Variational Bayesian inference of dynamical system models

Music City Center 

Parameter estimation for nonlinear dynamical systems, represented by ordinary differential equations (ODEs), using noisy and sparse data is a vital task in many fields. We recently introduced a method, MAGI (MAnifold-constrained Gaussian process Inference), which uses a Gaussian process explicitly conditioned on the manifold constraint that the derivative of the Gaussian process must satisfy the ODE system. By doing so, we completely bypass the need for numerical integration and achieve substantial savings in computational time. When the dimension of the underlying ODE system becomes high, the Hamiltonian Monte Carlo employed by MAGI slows down. In this talk we will show how Stein variational gradient descent, a variation Bayes method, can significantly speed up the computation. MAGI with variational Bayes is distinct from existing approaches as we provide a principled statistical construction under a Bayesian framework, which incorporates the ODE system through the manifold constraint. We demonstrate the accuracy and speed of the method using realistic examples based on physical experiments, including inference with unobserved system components, which often occur in real experiments.

ordinary differential equations

Gaussian process

manifold constraint

gradient descent

variational Bayes

missing component