Wave Physics as Representation: Tensor-Structured Neural Reconstruction for Ocean Acoustic Fields

Reconstructing three-dimensional (3D) complex ocean acoustic fields from sparse measurements is challenging due to highly oscillatory wave structures and restricted sensing patterns/routes. Existing learning-based approaches generally fall into two categories. First, purely data-driven models can learn complex field patterns from data, but do not explicitly exploit the underlying wave physics that can potentially enhance interpretability and reduce training costs. Second, physics-informed methods impose a specified physical equation as a reconstruction constraint, but usually require the environment-dependent parameters to be known, which is difficult to acquire in practice. As a result, practical 3D acoustic field reconstruction that is both physically grounded and robust to uncertain environmental information remains largely unexplored. This work takes an alternative route: instead of solving a fully specified wave equation, it extracts a structured representation from the mathematical form of wave physics and learns its components from data. Starting from the Helmholtz equation and normal mode propagation, we derive a structured spatial–angular tensor representation, termed the $S/c$ representation. Under a low-rank specialization, it takes the form of a rank-$(L,L,1)$ block-term tensor decomposition, which connects structured sampling patterns/routes often used in ocean sensing practice to sufficient conditions for field recovery. Furthermore, building on this tensor representation, we propose TIDAL, a neural reconstructor that uses the $S/c$ representation as an inductive bias for structured decoding and aligns information aggregation with the sampling geometry. The neural learner removes the need for known model parameters required by conventional physics-based recovery methods. Experiments across three structured sampling geometries show that TIDAL achieves the best reconstruction performance and fastest inference among baselines, with clear benefits from the physics-derived representation under limited data and model capacity.