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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 equation modeling shrinkage-induced fragmentation. The proposed method significantly reduces the computational cost by directly mapping the input parameters to the corresponding probability density functions, rather than solving the governing equations numerically. In particular, it enables efficient estimation of the density function in Monte Carlo simulations while maintaining or surpassing the accuracy compared to conventional finite difference methods. Validation on synthetic data demonstrates both the computational efficiency and the predictive reliability of the method. This work lays the foundation for data-driven inverse analysis of fragmentation and suggests the possibility of extending the framework beyond pre-specified model structures.

Takeaways, Limitations

Takeaways:
A computationally efficient neural network-based solver for shrinkage-induced fragmentation modeling is presented.
Monte Carlo simulations enable efficient evaluation of probability density functions.
Suggests the possibility of achieving higher accuracy than existing methods.
Establishing a foundation for data-based inverse analysis research and suggesting the possibility of expanding the model structure.
Limitations:
Only validation was performed on synthetic data, so generalization performance on real data requires further validation.
Further analysis is needed on the limitations and applicability of the proposed method.
Lack of specific guidance on how to extend beyond the pre-specified model structure.
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