A model-data weak formulation for simultaneous estimation of state and model bias

[摘要] We introduce a Petrov–Galerkin regularized saddle approximation which incorporates a ;;model” (partial differential equation) and ;;data” (M experimental observations) to yield estimates for both state and model bias. We provide an a priori theory that identifies two distinct contributions to the reduction in the error in state as a function of the number of observations, M: the stability constant increases with M; the model-bias best-fit error decreases with M. We present results for a synthetic Helmholtz problem and an actual acoustics system.

[发布机构] Elsevier