Parametric Nonlinear Volterra Series via Machine Learning: Transonic Aerodynamics

This study introduces an approach for modeling unsteady transonic aerodynamics within a parametric space using the Volterra series to capture aerodynamic responses and machine learning to enable interpolation. The first- and second-order Volterra kernels were derived from indicial aerodynamic responses obtained through computational fluid dynamics, with the second-order kernel calculated as a correction to the dominant linear response. Machine learning algorithms, specifically artificial neural network and Gaussian process regression, were used to interpolate kernel coefficients within a parameter space defined by the Mach number and angle of attack. The methodology was applied to two- and three-dimensional test cases in the transonic regime. The results underscore the benefit of including a second-order kernel to address strong nonlinearity and demonstrate the effectiveness of neural networks. The approach achieved a level of accuracy that appeared sufficient for use in conceptual design.