Learning unknown ODE models with Gaussian processes

Markus Heinonen, Cagatay Yildiz, Henrik Mannerström, Jukka Intosalmi, Harri Lähdesmäki
Proceedings of the 35th International Conference on Machine Learning, PMLR 80:1959-1968, 2018.

Abstract

In conventional ODE modelling coefficients of an equation driving the system state forward in time are estimated. However, for many complex systems it is practically impossible to determine the equations or interactions governing the underlying dynamics. In these settings, parametric ODE model cannot be formulated. Here, we overcome this issue by introducing a novel paradigm of nonparametric ODE modelling that can learn the underlying dynamics of arbitrary continuous-time systems without prior knowledge. We propose to learn non-linear, unknown differential functions from state observations using Gaussian process vector fields within the exact ODE formalism. We demonstrate the model’s capabilities to infer dynamics from sparse data and to simulate the system forward into future.

Cite this Paper

BibTeX
@InProceedings{pmlr-v80-heinonen18a, title = {Learning unknown {ODE} models with {G}aussian processes}, author = {Heinonen, Markus and Yildiz, Cagatay and Mannerstr{\"o}m, Henrik and Intosalmi, Jukka and L{\"a}hdesm{\"a}ki, Harri}, booktitle = {Proceedings of the 35th International Conference on Machine Learning}, pages = {1959--1968}, year = {2018}, editor = {Dy, Jennifer and Krause, Andreas}, volume = {80}, series = {Proceedings of Machine Learning Research}, month = {10--15 Jul}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v80/heinonen18a/heinonen18a.pdf}, url = {https://proceedings.mlr.press/v80/heinonen18a.html}, abstract = {In conventional ODE modelling coefficients of an equation driving the system state forward in time are estimated. However, for many complex systems it is practically impossible to determine the equations or interactions governing the underlying dynamics. In these settings, parametric ODE model cannot be formulated. Here, we overcome this issue by introducing a novel paradigm of nonparametric ODE modelling that can learn the underlying dynamics of arbitrary continuous-time systems without prior knowledge. We propose to learn non-linear, unknown differential functions from state observations using Gaussian process vector fields within the exact ODE formalism. We demonstrate the model’s capabilities to infer dynamics from sparse data and to simulate the system forward into future.} }
Endnote
%0 Conference Paper %T Learning unknown ODE models with Gaussian processes %A Markus Heinonen %A Cagatay Yildiz %A Henrik Mannerström %A Jukka Intosalmi %A Harri Lähdesmäki %B Proceedings of the 35th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2018 %E Jennifer Dy %E Andreas Krause %F pmlr-v80-heinonen18a %I PMLR %P 1959--1968 %U https://proceedings.mlr.press/v80/heinonen18a.html %V 80 %X In conventional ODE modelling coefficients of an equation driving the system state forward in time are estimated. However, for many complex systems it is practically impossible to determine the equations or interactions governing the underlying dynamics. In these settings, parametric ODE model cannot be formulated. Here, we overcome this issue by introducing a novel paradigm of nonparametric ODE modelling that can learn the underlying dynamics of arbitrary continuous-time systems without prior knowledge. We propose to learn non-linear, unknown differential functions from state observations using Gaussian process vector fields within the exact ODE formalism. We demonstrate the model’s capabilities to infer dynamics from sparse data and to simulate the system forward into future.
APA
Heinonen, M., Yildiz, C., Mannerström, H., Intosalmi, J. & Lähdesmäki, H.. (2018). Learning unknown ODE models with Gaussian processes. Proceedings of the 35th International Conference on Machine Learning, in Proceedings of Machine Learning Research 80:1959-1968 Available from https://proceedings.mlr.press/v80/heinonen18a.html.

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