Quantifying Uncertainty Using Physics-Based Covariance Models

Abstract: An important issue in quantifying uncertainty in the simulation of large-scale dynamical processes is to determine statistical models that appropriately account for their physical characteristics or nonstationarity. In this talk we describe a method to derive covariance kernels from underlying physical processes. Process nonstationarity is addressed implicitly by the physical parameterization and the resulting covariance matrices are typically full rank and well conditioned. Local processes can benefit from sparse representations and dimension splittings, which lead to both scalable solutions and reduced computational and storage requirements. We illustrate our approach on a data assimilation problem for reactive flows and kriging. Its potential application to numerical weather prediction models needed for energy systems operations with renewable resources is also discussed.