Abstract

We address an inverse problem for a dynamical system in the space of probability measures, namely, the problem of restoration of the time-evolution of a probability distribution from certain given statistical information. The dynamics of the distribution is described by a nonlocal continuity equation in the Wasserstein space of probability measures. For the simplest version of this problem, associated with a toy one-dimensional model of traffic flow, we derive a necessary optimality condition and design, on its base, a numerical algorithm of the type of gradient descent. We also discuss some technical aspects of the realization of the elaborated algorithm, and present the results of computational experiments implementing an eloquent numeric scenario.

Full Text
Published version (Free)

Talk to us

Join us for a 30 min session where you can share your feedback and ask us any queries you have

Schedule a call