A Physics-Informed Neural Network with Arc-Length Parametrisation for the Equilibrium Path of CSFM Discontinuity Regions

Abstract

The Compatible Stress Field Method (CSFM) gives the lower-bound capacity of a structural-concrete discontinuity region (D-region), but production solvers are load-controlled and stall at the limit point, leaving the post-peak softening branch unresolved. An arc-length-parametrised physics-informed neural network (PINN) traces the load-deflection path through the limit point in a single forward pass: because the load factor is a network output rather than an input, it folds back, avoiding the tangent-stiffness solve the secant CSFM constitutive resists. Four ingredients, each confirmed by ablation, make cracked-regime training converge: supervised elastic pre-training, a pointwise arc-length loss, a fixed weight on that loss held outside the adaptive balancer, and a smoothed constitutive that keeps gradients finite. On a deep beam the network folds onto an independently traced descending segment of about 1.7 mm across five seeds; on the canonical seed it overshoots the reference peak load factor by 14% at a matching peak deflection. The method also extends to an asymmetric corbel and a slender wall pier with added boundary-condition-aware ingredients, though those curves are anchored. It is a feasibility demonstration and a transferable recipe; the advantage over finite elements is amortised parametric inference and differentiability, not single-curve speed or accuracy.