Deep learning methods for high-dimensional fluid dynamics problems : application to flood modeling with uncertainty quantification

While impressive results have been achieved in the well-known fields where Deep Learning allowed for breakthroughs such as computer vision, its impact on different older areas is still vastly unexplored. In Computational Fluid Dynamics and especially in Flood Modeling, many phenomena are very high-dimensional, and predictions require the use of numerical simulations, which can be, while very robust and tested, computationally heavy and may not prove useful in the context of real-time predictions. This issue led to various attempts at developing Reduced-Order Modeling techniques, both intrusive and non-intrusive. One recent relevant addition is a combination of Proper Orthogonal Decomposition with Deep Neural Networks (POD-NN). Yet, to our knowledge, little has been performed in implementing uncertainty-aware regression tools in the example of the POD-NN framework. In this work, we aim at comparing different novel methods addressing uncertainty quantification in Neural Networks, pushing forward the POD-NN concept with Deep Ensembles and Bayesian Neural Networks, which we first test on benchmark problems, and then apply to a real-life application: flooding predictions in the Mille-Iles river in Laval, QC, Canada. Building a non-intrusive surrogate model, able to know when it doesn’t know, is still an open research area as far as neural networks are concerned.