Learning unknown ODE models with Gaussian processes

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Journal Title
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Conference article in proceedings
Date
2018
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Language
en
Pages
13
3120-3132
Series
Proceedings of the 35th International Conference on Machine Learning, ICML 2018, Volume 5, Proceedings of Machine Learning Research, Volume 80
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.
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Citation
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 , Proceedings of Machine Learning Research , vol. 80 , International Machine Learning Society , pp. 3120-3132 , International Conference on Machine Learning , Stockholm , Sweden , 10/07/2018 . < http://proceedings.mlr.press/v80/heinonen18a.html >