Global optimization for parameter estimation of differential-algebraic systems

2009 ◽  
Vol 63 (3) ◽  
Author(s):  
Michal Čižniar ◽  
Marián Podmajerský ◽  
Tomáš Hirmajer ◽  
Miroslav Fikar ◽  
Abderrazak Latifi
Keyword(s):  
Global Optimization ◽  
Parameter Estimation ◽  
Time Series Data ◽  
Optimization Method ◽  
Differential Algebraic Equations ◽  
Series Data ◽  
Global Optimality ◽  
Algebraic Equations ◽  
Estimation Of Parameters ◽  
Orthogonal Collocation

AbstractThe estimation of parameters in semi-empirical models is essential in numerous areas of engineering and applied science. In many cases, these models are described by a set of ordinary-differential equations or by a set of differential-algebraic equations. Due to the presence of non-convexities of functions participating in these equations, current gradient-based optimization methods can guarantee only locally optimal solutions. This deficiency can have a marked impact on the operation of chemical processes from the economical, environmental and safety points of view and it thus motivates the development of global optimization algorithms. This paper presents a global optimization method which guarantees ɛ-convergence to the global solution. The approach consists in the transformation of the dynamic optimization problem into a nonlinear programming problem (NLP) using the method of orthogonal collocation on finite elements. Rigorous convex underestimators of the nonconvex NLP problem are employed within the spatial branch-and-bound method and solved to global optimality. The proposed method was applied to two example problems dealing with parameter estimation from time series data.

Causation Entropy Identifies Sparsity Structure for Parameter Estimation of Dynamic Systems

2016 ◽  
Vol 12 (1) ◽  
Author(s):  
Pileun Kim ◽  
Jonathan Rogers ◽  
Jie Sun ◽  
Erik Bollt
Keyword(s):  
Parameter Estimation ◽  
Time Series Data ◽  
Multivariate Time Series ◽  
Measurement Data ◽  
Relative Magnitude ◽  
Initial Guess ◽  
Series Data ◽  
System Parameters ◽  
Estimation Problems ◽  
System States

Parameter estimation is an important topic in the field of system identification. This paper explores the role of a new information theory measure of data dependency in parameter estimation problems. Causation entropy is a recently proposed information-theoretic measure of influence between components of multivariate time series data. Because causation entropy measures the influence of one dataset upon another, it is naturally related to the parameters of a dynamical system. In this paper, it is shown that by numerically estimating causation entropy from the outputs of a dynamic system, it is possible to uncover the internal parametric structure of the system and thus establish the relative magnitude of system parameters. In the simple case of linear systems subject to Gaussian uncertainty, it is first shown that causation entropy can be represented in closed form as the logarithm of a rational function of system parameters. For more general systems, a causation entropy estimator is proposed, which allows causation entropy to be numerically estimated from measurement data. Results are provided for discrete linear and nonlinear systems, thus showing that numerical estimates of causation entropy can be used to identify the dependencies between system states directly from output data. Causation entropy estimates can therefore be used to inform parameter estimation by reducing the size of the parameter set or to generate a more accurate initial guess for subsequent parameter optimization.

scholarly journals Web-gLV: A Web Based Platform for Lotka-Volterra Based Modeling and Simulation of Microbial Populations

2019 ◽  
Vol 10 ◽  
Author(s):  
Bhusan K. Kuntal ◽  
Chetan Gadgil ◽  
Sharmila S. Mande
Keyword(s):  
Modeling And Simulation ◽  
Time Series Data ◽  
Microbial Populations ◽  
Series Data ◽  
Estimation Of Parameters ◽  
Valuable Contribution ◽  
Bacterial Populations ◽  
Web Based ◽  
Automatic Estimation ◽  
High Throughput Dna Sequencing

The affordability of high throughput DNA sequencing has allowed us to explore the dynamics of microbial populations in various ecosystems. Mathematical modeling and simulation of such microbiome time series data can help in getting better understanding of bacterial communities. In this paper, we present Web-gLV—a GUI based interactive platform for generalized Lotka-Volterra (gLV) based modeling and simulation of microbial populations. The tool can be used to generate the mathematical models with automatic estimation of parameters and use them to predict future trajectories using numerical simulations. We also demonstrate the utility of our tool on few publicly available datasets. The case studies demonstrate the ease with which the current tool can be used by biologists to model bacterial populations and simulate their dynamics to get biological insights. We expect Web-gLV to be a valuable contribution in the field of ecological modeling and metagenomic systems biology.

