PD-KINN: Kolmogorov–Arnold representation theorem enhanced peridynamic-informed neural network for predicting elastic deformation and brittle damage

Abstract

Fracture initiation in solids fundamentally arises from pre-existing discontinuities, such as crack networks and void distributions, which are ubiquitously observed in engineering structures. This paper presents an innovative unsupervised learning framework, termed Kolmogorov–Arnold representation theorem enhanced peridynamic-informed neural network (PD-KINN), designed to address challenges in elastic deformation characterization and brittle damage prediction. The framework integrates the novel Kolmogorov–Arnold networks (KANs) with traditional physics-informed neural networks (PINNs), this hybrid architecture demonstrates parameter-efficient learning while maintaining similar or better predictive performance. Notably, the network leverages the non-local integral operator of peridynamics to naturally describe discontinuous variables, making it effective in modeling material deformation and fracture. Moreover, the transfer learning technique is implemented to account for the incremental loading histories and crack path evolution. Finally, comparative validation against analytical and numerical solutions confirms PD-KINN’s superiority in handling fracture analysis of various solid structures under quasi-static loadings.