Numerical modeling of morphodynamics presents significant challenges in engineering due to uncertainties arising from inaccurate inputs, model errors, and limited computing resources. Accurate results are essential for optimizing strategies and reducing costs. This paper presents a step-by-step Bayesian methodology to conduct an uncertainty analysis of 2D numerical modeling-based morphodynamics, exemplified by a dam-break over a sand bed experiment. Initially, uncertainties from prior knowledge are propagated through the dynamical model using the Monte Carlo technique. This approach estimates the relative influence of each input parameter on results, identifying the most relevant parameters and observations for Bayesian inference and creating a numerical database for emulator construction. Given the computationally intensive simulations of Markov chain Monte Carlo (MCMC) sampling, a neural network emulator is used to approximate the complex 2D numerical model efficiently. Subsequently, a Bayesian framework is employed to characterize input parameter uncertainty variability and produce probability-based predictions.

翻译：形态动力学的数值模拟在工程领域面临重大挑战，这主要源于输入数据不精确、模型误差及计算资源有限所引致的不确定性。精确的模拟结果对于优化工程策略与降低成本至关重要。本文提出一种分步式贝叶斯方法，用于对基于二维数值模拟的形态动力学进行不确定性分析，并以砂质床面上的溃坝实验为例进行验证。首先，通过蒙特卡罗技术将先验知识中的不确定性在动力学模型中进行传播。该方法评估了各输入参数对结果影响的相对重要性，识别出贝叶斯推断中最关键的参数与观测数据，并构建了用于代理模型建立的数值数据库。鉴于马尔可夫链蒙特卡罗（MCMC）采样计算成本高昂，本研究采用神经网络代理模型高效近似复杂的二维数值模型。随后，通过贝叶斯框架量化输入参数的不确定性变异特征，并生成基于概率的预测结果。