Physics-Informed Spatiotemporal Neural Network for Unsteady Propeller Wake Prediction via Least-Squares Finite-Difference Framework

Accurate prediction of unsteady propeller wakes is essential for advancing marine propulsion analysis and hydrodynamic design. The wake exhibits complex three-dimensional interactions among blade loading, rotation, and turbulence, producing highly transient velocity and pressure fields. High-fidelity methods such as direct numerical simulation (DNS) and large-eddy simulation (LES) can resolve these dynamics but are computationally prohibitive for iterative design and real-time analysis. Physics-informed neural networks (PINNs) offer a promising alternative by embedding physical laws into learning, yet conventional MLP-based formulations struggle to capture instantaneous unsteady features, leading to phase shifts and over-smoothed predictions. To overcome these deficiencies, we propose PhyLSNN, a physics-informed spatiotemporal framework that integrates a convolutional encoder-ConvLSTM-decoder architecture with a least-squares finite-difference (LSFD) formulation of the Navier-Stokes residuals. This hybridization enables the network to preserve coherent temporal evolution and physically accurate flow representations. Trained on LES-derived propeller flow data, PhyLSNN achieves high-fidelity and temporally stable reconstruction of velocity and pressure fields with minimal computational demand. The findings highlight PhyLSNN as a robust and physics-consistent framework for unsteady propeller wake prediction, offering an efficient pathway toward performance assessment and hydrodynamic design optimization.