用神经网络快速预测材料收缩裂纹分布，效率远超传统方法。
Fragment size density estimator for shrinkage-induced fracture based on a physics-informed neural network
- 用物理信息神经网络直接映射参数到裂纹密度分布函数。
- 计算速度比传统有限差分法快，精度相当或更优。
- 适合需要高效反演分析的材料模拟与工程优化场景。
本文提出一种基于神经网络的求解器，用于求解描述收缩诱导断裂的积分微分方程。该方法无需数值求解控制方程，直接将输入参数映射至对应的概率密度函数，显著降低计算成本。特别地，该方法可在蒙特卡洛模拟中高效评估密度函数，且精度与传统有限差分法相当甚至更优。在合成数据上的验证表明，该方法兼具计算效率与预测可靠性。本研究为断裂行为的数据驱动逆分析奠定基础，并展示了该框架拓展至非预设模型结构的潜力。
原文摘要 · Abstract (English)
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.
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