Fragment size density estimator for shrinkage-induced fracture based on a physics-informed neural network
This work addresses computational efficiency in fragmentation modeling for materials science or engineering applications, but it is incremental as it applies an existing physics-informed neural network approach to a specific domain.
The paper tackled the problem of modeling shrinkage-induced fragmentation by developing a neural network solver for an integro-differential equation, which maps input parameters to probability density functions without solving the equation numerically, reducing computational costs while maintaining accuracy comparable to conventional methods.
This paper presents a neural network (NN)-based solver for an integro-differential equation that models shrinkage-induced fragmentation. The proposed method directly maps input parameters to the corresponding probability density function without numerically solving the governing equation, thereby significantly reducing computational costs. Specifically, it enables efficient evaluation of the density function in Monte Carlo simulations while maintaining accuracy comparable to or even exceeding that of conventional finite difference schemes. Validatation on synthetic data demonstrates both the method's computational efficiency and predictive reliability. This study establishes a foundation for the data-driven inverse analysis of fragmentation and suggests the potential for extending the framework beyond pre-specified model structures.