A surrogate model is developed to accurately approximate a two-dimensional hydrodynamics numerical solver in order to conduct a reduced-cost variance-based global sensitivity analysis of the hydraulic state. The impact of uncertainties in river bottom friction and boundary conditions on the simulated water depth is analyzed for quasi-unsteady flows. An autoencoder technique adapted to non-linear variable dimension reduction is used to reduce the multi-dimensional model output so that the formulation of the surrogate remains computationally parsimonious. In addition, following the divide-and-conquer principle, a mixture of local polynomial chaos expansions is proposed to deal with non-linearity in the hydraulic state with respect to uncertain inputs. Machine learning techniques are used to automatically partition the input space into clusters that are not affected by non-linearities and support accurate surrogates. This combined strategy is applied to a reach of the Garonne River where river and floodplains dynamics are simulated by the numerical solver Telemac-2D. The merits of this strategy are highlighted when the flood front reaches regions where the topography features a strong gradient and where, consequently, strong non-linearities occur between the water depth and friction as well as hydrologic input forcing. By applying this strategy, the \(Q_2\) metric improves by 90% compared to a classical polynomial chaos expansion surrogate, resulting in a much more reliable sensitivity analysis. This is particularly important in floodplain areas where human and economic activities are at stake.

开发了一种替代模型来精确逼近二维流体动力学数值求解器，以便对水力状态进行基于降低成本的方差的全局灵敏度分析。针对准不稳定流，分析了河底摩擦和边界条件的不确定性对模拟水深的影响。一种适用于非线性变量降维的自动编码器技术用于减少多维模型输出，以便代理的公式在计算上保持简洁。此外，根据分而治之的原则，提出了局部多项式混沌扩展的混合，以处理不确定输入的水力状态非线性。机器学习技术用于将输入空间自动划分为不受非线性影响并支持准确代理的集群。这种组合策略应用于加龙河河段，在那里河流和洪泛区动力学由数值求解器 Telemac-2D 模拟。当洪水前沿到达地形特征为强梯度的区域时，该策略的优点就凸显出来，因此水深和摩擦力以及水文输入强迫之间出现强非线性。通过应用这一策略，当洪水前沿到达地形特征为强梯度的区域时，该策略的优点就凸显出来，因此水深和摩擦力以及水文输入强迫之间出现强非线性。通过应用这一策略，当洪水前沿到达地形特征为强梯度的区域时，该策略的优点就凸显出来，因此水深和摩擦力以及水文输入强迫之间出现强非线性。通过应用这一策略，与经典多项式混沌扩展代理相比，\(Q_2\)指标提高了 90%，从而实现了更可靠的灵敏度分析。这在人类和经济活动受到威胁的洪泛区尤为重要。