Non-Intrusive Reduced-Order Modeling Using Uncertainty-Aware Deep Neural Networks and Proper Orthogonal Decomposition: Application to Flood Modeling

Abstract

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.

To be published in the Journal of Computational Physics

References in corpus (19)

• Distributed Representations of Words and Phrases and their Compositionality
• Auto-Encoding Variational Bayes
• Explaining and Harnessing Adversarial Examples
• Discovering governing equations from data: Sparse identification of nonlinear dynamical systems
• Generative Adversarial Networks
• What Uncertainties Do We Need in Bayesian Deep Learning for Computer Vision?
• Weight Uncertainty in Neural Networks
• B-PINNs: Bayesian Physics-Informed Neural Networks for Forward and Inverse PDE Problems with Noisy Data
• Can You Trust Your Model's Uncertainty? Evaluating Predictive Uncertainty Under Dataset Shift
• Machine Learning of Linear Differential Equations using Gaussian Processes
• Probabilistic Backpropagation for Scalable Learning of Bayesian Neural Networks
• Horovod: fast and easy distributed deep learning in TensorFlow
• Deep Learning of Vortex Induced Vibrations
• TensorFlow Distributions
• Recovering missing CFD data for high-order discretizations using deep neural networks and dynamics learning
• Quality of Uncertainty Quantification for Bayesian Neural Network Inference
• A non-intrusive reduced-order modeling method using polynomial chaos expansion
• Deep Sub-Ensembles for Fast Uncertainty Estimation in Image Classification
• An adaptive surrogate modeling based on deep neural networks for large-scale Bayesian inverse problems

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• Empowering Bayesian Neural Networks with Functional Priors through Anchored Ensembling for Mechanics Surrogate Modeling Applications
• Numerical assessments of a nonintrusive surrogate model based on recurrent neural networks and proper orthogonal decomposition: Rayleigh Benard convection
• A non-intrusive reduced-order modelling for uncertainty propagation of time-dependent problems using a B-splines Bézier elements-based method and Proper Orthogonal Decomposition: application to dam-break flows