1st Alps-Adriatic Inverse Problems Workshop 2019

Contribution List

17. On a semismooth* Newton method for generalized equations

Helmut Gfrerer

07/11/2019, 09:10

In this talk we introduce a new notion of semismoothness
which pertains both sets as well as multifunctions. In the case
of single-valued maps it is closely related with the standard
notion of semismoothness introduced by Qi and Sun in 1993.
Semismoothness can be equivalently characterized in terms of
regular, limiting and directional limiting coderivatives.

Then we present a semismooth*...

13. Iterative regularization for nonsmooth inverse problems

Christian Clason

07/11/2019, 09:50

We consider inverse problems for nonlinear forward models that are directionally but not Fréchet differentiable; examples include solution mappings for nonsmooth partial differential equations or variational inequalities. In this setting, standard derivative-based regularization methods such as Landweber or Levenberg--Marquardt iteration are inapplicable. We show that using elements of the...

10. Theoretical and numerical analysis of fundamental models in nonlinear acoustics

Mechthild Thalhammer

07/11/2019, 10:50

In this talk, I will present joint work with Barbara Kaltenbacher on fundamental models in nonlinear acoustics. In a first part, I will introduce a hierarchy of nonlinear damped wave equations that arise in the modelling of sound propagation in thermoviscous fluids. In a second part, I will discuss a rigorous result which implies that two classical models, the Kuznetsov and Westervelt...

11. A high-order discontinuous Galerkin approach for nonlinear sound waves

Vanja Nikolić

07/11/2019, 11:30

Accurate simulation of nonlinear sound waves offers a road to improving a variety of procedures in industry and medicine,
ranging from non-destructive detection of material damages to non-invasive treatments of medical disorders.
In this talk, we will discuss the spatial discretization of Westervelt’s quasi-linear acoustic equation by a high-order discontinuous Galerkin method.
The...

20. Control and controllability of PDEs with hysteresis

Pavel Krejcí

07/11/2019, 12:00

For a diffusion equation with a complex hysteresis operator we consider the problem
of controllability, that is, finding a control which guarantees that the solution reaches
a desired value at a given time. It is solved here by a constructive method based on
a two-parameter penalty argument. One small parameter penalizes the distance of
the solution at final time from the expected value, the...

21. Augmented GMRES-type versus CGNE methods for the solution of linear ill-posed problems

Andreas Neubauer

07/11/2019, 13:40

In this paper we compare (augmented) GMRES-type methods and (augmented) CGNE methods. The numerical results show that the CGNE method is more robust and is suitable for ill-posed problems with a much higher degree of ill-posedness. GMRES-type methods only yield useful results for very moderate ill-posed problems.

18. On Levenberg-Marquardt type methods for ill-posed operator equations

Antonio Leitao

07/11/2019, 14:20

On this talk we report on a joint work with Prof. B.Kaltenbacher on Levenberg-Marquardt type methods for solving nonlinear ill-posed operator equations in Hilbert spaces.
Moreover, we also discuss some recent research results on this iterative method.

19. Acceleration of sequential subspace optimization in Banach spaces by orthogonal search directions

Thomas Schuster

07/11/2019, 15:00

A standard solution technique for linear operator equations of first kind is the Landweber scheme which is an iterative method that uses the negative gradient of the current residual as search direction, which is then also called the Landweber direction. Though this method proves to be stable with respect to noisy data, it is known to be numerically slow for problems in Hilbert spaces and this...

4. Optimal convergence rates for sparsity promoting wavelet-regularization in Besov spaces

Thorsten Hohage

07/11/2019, 16:00

We report on joint work with Philip Miller on Tikhonov regularization for linear and nonlinear ill-posed operator equations with wavelet Besov norm penalties. We focus on Besov norms with fine index 1, which yield estimators that are sparse with respect to a wavelet frame. Our framework includes, among others, the Radon transform and some nonlinear inverse problems in differential equations...

22. Tikhonov regularization with oversmoothing penalty: phenomena, convergence and rates

Bernd Hofmann

07/11/2019, 16:40

The presentation is devoted to Tikhonov regularization under conditional stability
estimates for nonlinear ill-posed operator equations in Hilbert scales. Our focus
is on the case of oversmoothing penalties, for which the true solution no longer
attains a finite value. In this context, we present some new results on convergence
and recall assertions on rates. We strongly highlight the local...

