Liu, Zhongyi (2017) Estimating parameters of partial differential equations with gradient matching. [MSc]
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Abstract
Parameter inference in partial differential equations (PDEs) is a problem that many researchers are interested in. The conventional methods suffer from severe computational costs because these method require to solve the PDEs repeatedly by numerical integration. The concept of gradient matching have been proposed in order to reduce the computational complexity, which consists of two steps. First, the data are interpolated with certain smoothing methods. Then, the partial derivatives of the interpolants are calculated and the parameters are optimized to minimize the distance (measured by loss functions) between partial derivatives of interpolants and the PDE systems. In this article, we first studied the parameter inference accuracy of gradient matching based on two simple PDE models. Then the method of gradient matching was used to infer the parameters of PDE models describing cell movement and select the most appropriate model.
Item Type: | Masters Dissertation |
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Keywords: | Partial differential equations, gradient matching, Gaussian processes, cell movement, parameter inference. |
Course: | Postgraduate Courses > Statistics [MSc] |
Degree Level: | MSc |
College/School: | College of Science and Engineering > School of Mathematics and Statistics > Statistics |
ID Code: | 204 |
Deposited By: | Mrs Marie Cairney |
Supervisor: | Supervisor Email Macdonald, Dr. Benn Benn.Macdonald@glasgow.ac.uk Husmeier, Professor Dirk Dirk.Husmeier@glasgow.ac.uk Giughita, Miss Diana d.giurghita.1@research.gla.ac.uk |
Deposited On: | 18 May 2018 12:27 |
Last Modified: | 18 May 2018 13:29 |
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