Grid Computing, Parameter Estimation for Ordinary Differential Equations

2013 ◽  
pp. 870-871
Author(s):  
Ivan Merelli ◽  
Ettore Mosca ◽  
Luciano Milanesi
Keyword(s):  
Parameter Estimation ◽  
Differential Equations ◽  
Grid Computing ◽  
Ordinary Differential Equations ◽  
Computing Parameter

scholarly journals A Modified NM-PSO Method for Parameter Estimation Problems of Models

2012 ◽  
Vol 2012 ◽  
pp. 1-12 ◽  
Author(s):  
An Liu ◽  
Erwie Zahara ◽  
Ming-Ta Yang
Keyword(s):  
Genetic Algorithm ◽  
Parameter Estimation ◽  
Particle Swarm Optimization ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Optimization Problems ◽  
Particle Swarm ◽  
Swarm Optimization ◽  
Wide Range ◽  
Estimation Problems

Ordinary differential equations usefully describe the behavior of a wide range of dynamic physical systems. The particle swarm optimization (PSO) method has been considered an effective tool for solving the engineering optimization problems for ordinary differential equations. This paper proposes a modified hybrid Nelder-Mead simplex search and particle swarm optimization (M-NM-PSO) method for solving parameter estimation problems. The M-NM-PSO method improves the efficiency of the PSO method and the conventional NM-PSO method by rapid convergence and better objective function value. Studies are made for three well-known cases, and the solutions of the M-NM-PSO method are compared with those by other methods published in the literature. The results demonstrate that the proposed M-NM-PSO method yields better estimation results than those obtained by the genetic algorithm, the modified genetic algorithm (real-coded GA (RCGA)), the conventional particle swarm optimization (PSO) method, and the conventional NM-PSO method.

A Particle Swarm Optimization Algorithm and its Application in Hydrodynamic Equations

2012 ◽  
Vol 510 ◽  
pp. 472-477
Author(s):  
Jian Hui Zhou ◽  
Shu Zhong Zhao ◽  
Li Xi Yue ◽  
Yan Nan Lu ◽  
Xin Yi Si
Keyword(s):  
Parameter Estimation ◽  
Particle Swarm Optimization ◽  
Differential Equations ◽  
Fluid Mechanics ◽  
Ordinary Differential Equations ◽  
Optimization Algorithm ◽  
Multiple Solutions ◽  
Particle Swarm Optimization Algorithm ◽  
Swarm Optimization ◽  
Estimation Problems

In fluid mechanics, how to solve multiple solutions in ordinary differential equations is always a concerned and difficult problem. A particle swarm optimization algorithm combining with the direct search method (DSPO) is proposed for solving the parameter estimation problems of the multiple solutions in fluid mechanics. This algorithm has improved greatly in precision and the success rate. In this paper, multiple solutions can be found through changing accuracy and search coverage and multi-iterations of computer. Parameter estimation problems of the multiple solutions of ordinary differential equations are calculated, and the result has great accuracy and this method is practical.

scholarly journals A Robust Method for the Estimation of Kinetic Parameters for Systems Including Slow and Rapid Reactions—From Differential-Algebraic Model to Differential Model

Processes ◽  
2020 ◽  
Vol 8 (12) ◽  
pp. 1552
Author(s):  
Tapio Salmi ◽  
Esko Tirronen ◽  
Johan Wärnå ◽  
Jyri-Pekka Mikkola ◽  
Dmitry Murzin ◽  
...  
Keyword(s):  
Parameter Estimation ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Kinetic Parameters ◽  
Algebraic Model ◽  
Algebraic Equations ◽  
Robust Method ◽  
Differential Model ◽  
Chemical Systems

Reliable estimation of kinetic parameters in chemical systems comprising both slow and rapid reaction steps and rapidly reacting intermediate species is a difficult differential-algebraic problem. Consequently, any conventional approach easily leads to serious convergence and stability problems during the parameter estimation. A robust method is proposed to surmount this dilemma: the system of ordinary differential equations and nonlinear algebraic equations is converted to ordinary differential equations, which are solved in-situ during the parameter estimation. The approach was illustrated with two generic examples and an example from green chemistry: synthesis of dimethyl carbonate from carbon dioxide and methanol.

A Novel RNA Genetic Algorithm for the Parameter Estimation of the Fluid Mechanics with Multiple Solutions

2012 ◽  
Vol 204-208 ◽  
pp. 4679-4682
Author(s):  
Guo Hua Fang ◽  
Xin Yi Si ◽  
Xiao Ping Chen ◽  
Jian Hui Zhou
Keyword(s):  
Molecular Structure ◽  
Genetic Algorithm ◽  
Parameter Estimation ◽  
Differential Equations ◽  
Fluid Mechanics ◽  
Ordinary Differential Equations ◽  
Multiple Solutions ◽  
Difficult Problem ◽  
Great Accuracy ◽  
Estimation Problems

In fluid mechanics, to obtain the multiple solutions in ordinary differential equations is always a concerned and difficult problem. In this paper, a novel RNA genetic algorithm (NRNA-GA) inspired by RNA molecular structure and operators is proposed to solve the parameter estimation problems of the multiple solutions in fluid mechanics. This algorithm has improved greatly in precision and the success rate. Multiple solutions can be found through changing accuracy and search coverage and multi-iterations of computer. At last, parameter estimation of the ordinary differential equations with multiple solutions is calculated. We found that the result has great accuracy and this method is practical.

Sign in / Sign up

Export Citation Format

Share Document