An Efficient Solver for Cumulative Density Function-based Solutions of Uncertain Kinematic Wave Models
Abstract
We develop a numerical framework to implement the cumulative density function (CDF) method for obtaining the probability distribution of the system state described by a kinematic wave model. The approach relies on Monte Carlo Simulations (MCS) of the fine-grained CDF equation of system state, as derived by the CDF method. This fine-grained CDF equation is solved via the method of characteristics. Each method of characteristics solution is far more computationally efficient than the direct solution of the kinematic wave model, and the MCS estimator of the CDF converges relatively quickly. We verify the accuracy and robustness of our procedure via comparison with direct MCS of a particular kinematic wave system, the Saint-Venant equation.
Keywords
Cite
@article{arxiv.1901.08520,
title = {An Efficient Solver for Cumulative Density Function-based Solutions of Uncertain Kinematic Wave Models},
author = {Ming Cheng and Yi Qin and Akil Narayan and Xinghui Zhong and Xueyu Zhu and Peng Wang},
journal= {arXiv preprint arXiv:1901.08520},
year = {2024}
}
Comments
19 pages, 6 figures, 3 tables