Data-driven Evolutions of Critical Points

In this paper we are concerned with the learnability of energies from data obtained by observing time evolutions of their critical points starting at random initial equilibria. As a byproduct of our theoretical framework we introduce the novel concept of mean-field limit of critical point evolutions and of their energy balance as a new form of transport. We formulate the energy learning as a variational problem, minimizing the discrepancy of energy competitors from fulfilling the equilibrium condition along any trajectory of critical points originated at random initial equilibria. By Gamma-convergence arguments we prove the convergence of minimal solutions obtained from finite number of observations to the exact energy in a suitable sense. The abstract framework is actually fully constructive and numerically implementable. Hence, the approximation of the energy from a finite number of observations of past evolutions allows to simulate further evolutions, which are fully data-driven. As we aim at a precise quantitative analysis, and to provide concrete examples of tractable solutions, we present analytic and numerical results on the reconstruction of an elastic energy for a one-dimensional model of thin nonlinear-elastic rod.

Use of semantic technologies for the development of a dynamic trajectories generator in a Semantic Chemistry eLearning platform

ChemgaPedia is a multimedia, webbased eLearning service platform that currently contains about 18.000 pages organized in 1.700 chapters covering the complete bachelor studies in chemistry and related topics of chemistry, pharmacy, and life sciences. The eLearning encyclopedia contains some 25.000 media objects and the eLearning platform provides services such as virtual and remote labs for experiments. With up to 350.000 users per month the platform is the most frequently used scientific educational service in the German spoken Internet. In this demo we show the benefit of mapping the static eLearning contents of ChemgaPedia to a Linked Data representation for Semantic Chemistry which allows for generating dynamic eLearning paths tailored to the semantic profiles of the users.