We propose a general method for predicting multiple steps ahead of our target system and estimating simultaneously the prediction errors in a real time. The requirement of the proposed method is that we have a time series of the target system. We demonstrate the method by artificial data, real...

Covariance parameter estimation of Gaussian processes is analyzed in an asymptotic framework. The spatial sampling is a randomly perturbed regular grid and its deviation from the perfect regular grid is controlled by a single scalar regularity parameter. Consistency and asymptotic normality are...

One of the most difficult tasks in subsurface flow simulations is the reliable characterization of properties of the subsurface. A typical situation employs dynamic data integration such as sparse (in space and time) measurements to be matched with simulated responses associated with a set of...

The Maximum Likelihood (ML) and Cross Validation (CV) methods for estimating covariance hyper-parameters are compared, in the context of Kriging with a misspecified covariance structure. A two-step approach is used. First, the case of the estimation of a single variance hyper-parameter is...

The remediation of groundwater sites has been recognized as a difficult and expensive task for years. One of the challenges is that the success of remediation is usually contingent upon an appropriate level of characterization of the physical, chemical, and biological site properties. For...

During system development, large-scale, complex energy systems require multi-disciplinary efforts to achieve system quality, cost, and performance goals. As systems become larger and more complex, the number of possible system configurations and technologies, which meet the designer’s...

We consider periodic problems of autonomous systems of ordinary differential equations or differential algebraic equations. To quantify uncertainties of physical parameters, we introduce random variables in the systems. Phase conditions are required to compute the resulting periodic random...