Physics-Constrained Multilayer Perceptron for Flow Field Inversion in Coastal Acoustic Tomography

Accurate flow field inversion in coastal acoustic tomography (CAT) is crucial for improving ocean environmental monitoring, ecological management, marine engineering safety, and disaster early warning. The conventional tapered least squares (TLS) method primarily relies on Fourier expansion to represent the flow field and employs the L-curve method for regularization. However, this method often suffers from severe ill-posedness, leading to inaccurate inversion, local inversion anomalies, or even complete failure. To overcome these limitations, a novel inversion framework termed the physics-constrained multilayer perceptron (PCMLP) is proposed, which integrates physical constraints into a multilayer perceptron (MLP) architecture. Specifically, the MLP maps the forward-calculated range-averaged currents to the Fourier coefficients of the stream function, and a soft constraint penalizing the nonzero net flux through the domain boundary is incorporated to enhance the stability and accuracy of the inversion. Experimental results demonstrate that, when validated against acoustic Doppler current profiler (ADCP) measurements, the PCMLP model with λ = 0.01 reduces the mean absolute error of flow velocity inversion by 39.79% and the root mean square error by 33.01%, relative to the conventional TLS method, significantly improving the accuracy and stability of horizontal flow field inversion. After training, the PCMLP model requires approximately 19 times fewer multiply-accumulate operations per inference step than the TLS method, making it suitable for real-time or repeated deployments. The proposed method shows strong potential for broad applications in CAT-based flow field inversion and prediction, offering a robust and high-precision solution for ocean flow field observation.