155 research outputs found
The Back and Forth Nudging algorithm for data assimilation problems: theoretical results on transport equations
International audienceIn this paper, we consider the back and forth nudging algorithm that has been introduced for data assimilation purposes. It consists of iteratively and alternately solving forward and backward in time the model equation, with a feedback term to the observations. We consider the case of 1-dimensional transport equations, either viscous or inviscid, linear or not (BĂĽrgers' equation). Our aim is to prove some theoretical results on the convergence, and convergence properties, of this algorithm. We show that for non viscous equations (both linear transport and Burgers), the convergence of the algorithm holds under observability conditions. Convergence can also be proven for viscous linear transport equations under some strong hypothesis, but not for viscous Burgers' equation. Moreover, the convergence rate is always exponential in time. We also notice that the forward and backward system of equations is well posed when no nudging term is considered
Global sensitivity analysis for the boundary control of an open channel
The goal of this paper is to solve the global sensitivity analysis for a
particular control problem. More precisely, the boundary control problem of an
open-water channel is considered, where the boundary conditions are defined by
the position of a down stream overflow gate and an upper stream underflow gate.
The dynamics of the water depth and of the water velocity are described by the
Shallow Water equations, taking into account the bottom and friction slopes.
Since some physical parameters are unknown, a stabilizing boundary control is
first computed for their nominal values, and then a sensitivity anal-ysis is
performed to measure the impact of the uncertainty in the parameters on a given
to-be-controlled output. The unknown physical parameters are de-scribed by some
probability distribution functions. Numerical simulations are performed to
measure the first-order and total sensitivity indices
Modéliser les océans du globe
National audienceIl existe, sous la surface de nos océans, un immense réseau de courants marins, véritables tapis roulants des mers, qui transportent des masses d'eau absolument gigantesques. Ces courants à grande échelle, parmi lesquels figure le célèbre Gulf Stream, jouent un rôle primordial dans la dynamique des océans, et bien entendu dans l'équilibre thermo-dynamique de notre planète. Il est donc essentiel de pouvoir les comprendre afin d'anticiper d'éventuels déséquilibres qui pourraient advenir, par exemple, dans le cadre du réchauffement climatique
Introduction à l'apprentissage par problèmes
National audienceDans cet exposé on commence par expliquer ce qu'est l'apprentissage par problème, un genre particulier de pédagogie active. Ensuite on montre un exemple d'application en mathématiques en première année de licence, et on fait un bilan de cette expérience
A new method for data assimilation: the back and forth nudging algorithm
International audienceIn this paper, we propose an improvement to the Back and Forth Nudging algorithm for handling diffusion in the context of geophysical data assimilation. We detail the Diffusive Back and Forth Nudging algorithm, in which the sign of the diffusion term is changed in the backward integrations. We study the convergence of this algorithm, in particular for linear transport equations
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