Accelerating Gaussian Process Emulators for Computer Simulations Using Random Fourier Features

Music City Center 

Computer simulations are essential for exploring input-output relationships in engineering and science but can be computationally expensive for extensive what-if analyses. Gaussian process emulators offer a powerful statistical approach to approximating simulations, but their scalability is often hindered by the costly inversion of large correlation matrices. To overcome this challenge, we introduce new methods leveraging the random Fourier feature technique from computer science to accelerate Gaussian process emulators. Our approach enhances computational efficiency while maintaining accuracy, making it suitable for a broad range of simulations, including those with gradient information, functional outputs, and stochastic outputs. Through numerical experiments, we demonstrate that our methods outperform existing ones in speed and accuracy, with theoretical results validating these improvements.

Digital Engineering