Program

Schedule

We prepared a PDF document showing the schedule. Small changes due to availability of rooms and appointments of speakers are possible.


Overview of the Program

Compact Course A

Prof. Christian Kirches
Numerical Simulation and Optimization

Compact Course B

Dr. Susanne Krömker
Discrete Morse Theory in Visualization

Compact Course C

Prof. Thomas Richter
Finite Elements for Partial Differential Equations

Compact Course D

Prof. Ekaterina Kostina
Optimization Methods for Calibration and Validation of Dynamic Models

Overview Talks

Prof. Hans Georg Bock
Parameter Identification

Dr. Anja Milde
Modelling, Simulation and Optimization in an Industrial Context

Prof. Jean Louis Woukeng
Multiscale Analysis - Bridging Scales in Mathematical Modeling and Simulation.

Prof. Bruce Bassett
The Use and Limits of Artificial Intelligence in Fundamental Science 

Abstract:
Machine Learning and Artificial Intelligence (AI) are surging as topics of interest in industry. Here we review the key mathematical ideas and provide examples for their use from astronomy. We then discuss the future and limitations of AI as tools for the fundamental sciences.

Dr. Ian Durbach
Differentiating fish stocks using image classification

Abstract:
Otoliths are calcified structures in the inner ears of fish that exhibit stock-specific variation in shape, and which have been successfully used in analyses of various species of fish to determine stock identity. Most commonly, information about the shape of the otolith is conveyed by coefficients extracted by elliptical Fourier analysis, these coefficients forming features from which classification models can be constructed. Model construction is usually complicated by the problem that morphological effects are confounded with fish size, which should not be used to differentiate between stocks. This talk gives an introduction to stock differentiation using analyses of otolith images, and presents an application testing the hypothesis that each of three pelagic fish populations consist of two morphologically distinct stocks on the South and West coasts of South Africa.

Dr. Henri Laurie
Multfractality in species richness: how to compute the Renyi dimensions?

Absrtact: A multifractal on a simply connected plane figure can be thought of as scalar function which does not have a density at any point, among other ways to think about it. This makes it useful for describing natural phenomena with very irregular footprints, such as rainfall, earthquakes and the example considered here: species richness. One may characterise a multifractal via its Renyi dimensions, the computation of which I will focus on in this talk. I first present an algorithm based on synthetic subdivision of a domain (Perrier et al, 2006), and then an algorithm more applicable to the case of real data, where the subdivisions possibly do not cover the domain and also possibly overlap . Finally, I present an application of this method to the data of the South African Protea Atlas.

Perrier E., Tarquis A. and Dathe A. (2006). A program for fractal and multifractal analysis of two-dimensional binary images: computer algorithms versus
mathematical theory. Geoderma 134, 284–294.

Perrier, E., Laurie, H., 2008. Individual-based simulations of species richness maps: Testing a new multifractal approach. South African Journal of Science 104, 209–
215.


Course Details

A: Numerical Simulation and Optimization

This short compact course gives an introduction to modern numerical methods for the solution of nonlinear optimization problems constrained by ordinary differential equations (ODE) and differential-algebraic equations (DAE). Such problems are frequently encountered as computational models of challenging industrial processes and include, for example, automotive or chemical engineering problems. In four lectures, we give an overview on typical process control problems and suitable computational model, and on the core theoretical and algorithmic concepts underlying the direct approach to optimal control. We will get to know a particular approach, the direct multiple shooting method, in greater detail and will top off with a survey of more advanced topics in dynamic process control, such as uncertainties, feedback control, discrete controls, and hybrid systems.

Part 1: Nonlinear programming theory and algorithms
Part 2: Dynamic process models
Part 3: The direct approach to optimal control
Part 4: Advanced topics: uncertainties, feedback control, discrete controls, hybrid systems


B: Discrete Morse Theory in Visualization

The compact course introduces topological methods more and more
used in visualization for data reduction in 3D scalar fields. As input we
think of CT data but also 3D simulated data, e.g., when solving partial
differential equations (PDE) with Finite Element methods. The discretization
is often much finer as is needed for an insight in the quality of the data
in terms of sinks and sources, or other critical points. The basic data lives
on so-called cubical complexes. When looking for isosurfaces, we try to
figure out a threshold for surface extraction with high persistence values
of critical cells.
In four lectures, we give an introduction to the basic terms in topology
with algorithmic aspects for constructing discrete vector fields and show
results on simulated data from cytokine dynamics in lymph cells.

Part 1: What are topological methods? A brief introduction to Morse Theory

Part 2: Discrete Morse Theory – a new development for fast computations

Part 3: Algorithmic aspects

Part 4: Results on CT-data (measured data) and cytokine dynamics (simulated data)


C: Finite Elements for Partial Differential Equations

This short compact course gives an introduction to modern Finite
Element Methods for the discretization of partial differential
equations. Finite Element analysis is a powerful tool for modeling and
simulation of complex processes. The Finite Element method is based on
variational formulations of the partial differential equations. It is
very flexible and allows for rigorous error analysis and efficient
solution of the discretized problems.

In four lectures, we give an overview on the analytical background,
details on the discretization and the efficient realization of the
method.

Part 1: Functional analysis, variational formulations of partial
differential equations and the Galerkin method
Part 2: Finite Element Meshes and Finite Element Spaces
Part 3: Error estimation
Part 4: Efficient solution of the discretized Systems


D: Optimization Methods for Calibration and Validation of Dynamic Models

The application of mathematical methods for modeling, simulation and optimization (MSO) has become an indispensable tool for the understanding and mastering of complex processes in science and engineering. The prerequisite for the successful application of the MSO are detailed mathematical models, validated and calibrated by experimental data. This short compact course gives an introduction to the state-of-the-art numerical optimization methods for model validation and calibration. We start with mathematical formulation of parameter estimation problems in processes described by nonlinear differential equations. Then we will present particularly efficient "simultaneous" boundary value problems methods for parameter estimation in differential equations, which are based on constrained Gauss-Newton-type methods and a time domain decomposition by multiple shooting. The methods include a numerical analysis of the well-posedness of the problem and an assessment of the error of the resulting parameter estimates. Next we will discuss efficient optimal control methods for the determination of one, or several complementary, optimal experiments, which maximize the information gain subject to constraints such as experimental costs and feasibility, the range of model validity, or further technical constraints. Special emphasis will be placed on issues of robustness, i.e. how to reduce the sensitivity of the problem solutions with respect to uncertainties - such as outliers in the measurements for parameter estimation, and in particular the dependence of optimum experimental designs on the largely unknown values of the model parameters.

 

Part 1: Parameter estimation problems for processes described by nonlinear differential equations
Part 2: Numerical methods for parameter estimation
Part 3: Design of optimal experiments for information gain