Learning unknown ODE models with Gaussian processes

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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.
Original languageEnglish
Title of host publicationProceedings of the 35th International Conference on Machine Learning, ICML 2018
Pages3120-3132
Number of pages13
Volume5
ISBN (Electronic)9781510867963
Publication statusPublished - 2018
MoE publication typeA4 Article in a conference publication
EventInternational Conference on Machine Learning - Stockholm, Sweden
Duration: 10 Jul 201815 Jul 2018
Conference number: 35

Publication series

NameProceedings of Machine Learning Research
PublisherPMLR
Volume80
ISSN (Electronic)1938-7228

Conference

ConferenceInternational Conference on Machine Learning
Abbreviated titleICML
CountrySweden
CityStockholm
Period10/07/201815/07/2018

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  • Cite this

    Heinonen, M., Yildiz, C., Mannerström, H., Intosalmi, J., & Lähdesmäki, H. (2018). Learning unknown ODE models with Gaussian processes. In Proceedings of the 35th International Conference on Machine Learning, ICML 2018 (Vol. 5, pp. 3120-3132). (Proceedings of Machine Learning Research; Vol. 80). http://proceedings.mlr.press/v80/heinonen18a.html