Imperial College London
Alternate

DrAndrewDuncan

Faculty of Natural Sciences, Department of Mathematics

Senior Lecturer in Statistics and Data-Centric Engineering
 
 
 
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Contact

 

a.duncan

 
 
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Location

 

6M14Huxley BuildingSouth Kensington Campus

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Summary

 

Publications

Citation

BibTex format

@article{Pozharskiy:2020:10.3934/jcd.2020021,
author = {Pozharskiy, D and Wichrowski, NJ and Duncan, AB and Pavliotis, GA and Kevrekidis, IG},
doi = {10.3934/jcd.2020021},
journal = {Journal of Computational Dynamics},
pages = {511--536},
title = {Manifold learning for accelerating coarse-grained optimization},
url = {http://dx.doi.org/10.3934/jcd.2020021},
volume = {7},
year = {2020}
}
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RIS format (EndNote, RefMan)

TY  - JOUR
AB  - Algorithms proposed for solving high-dimensional optimization problems with no derivative information frequently encounter the "curse of dimensionality, " becoming ineffective as the dimension of the parameter space grows. One feature of a subclass of such problems that are effectively low-dimensional is that only a few parameters (or combinations thereof) are important for the optimization and must be explored in detail. Knowing these parameters/combinations in advance would greatly simplify the problem and its solution. We propose the data-driven construction of an effective (coarse-grained, "trend") optimizer, based on data obtained from ensembles of brief simulation bursts with an "inner" optimization algorithm, that has the potential to accelerate the exploration of the parameter space. The trajectories of this "effective optimizer" quickly become attracted onto a slow manifold parameterized by the few relevant parameter combinations. We obtain the parameterization of this low-dimensional, effective optimization manifold on the fly using data mining/manifold learning techniques on the results of simulation (inner optimizer iteration) burst ensembles and exploit it locally to "jump" forward along this manifold. As a result, we can bias the exploration of the parameter space towards the few, important directions and, through this "wrapper algorithm, " speed up the convergence of traditional optimization algorithms.
AU  - Pozharskiy,D
AU  - Wichrowski,NJ
AU  - Duncan,AB
AU  - Pavliotis,GA
AU  - Kevrekidis,IG
DO  - 10.3934/jcd.2020021
EP  - 536
PY  - 2020///
SN  - 2158-2505
SP  - 511
TI  - Manifold learning for accelerating coarse-grained optimization
T2  - Journal of Computational Dynamics
UR  - http://dx.doi.org/10.3934/jcd.2020021
UR  - http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000670031600015&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=1ba7043ffcc86c417c072aa74d649202
UR  - http://www.aimsciences.org/article/doi/10.3934/jcd.2020021
VL  - 7
ER  -
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