求解不确定运动波模型基于累积分布函数解的高效求解器
An Efficient Solver for Cumulative Density Function-based Solutions of Uncertain Kinematic Wave Models
AI总结：
本文开发了一个数值框架，利用蒙特卡洛模拟和特征线法求解CDF方程，高效获取不确定运动波模型的系统状态概率分布，并验证了其准确性与鲁棒性。
摘要：
我们开发了一个数值框架，以实现累积分布函数（CDF）方法，从而获取由运动波模型描述的系统状态的概率分布。该方法依赖于对由CDF方法导出的系统状态细粒度CDF方程进行蒙特卡洛模拟（MCS）。该细粒度CDF方程通过特征线法求解。每个特征线法求解的计算效率远高于直接求解运动波模型，且CDF的MCS估计量收敛相对较快。我们通过与特定运动波系统（即Saint-Venant方程）的直接MCS进行比较，验证了该方法的准确性与鲁棒性。
英文摘要：
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.
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