Statistical inference of dynamic systems via constrained Gaussian processes

Abstract: Parameter estimation of nonlinear dynamical system models from noisy and sparse experimental data is a vital task in many fields; it has challenged the existing inference methods, especially when there are unobserved system components. We propose a fast Bayesian inference method to estimate the ODE parameters with real data from biological/physical experiments via constrained Gaussian process. Our method utilizes Gaussian processes that are explicitly conditioned on the functional manifold that describes the ODE system. Using this constrained Gaussian process under the Bayesian paradigm, our method completely avoids the use of numerical solver and thus achieves dramatic saving in computational time. At the same time, our method also offers accurate inference, including uncertainly quantification. Our approach is distinct from the existing ones owing to its rigorous construction under the Bayesian framework. We demonstrate the speed and accuracy of the method using realistic examples, including examples with unobserved system components.

Mathematics

Audience: researchers in the topic

ICCM 2020