Polynomial ridge flowfield estimation

Abstract

Computational fluid dynamics plays a key role in the design process across many industries. Recently, there has been increasing interest in data-driven methods in order to exploit the large volume of data generated by such computations. This paper introduces the idea of using spatially correlated polynomial ridge functions for rapid flowfield estimation. Dimension reducing ridge functions are obtained for numerous points within training flowfields. The functions can then be used to predict flow variables for new, previously unseen, flowfields. Their dimension reducing nature alleviates the problems associated with visualizing high-dimensional datasets, enabling improved understanding of design spaces and potentially providing valuable physical insights. The proposed framework is computationally efficient; consisting of either readily parallelizable tasks or linear algebra operations. To further reduce the computational cost, ridge functions need only be computed at a small number of subsampled locations. The flow physics encoded within covariance matrices obtained from the training flowfields can then be used to predict flow quantities, conditional upon those predicted by the ridge functions at the sampled points. To demonstrate the efficacy of the framework, the incompressible flow around an ensemble of airfoils is used as a test case. The ridge functions' predictive accuracy is found to be competitive with a state-of-the-art convolutional neural network. The local ridge functions can also be reused to obtain surrogate models for integral quantities, avoiding the need for long-term storage of the training data. Finally, use of the ridge framework with varying boundary conditions is demonstrated on a transonic wing.