NII Technical Report (NII-2013-002E)：Improvements to the Cluster Newton Method for Underdetermined Inverse Problems
Key Points
The aim is to enhance the Cluster Newton method to effectively tackle underdetermined inverse problems in pharmacokinetics.
Proposed an algorithm using two parameters of the Beta distribution to control solution variety.
Enhanced the original CN method with an adaptive error margin for target value perturbations.
Implemented an analytical Jacobian to improve forward problem resolution.
Demonstrated greater control of solution variety in underdetermined scenarios.
Facilitated the identification of pharmacologically feasible parameters through improved algorithm.
Abstract
The Cluster Newton method (CN method) has proved to be very efficient at finding multiple solutions to underdetermined inverse problems. In the case of pharmacokinetics, underdetermined inverse problems are often given extra constraints to restrain the variety of solutions. In this paper, we propose an algorithm based on the two parameters of the Beta distribution to find families of solution near a solution of interest. This allows for a much greater control of the variety of solutions that can be obtained with the CN method. In addition, this algorithm facilitates the task of obtaining pharmacologically feasible parameters. Moreover, we also make some improvements to the original CN method including an adaptive margin of error for the perturbation of the target values and the use of an analytical Jacobian in the resolution of the forward problem.
NII Technical Report (NII-2020-002E)：Cluster Gauss-Newton method for finding multiple approximate minimisers of nonlinear least squares problems with applications to parameter estimation of pharmacokinetic models2020