Aalto University and FCAI professor Harri Lähdesmäki has with his colleagues introduced a new paradigm of non-parametric ordinary differential equations modeling that can learn the underlying dynamics of arbitrary continuous-time systems without prior knowledge.
For many complex systems it is practically impossible to determine equations or interactions that would govern the underlying dynamics. In these settings, a parametric ODE model cannot be formulated. Lähdesmäki and his team have now overcome this issue. They propose to learn non-linear, unknown differential functions from state observations using Gaussian process vector fields within the exact ODE formalism.
They demonstrate the model’s capabilities to infer dynamics from sparse data and to simulate the system forward into future.
See article by Markus Heinonen, Cagatay Yildiz, Henrik Mannerström, Jukka Intosalmi, Harri Lähdesmäki, ‘Learning unknown ODE models with Gaussian processes’:
https://arxiv.org/abs/1803.04303
The paper has been accepted to the International Conference on Machine Learning ICML 2018.