STAGE Quadratization of ODE models via Laurent monomials

Date de mise à jour de l’offre

Ecole Polytechnique :

Laboratoire d'informatique de l'École polytechnique (LIX) is a computer science laboratory of École Polytechinque doing research in many areas of computer science and applied mathematics. The internship will take place in the MAX team (http://www.lix.polytechnique.fr/max/max-web/max/max-home.en.html).

Description de la mission

Quadratization problem is, given a system of ODEs with polynomial right-hand side, transform the system to a system with quadratic right-hand side by introducing new variables. Such transformations have been used, for example, as a preprocessing step by model order reduction methods and for transforming chemical reaction networks.
Recently and algorithm has been developed (https://doi.org/10.48550/arXiv.2103.08013) to find optimal quadratizations with all the new variables being monomials. In the same paper (see Proposition 1), it has been observed that one may get a quadratization of lower order by allowing Laurent monomials. The goal of the internship will be to design and implement algorithms for finding such lower-order quadratizations.

Profil recherché

The interns is expected to - have programming experience in Python or Julia (experience with SymPy and/or Oscar is an advantage) and know basics of discrete algorithms.

Niveau de qualification requis

Bac
  • Employeur
    Ecole Polytechnique
  • Secteur d’activité de la structure
    Enseignement - Formation - Recherche
  • Effectif de la structure
    De 51 à 250 salariés
  • Site internet de la structure
    https://www.lix.polytechnique.fr
  • Type de stage ou contrat
    Stage pour lycéens et étudiants en formation initiale
  • Date prévisionnelle de démarrage
  • Durée du stage ou contrat
    Plus de 2 mois et jusqu'à 4 mois
  • Le stage est-il rémunéré ?
    Oui
  • Niveau de qualification requis

    Bac
  • Lieu du stage
    1 rue Honoré d’Estienne d’Orves
    91120 PALAISEAU
  • Accès et transports
    15 minutes from the Lozere station of RER B