Striking the right balance: Three-dimensional ocean sound speed field reconstruction using tensor neural networks

Accurately reconstructing a three-dimensional (3D) ocean sound speed field (SSF) is essential for various ocean acoustic applications, but the sparsity and uncertainty of sound speed samples across a vast ocean region make it a challenging task. To tackle this challenge, a large body of reconstruction methods has been developed, including spline interpolation, matrix/tensor-based completion, and deep neural networks (DNNs)-based reconstruction. However, a principled analysis of their effectiveness in 3D SSF reconstruction is still lacking. This paper performs a thorough analysis of the reconstruction error and highlights the need for a balanced representation model that integrates expressiveness and conciseness. To meet this requirement, a 3D SSF-tailored tensor DNN is proposed, which uses tensor computations and DNN architectures to achieve remarkable 3D SSF reconstruction. The proposed model not only includes the previous tensor-based SSF representation model as a special case but also has a natural ability to reject noise. The numerical results using the South China Sea 3D SSF data demonstrate that the proposed method outperforms state-of-the-art methods. The code is available at https://github.com/OceanSTARLab/Tensor-Neural-Network.