Orateur
Description
In this work we adapt recent model reduction approaches to predict the solutions of
time-dependent parametrized problems describing crowd motion in the presence of ob-
stacles. The problem of interest is a discrete contact model, which is formulated as a
constrained least-squares optimization statement. The parametric variations in the prob-
lem (associated with the geometric configuration of the system and with the initial posi-
tions of the particles) have a dramatic impact in the solution, both in terms of positions
and contact forces, which are represented by the Lagrange multipliers of the underling
saddle-point problem. Motivated by a slow decay of the Kolmogorov n-width, we inves-
tigate new developments and combinations of the reduced-basis method and supervised
machine-learning techniques to effectively estimate primal and dual solutions. The pro-
posed nonlinear compressive strategy is numerically validated by comparisons with more
standard linear and nonlinear approximations.
