Equation-free, coarse-grained computational optimization using timesteppers

Aditya Bindal, Marianthi G. Ierapetritou, Suhrid Balakrishnan, Antonios Armaou, Alexei G. Makeev, Ioannis G. Kevrekidis

Research output: Contribution to journalArticle

12 Citations (Scopus)

Abstract

System level optimization computations for engineering problems are typically based on continuum level, macroscopic system descriptions, obtained using accurate closures. In many cases, however, including micro/nanoscopic systems, the best available description is a fine scale (atomistic, stochastic or agent-based) model for which accurate, coarse-grained, system level descriptions are not known. The recently introduced equation-free approach [Theodoropoulos, K., Qian, Y.-H., Kevrekidis, I.G., 2000. "Coarse" stability and bifurcation analysis using timesteppers: a reaction diffusion example. Proceedings of the National Academy of Sciences 97, 9840-9843; Gear, C.W., Kevrekidis, I.G., Theodoropoulos, C., 2002. 'Coarse' integration/ bifurcation analysis via microscopic simulators: micro-Galerkin methods. Computers and Chemical Engineering 26, 941-963; Kevrekidis, I.G., Gear, C.W., Hummer, G., 2004. Equation-free: the computer-assisted analysis of complex, multiscale systems. A.I.Ch.E. Journal 50, 1346-1354; Kevrekidis, I.G., Gear, C.W., Hyman, J.M., Kevrekidis, P.G., Runborg, O., Theodoropoulos, K., 2003. Equation-free multiscale computation: enabling microscopic simulators to perform system-level tasks. Communications in Mathematical Sciences 1, 715-762] provides a computational bridge between the underlying microscopic process model and system level numerical computations. In this paper, we employ the equation-free approach to perform system level optimization by acting directly on microscopic/stochastic models. The approach substitutes the evaluation of closed form macroscopic equations with the design and execution of appropriately initialized short bursts of fine scale simulation; processing the simulation results yields estimates of the quantities (residuals, actions of Jacobians and Hessians) required for continuum computations. We illustrate the combination of "coarse timesteppers" with standard (both local and global) optimization techniques. The efficiency of alternative optimization formulations is compared; we see that it can be enhanced by exploiting a separation of time-scales in the system dynamics. The approach constitutes a computational "wrapper" around microscopic/stochastic simulators; yet it can also be wrapped around legacy continuum dynamic simulators.

Original languageEnglish (US)
Pages (from-to)779-793
Number of pages15
JournalChemical Engineering Science
Volume61
Issue number2
DOIs
StatePublished - Jan 1 2006

Fingerprint

Simulators
Gears
Optimization
Simulator
Continuum
Bifurcation (mathematics)
Bifurcation Analysis
Chemical engineering
Galerkin methods
Global optimization
Stochastic models
Large scale systems
Dynamical systems
Multiscale Computation
Engineering
Local Optimization
Wrapper
Agent-based Model
Communication
Reaction-diffusion

All Science Journal Classification (ASJC) codes

  • Chemistry(all)
  • Chemical Engineering(all)
  • Industrial and Manufacturing Engineering

