Parameter Estimation for the Reduced Fracture Model via a Direct Filter Method
<|reference_start|>Parameter Estimation for the Reduced Fracture Model via a Direct Filter Method: In this work, we present a numerical method that provides accurate real-time detection for the widths of the fractures in a fractured porous medium based on observational data on porous medium fluid mass and velocity. To achieve this task, an inverse problem is formulated by first constructing a forward formulation based on the reduced fracture model of the diffusion equation. A parameter estimation problem is then performed online by utilizing a direct filter method. Numerical experiments are carried out to demonstrate the accuracy of our method in approximating the target parameters.<|reference_end|>
@article{huynh2024parameter,
    title={Parameter Estimation for the Reduced Fracture Model via a Direct Filter
  Method},
    author={Phuoc Toan Huynh and Feng Bao and Thi-Thao-Phuong Hoang},
    journal={arXiv preprint arXiv:2409.16458},
    year={2024},
    archivePrefix={arXiv},
    eprint={2409.16458},
    primaryClass={math.NA cs.NA math.PR}
}