Prospects of neural SDEs for Bayesian smoothing
Typ
Examensarbete för masterexamen
Master's Thesis
Master's Thesis
Program
Engineering mathematics and computational science (MPENM), MSc
Publicerad
2024
Författare
Winqvist, Samuel
Wikman, Isak
Modellbyggare
Tidskriftstitel
ISSN
Volymtitel
Utgivare
Sammanfattning
Due to the importance of airspace defence for national security, the pursuit of efficient
and accurate methods for tracking airborne targets is of great interest. An essential
part of target tracking is to estimate the state of a target given (noisy) observations
from a radar. This involves calculating conditional probability distributions
given measurements (e.g. smoothing), which is associated with large computational
costs for high-dimensional and/or nonlinear target models. This thesis investigates
the possibility of alleviating such bottlenecks by employing neural stochastic differential
equations (neural SDEs) as generative models for the smoothing problem -
possibly allowing the use of more complex models in real-time applications. As part
of this work, it is first shown that SDE models can be used as generative models
for conditional distributions of target states given noisy measurements obtained at
discrete points of time. Secondly, this thesis presents a detailed description of how
the neural SDE is utilized as the generator of a so called Wasserstein Generative Adversarial
Network (WGAN) in signature space, meaning it can be trained to approximate
conditional probability distributions for the smoothing problem. Thirdly, the
SDE-model is evaluated with respect to a series of test-problems. Findings indicate
that the neural SDE can reproduce qualitative features for conditional distributions
for nonlinear problems, while further developments of the method and paradigms
for training are needed to achieve trained SDE-models which are perceived to (in
distribution) closely resemble their theoretically exact counterparts.
Beskrivning
Ämne/nyckelord
smoothing, filtering, target identification, nonlinear, neural networks, generative AI, neural SDE, particle filter, signature, Wasserstein, GAN, generative adversarial network.