This paper presents a neural network (NN)-based solver for the integral-differential equations modeling shrinkage-induced fracture. The proposed method significantly reduces computational costs by directly mapping input parameters to corresponding probability density functions, rather than numerically solving the governing equations. Specifically, it enables efficient evaluation of the density function in Monte Carlo simulations while maintaining or exceeding the accuracy of conventional finite difference techniques. Validation on synthetic data demonstrates both the computational efficiency and predictive reliability of the method. This study establishes a foundation for data-driven inverse analysis of fracture and suggests the potential for extending the framework beyond pre-specified model structures.