Efficient bridge pier scour profile prediction by an enhanced Bayesian DeepONet

This is the authors' abstract. We don't add key points for this paper.

Scour is one of the leading factors for bridge failures. However, the simulation cost of bridge pier scour is expensive due to turbulence and complex sediment transport. Leveraging the power of deep learning, we develop an enhanced Bayesian Deep Operator Network (DeepONet) for rapidly estimating the scour profile under clear-water scour conditions for parametric scour settings, providing more scour information than point estimation in many other machine-learning studies. We empower the DeepONet with several advanced techniques, including random Fourier features, sample-wise attention, multi-feature network fusion and knowledge-inspired constraints. In two predictive tasks, where the flow depth, the mean approach velocity and the median sediment size vary simultaneously in the first one, and the pier shape and the width change concurrently in the second one, the median normalized mean squared errors of test samples are lower than 0.05, which is better than the original DeepONet and more competitive than Fourier Neural Operator (FNO) in the second scenario. A computational cost analysis shows that while the cost of our method mainly hinges on the generation of training data, the trained models can predict for new scenarios almost instantly, demonstrating our competitive edges for scalability.