Hartmann, C. and Schütte, Ch. and Zhang, W. (2016) Model reduction algorithms for optimal control and importance sampling of diffusions. Nonlinearity, 29 (8). pp. 22982326. ISSN 09517715

PDF
 Submitted Version
866kB 
Official URL: http://iopscience.iop.org/article/10.1088/0951771...
Abstract
We propose numerical algorithms for solving complex, high dimensional control and importance sampling problems based on reducedorder models. The algorithms approach the “curse of dimensionality” by a combination of model reduction techniques for multiscale diffusions and stochastic optimization tools, with the aim of reducing the original, possibly highdimensional problem to a lower dimensional representation of the dynamics, in which only few relevant degrees of freedom are controlled or biased. Specifically, we study situations in which either an suitable set of slow collective variables onto which the dynamics can be projected is known, or situations in which the dynamics shows strongly localized behaviour in the small noise regime. The idea is to use the solution of the reducedorder model as a predictor of the exact solution that, in a corrector step, can be used together with the original dynamics, where no explicit assumptions about small parameters or scale separation have to be made. We illustrate the approach with simple, but paradigmatic numerical examples.
Item Type:  Article 

Subjects:  Mathematical and Computer Sciences > Mathematics > Applied Mathematics 
Divisions:  Department of Mathematics and Computer Science > Institute of Mathematics Department of Mathematics and Computer Science > Institute of Mathematics > Cellular Mechanics Group Department of Mathematics and Computer Science > Institute of Mathematics > BioComputing Group 
ID Code:  1552 
Deposited By:  INVALID USER 
Deposited On:  22 Jun 2015 12:19 
Last Modified:  03 Mar 2017 14:41 
Repository Staff Only: item control page