Physics-informed spatiotemporal neural network for unsteady propeller wake prediction via least squares finite-difference framework

The accurate prediction of unsteady propeller wake dynamics is pivotal for advancing marine propulsion analysis and hydrodynamic design. These wakes are characterized by complex three-dimensional interactions involving blade loading, rotation, and turbulence, resulting in highly transient velocity and pressure fields. High-fidelity methods such as direct numerical simulation and large-eddy simulation (LES) can resolve these dynamics but are computationally prohibitive for iterative design and real-time analysis. Physics-informed neural networks offer a promising alternative by embedding physical laws into learning, yet conventional multilayer perceptron-based formulations often fail to capture instantaneous unsteady features, leading to phase shifts and over-smoothed predictions. To address these challenges, we propose the physics-informed Least Squares Neural Network (PhyLSNN), a novel spatiotemporal framework for propeller wake prediction. The architecture integrates a convolutional encoder-convolutional long short-term memory-decoder backbone with a least squares finite-difference scheme to robustly compute 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.