Estimating Parameters of Partial Differential Equations with Gradient Matching

Liu, Z., Macdonald, B. , Husmeier, D. and Giurghita, D. (2017) Estimating Parameters of Partial Differential Equations with Gradient Matching. Other. University of Glasgow. (Unpublished)

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: Research Reports or Papers (Other)
• Status: Unpublished
• Glasgow Author(s) Enlighten ID: Giurghita, Miss Diana and Husmeier, Professor Dirk and Macdonald, Dr Benn
• Authors: Liu, Z., Macdonald, B., Husmeier, D., and Giurghita, D.
• College/School: College of Science and Engineering > School of Mathematics and Statistics > Statistics
• Publisher: University of Glasgow
• Copyright Holders: Copyright © 2017 The Authors
• Publisher Policy: Reproduced with the permission of the authors