R package for statistical inference in dynamical systems using kernel based gradient matching: KGode

Mu Niu (), Joe Wandy (), Rónán Daly (), Simon Rogers () and Dirk Husmeier ()
Additional contact information
Mu Niu: University of Glasgow
Joe Wandy: University of Glasgow
Rónán Daly: University of Glasgow
Simon Rogers: University of Glasgow
Dirk Husmeier: University of Glasgow

Computational Statistics, 2021, vol. 36, issue 1, No 30, 715-747

Abstract: 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.

Keywords: Ordinary differential equations; Gradient matching; Reproducing kernel Hilbert space; Regularization; Time warping; Residual bootstrap (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s00180-020-01014-x

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