PC-LNN: A physics-constrained liquid neural network for multi-scale ship radiated noise recognition

Ship radiated noise (SRN), as an inherent acoustic feature of ships during underwater operation, serves as an important information source for underwater target recognition and tracking. However, due to the complex marine environment, underwater noise is highly non-stationary, high- and low-frequency features are imbalanced, and data availability is limited, making it challenging to develop an accurate and interpretable model for SRN recognition. To address the aforementioned issues, this paper proposes a physics-constrained liquid neural network with multi-scale frequency decomposition model (PC-LNN). The PC-LNN firstly decomposes the raw signal into high- and low-frequency branches based on acoustic physical mechanisms, enabling decoupled multi-scale spectral representation. The features are then fed into the liquid neural network for continuous-time dynamic modeling and feature fusion. During training, a physics-consistent loss function that jointly composed of temporal smoothing constraints, low-frequency attenuation constraints, and high-frequency peak constraints is employed. The experimental results demonstrate that the recognition precision of this model can reach 99.83%, confirming its superior performance and robustness in underwater acoustic target recognition which demonstrates a strong practical value.