English
 
User Manual Privacy Policy Disclaimer Contact us
  Advanced SearchBrowse

Item

ITEM ACTIONSEXPORT

Released

Paper

Solving Optimal Control Problems governed by Random Navier-Stokes Equations using Low-Rank Methods

MPS-Authors
/persons/resource/persons86253

Benner,  Peter
Computational Methods in Systems and Control Theory, Max Planck Institute for Dynamics of Complex Technical Systems, Max Planck Society;

/persons/resource/persons130597

Onwunta,  Akwum
Computational Methods in Systems and Control Theory, Max Planck Institute for Dynamics of Complex Technical Systems, Max Planck Society;

/persons/resource/persons86493

Stoll,  Martin
Numerical Linear Algebra for Dynamical Systems, Max Planck Institute for Dynamics of Complex Technical Systems, Max Planck Society;

Locator
There are no locators available
Fulltext (public)

1703.06097.pdf
(Preprint), 2MB

Supplementary Material (public)
There is no public supplementary material available
Citation

Benner, P., Dolgov, S., Onwunta, A., & Stoll, M. (in preparation). Solving Optimal Control Problems governed by Random Navier-Stokes Equations using Low-Rank Methods.


Cite as: http://hdl.handle.net/21.11116/0000-0000-2E27-2
Abstract
Many problems in computational science and engineering are simultaneously characterized by the following challenging issues: uncertainty, nonlinearity, nonstationarity and high dimensionality. Existing numerical techniques for such models would typically require considerable computational and storage resources. This is the case, for instance, for an optimization problem governed by time-dependent Navier-Stokes equations with uncertain inputs. In particular, the stochastic Galerkin finite element method often leads to a prohibitively high dimensional saddle-point system with tensor product structure. In this paper, we approximate the solution by the low-rank Tensor Train decomposition, and present a numerically efficient algorithm to solve the optimality equations directly in the low-rank representation. We show that the solution of the vorticity minimization problem with a distributed control admits a representation with ranks that depend modestly on model and discretization parameters even for high Reynolds numbers. For lower Reynolds numbers this is also the case for a boundary control. This opens the way for a reduced-order modeling of the stochastic optimal flow control with a moderate cost at all stages.