Parameter identification techniques applied to an environmental pollution model

Abstract

The retrieval of parameters related to an environmental model is explored. We address computational challenges occurring due to a significant numerical difference of up to two orders of magnitude between the two model parameters we aim to retrieve. First, the corresponding optimization problem is poorly scaled, causing minimization algorithms to perform poorly (see Gill et al.,practical optimization, AP,1981,401pp). This issue is addressed by proper rescaling. Difficulties also arise from the presence of strong nonlinearity and ill-posedness which means that the parameters do not converge to a single deterministic set of values, but rather there exists a range of parameter combinations that produce the same model behavior. We address these computational issues by the addition of a regularization term in the cost function. All these computational approaches are addressed in the framework of variational adjoint data assimilation. The used observational data are derived from numerical simulation results located at only two spatial points. The effect of different initial guess values of parameters on retrieval results is also considered. As indicated by results of numerical experiments, the method presented in this paper achieves a near perfect parameter identification, and overcomes the indefiniteness that may occur in inversion process even in the case of noisy input data.

Visual inference of flow flux via free surface PDE model and image sequence assimilation

“…The second is that the filtering method is sequential. In practice, the variational framework is more proper to deal with the parameter identification problem [30]. For our problem, the filtering method is more suitable since it can provide estimation once the image observation is done.…”