Fragment size density estimator for shrinkage-induced fracture based on a physics-informed neural network

TL;DR

This paper introduces a physics-informed neural network that efficiently estimates fragment size density functions for shrinkage-induced fracture, reducing computational costs while maintaining high accuracy.

Contribution

It develops a neural network-based solver for an integro-differential equation modeling fragmentation, enabling direct density estimation without traditional numerical methods.

Findings

The method achieves high accuracy comparable to finite difference schemes.

It significantly reduces computational costs in Monte Carlo simulations.

Validation confirms the model's predictive reliability.

Abstract

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.