MODELING NON-STATIONARITY WITH DEEP GAUSSIAN PROCESSES: APPLICATIONS IN AEROSPACE ENGINEERING
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 wit...
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| Format: | Theses |
| Language: | Indonesia |
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| Online Access: | https://digilib.itb.ac.id/gdl/view/80575 |
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| Institution: | Institut Teknologi Bandung |
| Language: | Indonesia |
| Summary: | 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. |
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