MODELING NON-STATIONARITY WITH DEEP GAUSSIAN PROCESSES: APPLICATIONS IN AEROSPACE ENGINEERING

• Main Author: Faiz Izzaturrahman, Muhammad
• Format: Theses
• Language: Indonesia
• Subjects: Teknik (Rekayasa, enjinering dan kegiatan berkaitan)
• Online Access: https://digilib.itb.ac.id/gdl/view/80575
• Institution: Institut Teknologi Bandung

Non-stationary responses are prevalent in much of the data sets aerospace engineers face. From the resulting flow variables in a shock-dominated flow to the highly non-linear relationships entailed in an aeroelastic wind turbine simulation. Complex responses calls for a more complex model and with the rising trend in hierarchical models, Deep Gaussian Processes (DGP) introduces itself competitive, by offering a probabilistic framework for deep learning. Formulated as a composition of Gaussian Processes (GP), the resulting DGP model is more expressive. However, at the cost of an intractable posterior distribution. With the current state-of-the-art Doubly Stochastic DGP utilizing variational inference to approximate the posterior, recent studies has shown the assumptions used in the latter model unsuitable for several cases. To that end, a new sampling approach to inference, dubbed the DGP with Stochastic Imputation (DGP-SI) has been recently proposed in order to overcome the problems faced with variational inference. The present study considers the task of providing a benchmark for surrogate modeling with the DGP-SI model. This is done through three aerospace-related problems of increasing dimension and sampling size, wherein, all datasets display a discontinuous-like feature. A stationary GPR model is used to provide a comparison for the DGP-SI. Results indicate that on average, the DGP-SI performs better than the GPR model for the two- and three- dimensional problems. However, in increasing the dimensions, the DGP-SI performs slightly worse than the GPR but remains variable in its performance indicating a greater potential to improve. Which is proven by increasing the number of training samples, yet, at the expense of computational cost.