63 Probabilistic forecast of nonlinear dynamical systems with uncertainty quantification

Oregon Convention Center 

Data-driven modeling is useful for reconstructing nonlinear dynamical systems when the underlying process is unknown or too expensive to compute. In this work, we first extend parallel partial Gaussian processes to predict the vector-valued transition function and quantify uncertainty of predictions by posterior sampling. Second, we show the equivalence between dynamic mode decomposition (DMD) and the maximum likelihood estimator of the transition matrix in the linear state space model, offering a probabilistic generative model for DMD and enabling uncertainty quantification. For systems containing noises, the lack of noise term in DMD prohibits reliable estimation of the dimensions and transition matrix. We integrate Kalman Filter into a fast expectation-maximization (E-M) algorithm for reducing the computation order and no additional numerical optimization is required in each step of the E-M algorithm. We study two examples in climate science and simulating quantum many-body systems far from equilibrium. The examples indicate that uncertainty of forecast can be properly quantified, whereas model or input misspecification can degrade the accuracy of uncertainty quantification.

Bayesian priors

Dynamic mode decomposition

Forecast

Gaussian processes

Noisy systems

Uncertainty quantification 

Uncertainty Quantification in Complex Systems Interest Group