Abstract |
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. |