A New Cost Function for Parameter Estimation of Chaotic Systems Using Return Maps as Fingerprints

2014 ◽  
Vol 24 (10) ◽  
pp. 1450134 ◽  
Author(s):  
Sajad Jafari ◽  
Julien C. Sprott ◽  
Viet-Thanh Pham ◽  
S. Mohammad Reza Hashemi Golpayegani ◽  
Amir Homayoun Jafari
Keyword(s):  
Parameter Estimation ◽  
Cost Function ◽  
Chaotic Systems ◽  
Time Series Data ◽  
Initial Conditions ◽  
Model Systems ◽  
Series Data ◽  
Return Maps ◽  
Active Interest ◽  
The Time Domain

Estimating parameters of a model system using observed chaotic scalar time series data is a topic of active interest. To estimate these parameters requires a suitable similarity indicator between the observed and model systems. Many works have considered a similarity measure in the time domain, which has limitations because of sensitive dependence on initial conditions. On the other hand, there are features of chaotic systems that are not sensitive to initial conditions such as the topology of the strange attractor. We have used this feature to propose a new cost function for parameter estimation of chaotic models, and we show its efficacy for several simple chaotic systems.

scholarly journals Linear Hybrid Deterministic Dynamic Modeling for Time-to-Event Processes: State and Parameter Estimations

2016 ◽  
Vol 5 (6) ◽  
pp. 32
Author(s):  
E. A. Appiah ◽  
G. S. Ladde
Keyword(s):  
Parameter Estimation ◽  
Discrete Time ◽  
Chemical Engineering ◽  
Time Series Data ◽  
Survival Function ◽  
Series Data ◽  
Dynamic Processes ◽  
Time To Event ◽  
Deterministic Dynamic ◽  
Special Cases

In this work, we initiate an innovative alternative modeling approach for time-to-event dynamic processes. The proposed approach is composed of the following basic components: (1) development of continuous-time state of dynamic process, (2) introduction of discrete-time dynamic intervention process, (3) formulation of continuous and discrete-time interconnected dynamic system, (4) utilizing Euler-type discretized schemes, and (5) introduction of conceptual and computational state and parameter estimation procedures. The presented approach is motivated by state and parameter estimation of time-to-event processes in biological, chemical, engineering, epidemiological, medical, military, multiple-markets and social dynamic processes under the influence of discrete-time intervention processes. The role and scope of our approach is exhibited by presenting several well-known hazard/risk rate and survival function estimates as special cases. Moreover, conceptual algorithms are illustrated by time-series data sets under the influence of intervention processes.

Numerical Methods for Parameter Estimation in Nonlinear Differential Algebraic Equations

2007 ◽  
Vol 30 (2) ◽  
pp. 376-408 ◽  
Author(s):  
Hans Georg Bock ◽  
Ekaterina Kostina ◽  
Johannes P. Schlöder
Keyword(s):  
Parameter Estimation ◽  
Numerical Methods ◽  
Differential Algebraic Equations ◽  
Algebraic Equations

DIMSUM: an expert system for multiexponential model discrimination

1992 ◽  
Vol 262 (4) ◽  
pp. E546-E556
Author(s):  
A. T. Marino ◽  
J. J. Distefano ◽  
E. M. Landaw
Keyword(s):  
Parameter Estimation ◽  
Expert System ◽  
Time Series Data ◽  
Weighted Least Squares ◽  
Learning Rule ◽  
Search Space ◽  
Series Data ◽  
Model Discrimination ◽  
Rule Based ◽  
Statistical Results

DIMSUM is a highly automated, rule-based expert system designed to fit multiexponential models of increasing dimension to time series data, followed by selection of the best candidate model based on a user-modifiable and weighted decision tree of statistical criteria for model discrimination. The major features of DIMSUM are 1) an interactive and friendly user interface; 2) options for incorporating prior information about the parameters, the data, and/or the system from which the data were collected, in the form of equality and inequality constraints; 3) a built-in algorithm for automatically obtaining starting values for parameter estimation; 4) a robust weighted least-squares parameter estimation algorithm operating in an adaptive, user-adjustable search space; 5) comprehensive statistical results comparing different order candidate models fitted to the data; and 6) a novel, user-modifiable (learning) rule-based advisory subsystem providing an “expert's” interpretation of these statistical results and an explanation of all advice.

PARAMETER ESTIMATION USING KALMAN FILTERS WITH CONSTRAINTS

2006 ◽  
Vol 16 (04) ◽  
pp. 1067-1078 ◽  
Author(s):  
DAVID M. WALKER
Keyword(s):  
Parameter Estimation ◽  
Chaotic Dynamics ◽  
Time Series Data ◽  
Series Data ◽  
Estimation Algorithms ◽  
Additional Information ◽  
Chua Circuit ◽  
Unstable Fixed Point ◽  
Using Data ◽  
Dynamical Information

We suggest incorporating dynamical information such as locations of unstable fixed points into parameter estimation algorithms in order to improve the method of reconstructing dynamics from time series data. We show how the process of reconstruction using nonlinear filters such as the extended Kalman filter can be easily modified to take advantage of the additional information. We demonstrate the methods using data from two systems exhibiting chaotic dynamics — the Chua circuit and Chen's equations. In both cases we find the models reconstructed using constraints that better approximate the unstable fixed point structure of the underlying systems.

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