Niu, M., Wandy, J. , Daly, R. , Rogers, S. and Husmeier, D. (2021) R package for statistical inference in dynamical systems using kernel based gradient matching: KGode. Computational Statistics, 36(1), pp. 715-747. (doi: 10.1007/s00180-020-01014-x)
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Abstract
Many processes in science and engineering can be described by dynamical systems based on nonlinear ordinary differential equations (ODEs). Often ODE parameters are unknown and not directly measurable. Since nonlinear ODEs typically have no closed form solution, standard iterative inference procedures require a computationally expensive numerical integration of the ODEs every time the parameters are adapted, which in practice restricts statistical inference to rather small systems. To overcome this computational bottleneck, approximate methods based on gradient matching have recently gained much attention. The idea is to circumvent the numerical integration step by using a surrogate cost function that quantifies the discrepancy between the derivatives obtained from a smooth interpolant to the data and the derivatives predicted by the ODEs. The present article describes the software implementation of a recent method that is based on the framework of reproducing kernel Hilbert spaces. We provide an overview of the methods available, illustrate them on a series of widely used benchmark problems, and discuss the accuracy–efficiency trade-off of various regularization methods.
| Item Type: | Articles |
|---|---|
| Status: | Published |
| Refereed: | Yes |
| Glasgow Author(s) Enlighten ID: | Niu, Dr Mu and Daly, Dr Ronan and Wandy, Dr Joe and Husmeier, Professor Dirk and Rogers, Dr Simon |
| Authors: | Niu, M., Wandy, J., Daly, R., Rogers, S., and Husmeier, D. |
| College/School: | College of Medical Veterinary and Life Sciences > School of Cancer Sciences College of Science and Engineering > School of Computing Science College of Science and Engineering > School of Mathematics and Statistics |
| Journal Name: | Computational Statistics |
| Publisher: | Springer |
| ISSN: | 0943-4062 |
| ISSN (Online): | 1613-9658 |
| Published Online: | 23 July 2020 |
| Copyright Holders: | Copyright © 2020 The Authors |
| First Published: | First published in Computational Statistics 36(1): 715-747 |
| Publisher Policy: | Reproduced in accordance with the copyright policy of the publisher |
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