Learning unknown ODE models with Gaussian processes

2018/03/12 by Markus Heinonen, Çağatay Yıldız, Heinonen, Markus +7 · 13 citations
Computer Science · Engineering · #Advanced Multi-Objective Optimization Algorithms #Control Systems and Identification #FOS: Computer and information sciences #Gaussian Processes and Bayesian Inference #Machine Learning (stat.ML)

paper · pdf · doi:10.48550/arxiv.1803.04303

openalex publication_date 2018/03/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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