Learning unknown ODE models with Gaussian processes
This provides a new paradigm for modeling continuous-time systems where parametric equations are unavailable, addressing a bottleneck in fields like physics or biology.
The authors tackled the problem of modeling complex systems with unknown governing equations by introducing a nonparametric ODE approach using Gaussian process vector fields, which can infer dynamics from sparse data and simulate future states without prior knowledge.
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.