The use of adjoint problems solution in the identification of input parameters for transport models and planning of experiments

Abstract

In the numerical identification input model transport parameters of passive admixture in the measurement data raises the question of constructing the optimal plans for performing the measurement. From a mathematical point of view, the solution of inverse problems, the optimal plan is treated as a net of measurement points distributed across space and time that gives the best conditioning of identification input parameters of numerical simulations against measurements. Computational properties of algorithms for solving inverse problems can largely be improved by optimal schemes of measurements. At the core of the algorithms for optimal planning is the creation and study of the properties of Fisher information matrix, which is based on the Jacobian matrix characterizing the admixture concentration field variation dependence of variations parameters of the problem. For example, the one-dimensional problem of the transfer of passive admixtures discusses the assessment component of this matrix by a series of adjoint tasks of a special kind. As a result of numerical experiments with the one-dimensional model of transport of passive tracer shows that the best convergence of the variational algorithm for identifying the initial field of concentration is in the selection of measurement points in the region of maximum values. This scheme of measuring net leads to improved conditioning of the problem being solved. Additional information about the location of the boundaries of the pollution are also important in the algorithm initialization the initial distribution. Similar calculations are carried out with a three-dimensional model for the Azov sea. The results can be used for solving various ecological orientation problems in the study of the sources pollution influence of anthropogenic nature in the Azov and Black seas waters.