We consider an optimal control problem for the three-dimensional non-linear Primitive Equations of the ocean in a vertically bounded and horizontally periodic domain. We aim to reconstruct the initial state of the ocean from Lagrangian observations. This inverse problem is formulated as an optimal control problem which consists in minimizing a cost function representing the least square error between Lagrangian observations and their model counterpart, plus a regularization term. This paper proves...
In 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 (Burgers’ equation). Our aim is to prove some theoretical results on the convergence, and convergence properties, of this algorithm. We...
In 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 (Burgers’ equation). Our aim is to prove some theoretical results on the
convergence,...
In 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 (Burgers’ equation). Our aim is to prove some theoretical results on the
convergence,...
We present a reduced basis offline/online procedure for viscous Burgers initial boundary value problem, enabling efficient approximate computation of the solutions of this equation for parametrized viscosity and initial and boundary value data. This procedure comes with a fast-evaluated rigorous error bound certifying the approximation procedure. Our numerical experiments show significant computational savings, as well as efficiency of the error bound.
Many mathematical models involve input parameters, which are not precisely known. Global sensitivity analysis aims to identify the parameters whose uncertainty has the largest impact on the variability of a quantity of interest (output of the model). One of the statistical tools used to quantify the influence of each input variable on the output is the Sobol sensitivity index. We consider the statistical estimation of this index from a finite sample of model outputs: we present two estimators and...
Global sensitivity analysis of a numerical code, more specifically estimation of Sobol indices associated with input variables, generally requires a large number of model runs. When those demand too much computation time, it is necessary to use a reduced model (metamodel) to perform sensitivity analysis, whose outputs are numerically close to the ones of the original model, while being much faster to run. In this case, estimated indices are subject to two kinds of errors: sampling error, caused...
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