Cite this

Bindal, A., Ierapetritou, M. G., Balakrishnan, S., Armaou, A., Makeev, A. G., & Kevrekidis, I. G. (2006). Equation-free, coarse-grained computational optimization using timesteppers. Chemical Engineering Science, 61(2), 779-793. https://doi.org/10.1016/j.ces.2005.06.034
Bindal, Aditya ; Ierapetritou, Marianthi G. ; Balakrishnan, Suhrid ; Armaou, Antonios ; Makeev, Alexei G. ; Kevrekidis, Ioannis G. / Equation-free, coarse-grained computational optimization using timesteppers. In: Chemical Engineering Science. 2006 ; Vol. 61, No. 2. pp. 779-793.
@article{c9e0d7443ede4ecb99b80277255b2a06,
title = "Equation-free, coarse-grained computational optimization using timesteppers",
abstract = "System level optimization computations for engineering problems are typically based on continuum level, macroscopic system descriptions, obtained using accurate closures. In many cases, however, including micro/nanoscopic systems, the best available description is a fine scale (atomistic, stochastic or agent-based) model for which accurate, coarse-grained, system level descriptions are not known. The recently introduced equation-free approach [Theodoropoulos, K., Qian, Y.-H., Kevrekidis, I.G., 2000. {"}Coarse{"} stability and bifurcation analysis using timesteppers: a reaction diffusion example. Proceedings of the National Academy of Sciences 97, 9840-9843; Gear, C.W., Kevrekidis, I.G., Theodoropoulos, C., 2002. 'Coarse' integration/ bifurcation analysis via microscopic simulators: micro-Galerkin methods. Computers and Chemical Engineering 26, 941-963; Kevrekidis, I.G., Gear, C.W., Hummer, G., 2004. Equation-free: the computer-assisted analysis of complex, multiscale systems. A.I.Ch.E. Journal 50, 1346-1354; Kevrekidis, I.G., Gear, C.W., Hyman, J.M., Kevrekidis, P.G., Runborg, O., Theodoropoulos, K., 2003. Equation-free multiscale computation: enabling microscopic simulators to perform system-level tasks. Communications in Mathematical Sciences 1, 715-762] provides a computational bridge between the underlying microscopic process model and system level numerical computations. In this paper, we employ the equation-free approach to perform system level optimization by acting directly on microscopic/stochastic models. The approach substitutes the evaluation of closed form macroscopic equations with the design and execution of appropriately initialized short bursts of fine scale simulation; processing the simulation results yields estimates of the quantities (residuals, actions of Jacobians and Hessians) required for continuum computations. We illustrate the combination of {"}coarse timesteppers{"} with standard (both local and global) optimization techniques. The efficiency of alternative optimization formulations is compared; we see that it can be enhanced by exploiting a separation of time-scales in the system dynamics. The approach constitutes a computational {"}wrapper{"} around microscopic/stochastic simulators; yet it can also be wrapped around legacy continuum dynamic simulators.",
author = "Aditya Bindal and Ierapetritou, {Marianthi G.} and Suhrid Balakrishnan and Antonios Armaou and Makeev, {Alexei G.} and Kevrekidis, {Ioannis G.}",
year = "2006",
month = "1",
day = "1",
doi = "10.1016/j.ces.2005.06.034",
language = "English (US)",
volume = "61",
pages = "779--793",
journal = "Chemical Engineering Science",
issn = "0009-2509",
publisher = "Elsevier BV",
number = "2",

}

Bindal, A, Ierapetritou, MG, Balakrishnan, S, Armaou, A, Makeev, AG & Kevrekidis, IG 2006, 'Equation-free, coarse-grained computational optimization using timesteppers', Chemical Engineering Science, vol. 61, no. 2, pp. 779-793. https://doi.org/10.1016/j.ces.2005.06.034

Equation-free, coarse-grained computational optimization using timesteppers. / Bindal, Aditya; Ierapetritou, Marianthi G.; Balakrishnan, Suhrid; Armaou, Antonios; Makeev, Alexei G.; Kevrekidis, Ioannis G.

In: Chemical Engineering Science, Vol. 61, No. 2, 01.01.2006, p. 779-793.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Equation-free, coarse-grained computational optimization using timesteppers

AU - Bindal, Aditya

AU - Ierapetritou, Marianthi G.

AU - Balakrishnan, Suhrid

AU - Armaou, Antonios

AU - Makeev, Alexei G.

AU - Kevrekidis, Ioannis G.

