Modeling Vertical Planing Boat Motions using a Neural-Corrector Method

The dynamics of high-speed planing craft are complex and nonlinear. Standard analysis methods, such as linear potential theory, while convenient and computationally efficient, are often not suitable for use in predicting the dynamics of such craft because physical realities or design requirements invalidate the inherent assumptions. High-fidelity methods, such as state-of-the-art CFD simulations, can offer accurate solutions, but these methods are limited by computational cost and numerical sensitivity. In addition, these methods are not efficient enough to provide rapid evaluation of operability, i.e. simulations over a wide range of operating conditions and environments. This leaves few practical analysis options for small, high-speed craft designers who need to perform such predictions. In this paper, the authors present a neural-corrector method that shows promise in providing efficient predictions of vertical planing craft motions. The method retains higher-order terms typically truncated in the classical coupled 2-DOF system of ordinary differential equations using Long Short-Term Memory (LSTM) recurrent neural networks. In this manner, the robust solution provided by the linear model is retained, and the LSTM networks act as higher-order correctors. The correctors primarily regress on the solution, affording familiar numerical integration techniques for systems of nonlinear differential equations. Training and validation results from the method are compared to nonlinear simulations of 2-DOF motion of a Generic Prismatic Planing Hull (GPPH) at forward speed in head seas, with time histories given for both regular and irregular waves.