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.Comment: 11 pages, 2 page appendi
