Data assimilation strives to determine optimally the state of an evolving physical system from a limited number of observations. The present study proposes to apply the extended Kalman filter (EKF) method of data assimilation to baseline models in the nuclear weapons program as a certification tool for the model's predictive capabilities and associated uncertainty quantification. EKF solves the full nonlinear state evolution in time and estimates its time-dependent error-covariance matrix (i.e., uncertainties) through a first-order approximation. The state variables and model parameters are updated by the blending of past model evolution with currently available data, along with their associated minimized errors. These variables and parameters are then used as initial conditions for further prediction till the next time at which data becomes available, or if data is no longer available, till any desired future time.
The EKF method has the capabilities to fulfill several important requirements that have been addressed in numerous white papers or reports of weapon certification. These requirements are: (1) predictive capabilities, (2) ability to utilize sparse data, and (3) performance gates obtained for different stages in time. Most importantly, EKF estimates uncertainties requiring the full assessment of the errors of computer codes and available data; this is one essential part of physics-based certification. Results of assimilating data from a 1-D flyer plate experiment will be given in the talk.