Deep Learning research is advancing at a fantastic rate, and there is much to gain from transferring this knowledge to older fields like Computational Fluid Dynamics in practical engineering contexts. This work compares state-of-the-art methods that address uncertainty quantification in Deep Neural Networks, pushing forward the reduced-order modeling approach of Proper Orthogonal Decomposition-Neural Networks (POD-NN) with Deep Ensembles and Variational Inference-based Bayesian Neural Networks on two-dimensional problems in space. These are first tested on benchmark problems, and then applied to a real-life application: flooding predictions in the Mille Îles river in the Montreal, Quebec, Canada metropolitan area. Our setup involves a set of input parameters, with a potentially noisy distribution, and accumulates the simulation data resulting from these parameters. The goal is to build a non-intrusive surrogate model that is able to know when it does not know, which is still an open research area in Neural Networks (and in AI in general). With the help of this model, probabilistic flooding maps are generated, aware of the model uncertainty. These insights on the unknown are also utilized for an uncertainty propagation task, allowing for flooded area predictions that are broader and safer than those made with a regular uncertainty-uninformed surrogate model. Our study of the time-dependent and highly nonlinear case of a dam break is also presented. Both the ensembles and the Bayesian approach lead to reliable results for multiple smooth physical solutions, providing the correct warning when going out-of-distribution. However, the former, referred to as POD-EnsNN, proved much easier to implement and showed greater flexibility than the latter in the case of discontinuities, where standard algorithms may oscillate or fail to converge.

深度学习的研究以惊人的速度前进，将这些知识转移到实际工程环境中的较旧领域（例如计算流体动力学）有很多收获。这项工作比较了解决深度神经网络中不确定性量化问题的最新方法，并推动了具有深度集成和基于变分推理的贝叶斯神经网络的正交分解神经网络（POD-NN）降阶建模方法的发展。关于空间二维问题的网络。首先对基准问题进行测试，然后将其应用于实际应用：加拿大蒙特利尔，魁北克，大都会地区的MilleÎles河中的洪水预报。我们的设置涉及一组输入参数，这些参数可能具有嘈杂的分布，并累积由这些参数得出的仿真数据。目标是建立一个能够在不知道时知道的非侵入式代理模型，这在神经网络（以及一般来说在AI中）仍然是一个开放的研究领域。在该模型的帮助下，在知道模型不确定性的情况下生成了概率泛洪图。这些对未知数的洞察力也可用于不确定性传播任务，从而使洪泛区预测比使用常规不确定性不知情的替代模型所进行的预测更为广泛和安全。还介绍了我们对水坝溃坝的时间依赖性和高度非线性情况的研究。集成和贝叶斯方法都可以为多种平滑的物理解决方案提供可靠的结果，从而可以在分发不当时提供正确的警告。但是，前者