This paper presents a neural network (NN)-based solver for the integral-differential equation modeling shrinkage-induced fragmentation. The proposed method significantly reduces the computational cost by directly mapping the input parameters to the corresponding probability density functions, rather than solving the governing equations numerically. In particular, it enables efficient estimation of the density function in Monte Carlo simulations while maintaining or surpassing the accuracy compared to conventional finite difference methods. Validation on synthetic data demonstrates both the computational efficiency and the predictive reliability of the method. This work lays the foundation for data-driven inverse analysis of fragmentation and suggests the possibility of extending the framework beyond pre-specified model structures.