Neural Ordinary Differential Equations for rotorcraft aerodynamics

Abstract

High-fidelity computational simulations of aerodynamics and structural dynamics on rotorcraft are essential for helicopter design, testing, and evaluation. These simulations usually entail a high computational cost even with modern high-performance computing resources. Reduced order models can significantly reduce the computational cost of simulating rotor revolutions. However, reduced order models are less accurate than traditional numerical modeling approaches, making them unsuitable for research and design purposes. This study explores the use of a new modified Neural Ordinary Differential Equation (NODE) approach as a machine learning alternative to reduced order models in rotorcraft applications—specifically to predict the pitching moment on a rotor blade section from an initial condition, mach number, chord velocity and normal velocity. The results indicate that NODEs cannot outperform traditional reduced order models, but in some cases they can outperform simple multilayer perceptron networks. Additionally, the mathematical structure provided by NODEs seems to favor time-dependent predictions. We demonstrate how this mathematical structure can be easily modified to tackle more complex problems. The work presented in this report is intended to establish an initial evaluation of the usability of the modified NODE approach for time-dependent modeling of complex dynamics over seen and unseen domains.