Deep neural network for learning wave scattering and interference of underwater acoustics

It is challenging to construct generalized physical models of underwater wave propagation owing to their complex physics and widely varying environmental parameters and dynamical scales. In this article, we present a deep convolutional recurrent autoencoder network (CRAN) for data-driven learning of complex underwater wave scattering and interference. We specifically consider the dynamics of underwater acoustic scattering from various non-uniform seamount shapes leading to complex wave interference patterns of back-scattered and forward-propagated waves. The CRAN consists of a convolutional autoencoder for learning low-dimensional system representation and a long short-term memory (LSTM)-based recurrent neural network for predicting system evolution in low dimensions. The convolutional autoencoder enables efficient dimension reduction of wave propagation by independently learning global and localized wave features. To improve the time horizon of wave dynamics prediction, we introduce an LSTM architecture with a single-shot learning mechanism and optimal time-delayed data embedding. On training the CRAN over 30 cases containing various seamount geometries and acoustic source frequencies, we can predict wave propagation up to a time horizon of 5 times the initiation sequence length for 15 out-of-training cases with a mean L2 error of approximately 10%. For selected out-of-training cases, the prediction time horizon could be increased to 6 times the initiation sequence length. Importantly, such predictions are obtained with physically consistent wave scattering and wave interference patterns and at 50% lower L2 error compared to routinely use standard LSTMs. These results demonstrate the potential of employing such deep neural networks for learning complex underwater ocean acoustic propagation physics.