A Python Toolbox for Data-Driven Aerodynamic Modeling Using Sparse Gaussian Processes

Abstract

In aerodynamics, characterizing the aerodynamic behavior of aircraft typically requires a large number of observation data points. Real experiments can generate thousands of data points with suitable accuracy, but they are time-consuming and resource-intensive. Consequently, conducting real experiments at new input configurations might be impractical. To address this challenge, data-driven surrogate models have emerged as a cost-effective and time-efficient alternative. They provide simplified mathematical representations that approximate the output of interest. Models based on Gaussian Processes (GPs) have gained popularity in aerodynamics due to their ability to provide accurate predictions and quantify uncertainty while maintaining tractable execution times. To handle large datasets, sparse approximations of GPs have been further investigated to reduce the computational complexity of exact inference. In this paper, we revisit and adapt two classic sparse methods for GPs to address the specific requirements frequently encountered in aerodynamic applications. We compare different strategies for choosing the inducing inputs, which significantly impact the complexity reduction. We formally integrate our implementations into the open-source Python toolbox SMT, enabling the use of sparse methods across the GP regression pipeline. We demonstrate the performance of our Sparse GP (SGP) developments in a comprehensive 1D analytic example as well as in a real wind tunnel application with thousands of training data points.