European Numerical Mathematics and
Advanced Applications Conference 2019
30th sep - 4th okt 2019, Egmond aan Zee, The Netherlands
08:30   MS18: Model order reduction in optimisation, control, and data assimilation (Part 1)
Chair: Michael Hinze
08:30
25 mins
Optimal reduced model spaces for state estimation
Olga Mula
Abstract: In recent years, the problem of reconstructing an unknown function u of a Hilbert space V from measurement observations has attracted significant attention in the field of reduced modelling. Several algorithms involving reduced bases have been proposed but the choice of the basis is generally not adapted to the underlying observation space of the recovery problem. This may lead to stability issues and degrade the reconstruction. In this work, we present results on the existence and practical construction of reduced models which are optimal for the state estimation problem. This is a joint work with A.~Cohen, W.~Dahmen, R.~DeVore, J.~Fadili and J.~Nichols.
08:55
25 mins
A low-rank approach to the solution of weak constraint variational data assimilation problems
Melina Freitag
Abstract: Weak constraint four-dimensional variational data assimilation is an important method for incorporating data (typically observations) into a model. The linearised system arising within the minimisation process can be formulated as a saddle point problem. In this talk, we present a low-rank approach which exploits the structure of the saddle point system using techniques and theory from solving large scale matrix equations. Numerical experiments with the linear advection-diffusion equation, and the nonlinear Lorenz-95 model demonstrate the effectiveness of a low-rank Krylov subspace solver when compared to a standard Krylov method. This is joint work with Daniel Green (Bath).
09:20
25 mins
Reduced basis approximation and a posteriori error bounds for data assimilation
Sébastien Boyaval, Martin Grepl, Karen Veroy-Grepl
Abstract: Assimilating data in dynamical systems is always a costly computational task, whatever the objective (predicting, filtering or smoothing). Many techniques are used in practice to reduce that cost in the various existing approaches to assimilation, sequential or variational. We will discuss the opportunity of using error bounds to guide the construction of a reduced basis for the state space, when the model depends smoothly on parameters, especially in the case of linear time-independent parabolic PDEs.