference engine verified against SPW2006 provides 8612 cantilever and 10,805 anchored simulations, each with 101-node profiles of displacement, bending moment, shear force, subgrade reaction and net pressure. The surrogate embeds physics in its architecture rather than in a training penalty: its tiers follow the causal structure of the governing equation, and a Hurdle classifier enforces subgrade-reaction non-negativity by construction, returning exact zeros at 99% of yielded nodes. It attains a ten-seed mean R 2 of at least 0.986 and 0.981 on the A0 and A1 structural fields. A deep operator network matches it on displacement and bending moment but not on the geomechanical fields, where its unconstrained linear output returns negative stiffness at 30.6% of nodes. Without pointwise enforcement of the governing equation, the predicted fields remain force-consistent within a few per cent of peak moment at the median. The surrogate is 6.5 to 13 times cheaper per call than a median single-thread solve, about 30 times in single-thread batches and over 800 times on a graphics processor. It is verified numerically rather than validated against field measurements. Applicability is set by the excavation ratio H / L , an input, so queries are gated before inference by a three-zone rule that retains the solver as fallback.