Online prediction of dynamical system behavior based on a combination of simulation data and sensor measurement data has numerous applications. Examples include predicting safe flight configurations, forecasting storms and wildfire spread, estimating railway track and pipeline health conditions. In such applications, high-fidelity simulations may be used to accurately predict a system’s dynamical behavior offline (“non-real time”). However, due to the computational expense, these simulations have limited usage for online (“real-time”) prediction of a system’s behavior. To remedy this, one possible approach is to allocate a significant portion of the computational effort to obtain data through offline simulations. The obtained offline data can then be combined with online sensor measurements for online estimation of the system’s behavior with comparable accuracy as the off-line, high-fidelity simulation. The main contribution of this paper is in the construction of a fast data-driven spatiotemporal prediction framework that can be used to estimate general parametric dynamical system behavior. This is achieved through three steps. First, high-order singular value decomposition is applied to map high-dimensional offline simulation datasets into a subspace. Second, Gaussian processes are constructed to approximate model parameters in the subspace. Finally, reduced-order particle filtering is used to assimilate sparsely located sensor data to further improve the prediction. The effectiveness of the proposed approach is demonstrated through a case study. In this case study, aeroelastic response data obtained for an aircraft through simulations is integrated with measurement data obtained from a few sparsely located sensors. Through this case study, the authors show that along with dynamic enhancement of the state estimates, one can also realize a reduction in uncertainty of the estimates.

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