Cluster newton method for sampling multiple solutions of an underdetermined inverse problem: Parameter identification for pharmacokinetics

In daily life, if we lack information for making a decision, we often consider multiple possibilities. However, if we are given an underdetermined inverse problem, we often add mathematically convenient constraints and consider only one of many possible solutions even though it may be beneficial for the application to consider multiple solutions. We propose an algorithm for simultaneously finding multiple solutions of an underdetermined inverse problem that are suitably distributed, guided by a priori information on which part of the solution manifold is of interest. Through numerical experiments, we show that our algorithm is a fast, accurate and robust solution method, especially applicable to ODE coefficient identification problems. We give an example of applying this algorithm to a parameter identification problem in pharmacokinetics.