Adaptive peridynamic neural operators with fracture-aware topology

Predicting fracture in complex engineering systems requires the simultaneous treatment of nonlocal constitutive behaviour, multi-physics loading and multi-scale crack propagation – a combination that no existing framework addresses in a unified, data-driven way. Existing peridynamic neural operators use a fixed horizon that either over-smooths the crack tip or sacrifices the nonlocal bulk response, and none track how a material’s connectivity changes as it fractures. We introduce the adaptive peridynamic neural operator with fracture-aware topology, which learns bond-level constitutive laws inside a damage-adaptive peridynamic operator, couples a coarse (bulk) and fine (crack-tip) operator through a multi-fidelity mixture and tracks the topology of the fracturing domain through a bond-count invariant, while remaining trainable from simulation or experimental data. Applied to biological soft tissue, ductile metals, polymers, concrete and foams, the adaptive peridynamic neural operator with fracture-aware topology achieves a mean prediction error ≈ 4 . 1 % , against 9 . 0 % for the base peridynamic neural operator and 15 . 8 % for the Fourier neural operator. Five extended physics features (anisotropic horizon, thermomechanical coupling, grain-boundary kernel, learned Paris fatigue law, electro-mechanical coupling) extend the framework to artificial intelligence chip reliability – silicon die cracking, copper pillar fatigue, underfill delamination, through-silicon via (TSV) liner cracking and low-k dielectric fracture – where the full model reaches ≈ 2 . 7 % mean prediction error ( 70 % lower than the base peridynamic neural operator), outperforms the ANSYS cohesive-zone finite element method by 3 . 5 × in accuracy while running 18 × faster and yields three quantitative design rules for bump pitch, low-k material selection and TSV keep-out zones.