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Section: New Results

Methods for the interaction data - simulation

Participants : Jean-Frédéric Gerbeau, Damiano Lombardi, Sanjay Pant, Irène Vignon-Clementel.

In [38] we proposed an information theoretical framework to study the practical identifiability of dynamical systems. The fundamental question arising in parameter estimation problems is whether, given a set of observations of the system, it is possible to retrieve the parameters values. The method proposed exploits a database of direct numerical simulations and study the parameters-to-observables map by means of differential entropies. Contrary to other approaches proposed in the literature it is not restricted to ordinary differential equations and take the experimental noise into account. Several test cases were performed on a large spectrum of bio-physical systems, providing promising results.

In [60] we studied a differential entropy estimator based on $kp-$neighbours, aiming at applying a Bayesian framework and some information-theoretic ideas to inverse problems. The goal of this work is to estimate the Shannon differential entropy in high dimensional settings, in possible presence of functional or nearly functional dependences. A modification of the Kozachenko-Leonenko estimator is proposed, consisting of introducing a local gaussian approximation to the probability measure. Test-cases were performed to assess the properties of the method and to compare its performances with other methods proposed in the literature.

The articles [37] , presented in the section about biological flows, and [24] , presented in the section about electrophysiology, also present methods concerning the interaction data - simulation.