Continuum-kinematics-inspired peridynamics (CPD) is an alternative formulation of peridynamics and a geometrically exact framework proposed by Javili et al. [1]. The most common numerical implementation of CPD adopts a mesh-free discretisation approach, where the interaction between material points is characterised by one-neighbour, two-neighbour and three-neighbour interactions within a finite horizon. The resulting nonlocal governing equations involve multiple integrals over the horizon, whose repeated numerical evaluation at each material point and deformation step leads to a substantial computational burden, rendering large-scale CPD simulations prohibitively expensive [2]. To address this challenge, this work proposes a surrogate neural network to approximate the integral operations in CPD. The neural network is trained on high-fidelity datasets generated from numerical CPD simulations and is designed to approximate the stored energy contributions arising from interactions. The explicit numerical integration is replaced with data-driven inference, and the approximated solution is embedded within the CPD framework. Finally, the versatility of the presented approach is illustrated with a variety of numerical examples. The results highlight the computational advantage of neural-network-assisted CPD simulation.