Sparsity-promoting PC-EnKF Method With Rotation For Inversing Topographic Parameters In Shallow Water Equation

The ensemble Kalman filter developed from the polynomial chaos expansion(PC-EnKF for short)is competitive for solving the nonlinear high-dimensional inverse problem with the advantage of non-intrusive method and the sampling in high-dimensional space.However,the so called "curse of dimensionality" is also frequently encountered,which can be relieved or overcome by solving an optimization problem derived from using the elastic net regularization to constrain the polynomial chaos expansion coefficients.The regularization parameters can be determined based on the Bayesian information criterion(BIC).Furthermore,the iterative rotation technique is considered for improving the sparsity of coefficients and the accuracy of computational results.In the process of performing the iterative rotation,the sensitivity information of the output vector with respect to the random input variables are used for constructing the rotation transformation matrix.The results of retrieving topography in 2D shallow water equations show that the algorithm designed in the current study is feasible,and the effect of the iterative rotation is obvious.It is also indicated that the PC-EnKF is of considerable potential in solving the practical nonlinear high-dimensional inverse problem.