Scientific Computation and Applied & Industrial Mathematics Seminar: Robert Kircheis
Date
-
Topic
Numerical Methods for Parameter Estimation and Optimum Experimental Design for Nonlinear PDE Models
Speakers
Details
Abstract:
To fit a model of a process described by a system of Partial Differential Algebraic Equations to a given set of experimental data we have to solve constrained, nonlinear parameter estimation problems.
Since the data usually contains statistical errors the parameters are random variables too. The uncertainty of a parameter estimation can be quantified by the variance-covariance matrix of the estimator.
For minimizing the confidence region of the parameter estimation an optimized experimental setup is needed. We present our approach for the minimization of quality criteria on the variance-covariance matrix of the parameters. Thereby process controls and the layout of measurements are the optimization variables.
Our approach are derivative based optimization strategies. We introduce the general Optimum Experimental Design optimization problem and the methods implemented in the software package VPLAN, such as Quasi-Newton methods, tailored derivative evaluation by Internal Numerical Differentiation and Automatic Differentiation and exploitation of multiple experiment structures. To use experimental design for practical problems, we have developed strategies including robustification, multiple experiment formulations, a sequential strategy and an online-approach.
In the second part of the talk we give an overview of parameter estimation methods to fit the parameters to the data. We treat this kind of problems by (reduced) Gauss-Newton-Type methods and multiple-shooting. Furthermore, we will give a short outlook on what is next to come (multiple shooting for OED, Proper Orthogonal Decomposition (POD) and reduced approach).
To fit a model of a process described by a system of Partial Differential Algebraic Equations to a given set of experimental data we have to solve constrained, nonlinear parameter estimation problems.
Since the data usually contains statistical errors the parameters are random variables too. The uncertainty of a parameter estimation can be quantified by the variance-covariance matrix of the estimator.
For minimizing the confidence region of the parameter estimation an optimized experimental setup is needed. We present our approach for the minimization of quality criteria on the variance-covariance matrix of the parameters. Thereby process controls and the layout of measurements are the optimization variables.
Our approach are derivative based optimization strategies. We introduce the general Optimum Experimental Design optimization problem and the methods implemented in the software package VPLAN, such as Quasi-Newton methods, tailored derivative evaluation by Internal Numerical Differentiation and Automatic Differentiation and exploitation of multiple experiment structures. To use experimental design for practical problems, we have developed strategies including robustification, multiple experiment formulations, a sequential strategy and an online-approach.
In the second part of the talk we give an overview of parameter estimation methods to fit the parameters to the data. We treat this kind of problems by (reduced) Gauss-Newton-Type methods and multiple-shooting. Furthermore, we will give a short outlook on what is next to come (multiple shooting for OED, Proper Orthogonal Decomposition (POD) and reduced approach).
