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Learning unknown ODE models with Gaussian processes
Markus Heinonen · Cagatay Yildiz · Henrik Mannerström · Jukka Intosalmi · Harri Lähdesmäki

Thu Jul 12 09:15 AM -- 12:00 PM (PDT) @ Hall B #71

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.

Author Information

Markus Heinonen (Aalto University)
Cagatay Yildiz (Aalto University)
Henrik Mannerström (Aalto University)
Jukka Intosalmi (Aalto University)
Harri Lähdesmäki (Aalto University)

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