Maximum entropy principle for stochastic models in computational sciences

Christian Soize (1)

1 MSME - Laboratoire de Modélisation et Simulation Multi Echelle

The construction of probabilistic models in computational sciences such as in computational mechanics requires the effective construction of probability distributions of random variables in high dimension. This paper deals with the effective construction of the probability distribution in high dimension of a vector-valued random variable using the maximum entropy principle. The integrals in high dimension are then calculated in constructing the stationary solution of an Ito stochastic differential equation associated with its invariant measure. A random generator of independent realizations is explicitly constructed in the paper. Three fundamental applications are presented for nonstationary stochastic process, for random fields and for random matrices.

Mots clés: uncertainty quantification; maximum entropy principle; high stochastic dimension; stochastic process; random field; random matrix

Domaines: Mécanique [physics.med-ph]; Probabilités [math.PR]; Statistiques [math.ST]

Christian Soize. Maximum entropy principle for stochastic models in computational sciences. (Plenary Lecture) The Inaugural International Conference of the Engineering Mechanics Institute, May 2008, Minneapolis, Minnesota, United States. pp.1-20. ⟨hal-00691717⟩