Green, David K. E. and Rindler, Filip (2019) Model inference for ordinary differential equations by parametric polynomial kernel regression. In: UNCECOMP 2019 : 3rd International Conference on Uncertainty Quantification in Computational Sciences and Engineering, Crete, Greece, 24-26 Jun 2019. Published in: UNCECOMP 2019 3rd ECCOMAS Thematic Conference on Uncertainty Quantification in Computational Sciences and Engineering pp. 263-285. doi:10.7712/120219.6340.18533

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Abstract

Model inference for dynamical systems aims to estimate the future behaviour of a system from observations. Purely model-free statistical methods, such as Artificial Neural Networks, tend to perform poorly for such tasks. They are therefore not well suited to many
questions from applications, for example in Bayesian filtering and reliability estimation.
This work introduces a parametric polynomial kernel method that can be used for inferring the future behaviour of Ordinary Differential Equation models, including chaotic dynamical systems, from observations. Using numerical integration techniques, parametric representations of Ordinary Differential Equations can be learnt using Backpropagation and Stochastic Gradient Descent. The polynomial technique presented here is based on a nonparametric
method, kernel ridge regression. However, the time complexity of nonparametric kernel ridge regression scales cubically with the number of training data points. Our parametric polynomial
method avoids this manifestation of the curse of dimensionality, which becomes particularly relevant when working with large time series data sets.
Two numerical demonstrations are presented. First, a simple regression test case is used to illustrate the method and to compare the performance with standard Artificial Neural Network
techniques. Second, a more substantial test case is the inference of a chaotic spatio-temporal dynamical system, the Lorenz–Emanuel system, from observations. Our method was able to
successfully track the future behaviour of the system over time periods much larger than the training data sampling rate. Finally, some limitations of the method are presented, as well as
proposed directions for future work to mitigate these limitations.

Item Type:	Conference Item (Paper)
Subjects:	Q Science > QA Mathematics
Divisions:	Faculty of Science, Engineering and Medicine > Science > Mathematics
Journal or Publication Title:	UNCECOMP 2019 3rd ECCOMAS Thematic Conference on Uncertainty Quantification in Computational Sciences and Engineering
Publisher:	Proceedia
Official Date:	24 April 2019
Dates:	Date Event 24 April 2019 Accepted
Page Range:	pp. 263-285
DOI:	10.7712/120219.6340.18533
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Restricted or Subscription Access
Date of first compliant deposit:	24 April 2019
Date of first compliant Open Access:	2 May 2019
Conference Paper Type:	Paper
Title of Event:	UNCECOMP 2019 : 3rd International Conference on Uncertainty Quantification in Computational Sciences and Engineering
Type of Event:	Conference
Location of Event:	Crete, Greece
Date(s) of Event:	24-26 Jun 2019
Related URLs:	Publisher

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