PY - 2006/1/1

Y1 - 2006/1/1

N2 - System level optimization computations for engineering problems are typically based on continuum level, macroscopic system descriptions, obtained using accurate closures. In many cases, however, including micro/nanoscopic systems, the best available description is a fine scale (atomistic, stochastic or agent-based) model for which accurate, coarse-grained, system level descriptions are not known. The recently introduced equation-free approach [Theodoropoulos, K., Qian, Y.-H., Kevrekidis, I.G., 2000. "Coarse" stability and bifurcation analysis using timesteppers: a reaction diffusion example. Proceedings of the National Academy of Sciences 97, 9840-9843; Gear, C.W., Kevrekidis, I.G., Theodoropoulos, C., 2002. 'Coarse' integration/ bifurcation analysis via microscopic simulators: micro-Galerkin methods. Computers and Chemical Engineering 26, 941-963; Kevrekidis, I.G., Gear, C.W., Hummer, G., 2004. Equation-free: the computer-assisted analysis of complex, multiscale systems. A.I.Ch.E. Journal 50, 1346-1354; Kevrekidis, I.G., Gear, C.W., Hyman, J.M., Kevrekidis, P.G., Runborg, O., Theodoropoulos, K., 2003. Equation-free multiscale computation: enabling microscopic simulators to perform system-level tasks. Communications in Mathematical Sciences 1, 715-762] provides a computational bridge between the underlying microscopic process model and system level numerical computations. In this paper, we employ the equation-free approach to perform system level optimization by acting directly on microscopic/stochastic models. The approach substitutes the evaluation of closed form macroscopic equations with the design and execution of appropriately initialized short bursts of fine scale simulation; processing the simulation results yields estimates of the quantities (residuals, actions of Jacobians and Hessians) required for continuum computations. We illustrate the combination of "coarse timesteppers" with standard (both local and global) optimization techniques. The efficiency of alternative optimization formulations is compared; we see that it can be enhanced by exploiting a separation of time-scales in the system dynamics. The approach constitutes a computational "wrapper" around microscopic/stochastic simulators; yet it can also be wrapped around legacy continuum dynamic simulators.

AB - System level optimization computations for engineering problems are typically based on continuum level, macroscopic system descriptions, obtained using accurate closures. In many cases, however, including micro/nanoscopic systems, the best available description is a fine scale (atomistic, stochastic or agent-based) model for which accurate, coarse-grained, system level descriptions are not known. The recently introduced equation-free approach [Theodoropoulos, K., Qian, Y.-H., Kevrekidis, I.G., 2000. "Coarse" stability and bifurcation analysis using timesteppers: a reaction diffusion example. Proceedings of the National Academy of Sciences 97, 9840-9843; Gear, C.W., Kevrekidis, I.G., Theodoropoulos, C., 2002. 'Coarse' integration/ bifurcation analysis via microscopic simulators: micro-Galerkin methods. Computers and Chemical Engineering 26, 941-963; Kevrekidis, I.G., Gear, C.W., Hummer, G., 2004. Equation-free: the computer-assisted analysis of complex, multiscale systems. A.I.Ch.E. Journal 50, 1346-1354; Kevrekidis, I.G., Gear, C.W., Hyman, J.M., Kevrekidis, P.G., Runborg, O., Theodoropoulos, K., 2003. Equation-free multiscale computation: enabling microscopic simulators to perform system-level tasks. Communications in Mathematical Sciences 1, 715-762] provides a computational bridge between the underlying microscopic process model and system level numerical computations. In this paper, we employ the equation-free approach to perform system level optimization by acting directly on microscopic/stochastic models. The approach substitutes the evaluation of closed form macroscopic equations with the design and execution of appropriately initialized short bursts of fine scale simulation; processing the simulation results yields estimates of the quantities (residuals, actions of Jacobians and Hessians) required for continuum computations. We illustrate the combination of "coarse timesteppers" with standard (both local and global) optimization techniques. The efficiency of alternative optimization formulations is compared; we see that it can be enhanced by exploiting a separation of time-scales in the system dynamics. The approach constitutes a computational "wrapper" around microscopic/stochastic simulators; yet it can also be wrapped around legacy continuum dynamic simulators.

UR - http://www.scopus.com/inward/record.url?scp=27144474905&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=27144474905&partnerID=8YFLogxK

U2 - 10.1016/j.ces.2005.06.034

DO - 10.1016/j.ces.2005.06.034

M3 - Article

AN - SCOPUS:27144474905

VL - 61

SP - 779

EP - 793

JO - Chemical Engineering Science

JF - Chemical Engineering Science

SN - 0009-2509

IS - 2

ER -