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

Created by
  • Haebom

Author

Shinichi Ito

Outline

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.

Takeaways, Limitations

Takeaways:
The computational cost of shrinkage-induced fracture modeling can be significantly reduced.
It provides results with higher or similar accuracy than existing methods.
Enables efficient density functional evaluation in Monte Carlo simulations.
It presents new possibilities for data-driven inverse interpretation.
It has the potential to relax constraints on model structure.
Limitations:
Currently, only validation has been performed on synthetic data, and validation on real data is needed.
Further studies are needed to determine the generality of the proposed method and its applicability to various fracture phenomena.
No specific methodology has been presented for extending the model beyond the pre-specified structure.
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