27. A multiplicative iterative method for ill-posed problems

Elena Resmerita

07/11/2019, 17:20

We present a multiplicative entropic type method for ill-posed equations, which has a closed form and preserves nonnegativity of the iterates. Interestingly, this has been investigated in finite dimensional optimization under different names/versions, while related methods have been considered in inverse problems as well. We discuss convergence and error estimates, and test the method on...

23. The tangential cone condition for some coefficient identification model problems in parabolic PDEs.

Tram Ngoc Nguyen

07/11/2019, 17:50

The tangential condition was introduced in [Hanke, Neubauer, and Scherzer, 1995] as a sufficient condition for convergence of the Landweber iteration for solving ill-posed problems. This condition ensures nonlinearity of the forward operator fits together with the data misfit. In this talk, we present a series of time dependent benchmark inverse problems for which we can verify this condition....

24. A Random Wanderers guide to the Diffusion Equation Universe

Bill Rundell

08/11/2019, 09:00

The classical reaction-diffusion equation can be stated as the rate of change of the state variable $u$ equals the sum of a diffusion operator and a (often nonlinear) reaction term: $u_t = -L\,u + f(u)$, where typically $-L$ is an elliptic operator. The equation, while known in form, can have specific parameters undetermined; for example coefficients in $L$ or the function $f$ itself.
We look...

25. Data driven regularization by projection

Otmar Scherzer

08/11/2019, 09:40

Regularization methods for inverse problems can be based on mathematical forward methods which represent the Physics and Chemistry
as precise as possible. With the rise of the area of big data, methods that combine forward modelling with data driven techniques have been
being developed. In this talk we demonstrate that regularisation by projection can be formulated in a purely data driven...

16. Inverse Scheme for Acoustic Source Localization based on Adjoint Method

Manfred Kaltenbacher

08/11/2019, 10:10

We propose an inverse scheme for acoustic source localization based on solving the corresponding partial differential equation in the frequency domain (Helmholtz equation) by applying the Finite Element (FE) method. This allows us to fully take into account the actual boundary conditions as given in the measurement setup. To recover the source locations, an inverse scheme based on a sparsity...

28. Mathematical modelling and statistical inference for large-scale models of cancer signalling

Jan Hasenauer

08/11/2019, 11:00

The sequencing of cancer biopsies revealed that cancer is multi-factorial diseases, which strongly vary between patients. This inter-patient variability poses a challenge for clinicians. A priori it is not clear which drug will be most beneficial for a specific patient. Here, we approach the problem of drug response prediction using mechanistic mathematical models. We develop a mathematical...

26. A Collection of Inverse Problems in Engineering Applications

Tom Lahmer

08/11/2019, 11:30

The talk presents a series of examples, where engineers are actually faced with inverse problems of different types. Solution strategies and results are given for several examples including poroelasticity and piezoelectricity. The inverse problems are mainly of parameter and source identification type.

A new series of inverse problems comes up by the rapid developments in additive printing...

14. All-at-once formulations of inverse problems within the Bayesian approach

Anna Schlintl

08/11/2019, 12:00

The all-at-once-formulation for deterministic inverse problems has recently been considered. Our goal is to put this approach in a Bayesian framework. The advantages of our approach are the additional choice of a prior also for the state variable and the possibility to take into account perturbations in the model. By means of the inverse source problem and the backward heat equation we test...

8. Minimization based formulations of the EIT problem with the CEM

Kha Van Huynh

08/11/2019, 12:15

One of the recent approaches to solving inverse problems is to use the all-at-once formulation where both the state and the parameter are considered as unknowns. The advantage of this method is to avoid using the parameter-to-state map, which is usually difficult to determine in real problems and sometimes leads to strictly restrictive conditions. In this talk, we regularize the electrical...

5. Modelling approaches to assess the reliability of semiconductor devices

Olivia Pfeiler

08/11/2019, 13:30

One research area of KAI – Kompetenzzentrum Automobil- und Industrieelektronik is the reliability of semiconductor devices. Often, the reliability is assessed by extensive testing. To save test resources, we develop lifetime models describing the degradation of the devices under application conditions. To achieve good results we research three approaches: statistical lifetime models, FEM...

15. Stochastic state space modeling of thermo-mechanical fatigue

Barbara Pedretscher

08/11/2019, 13:45

Modeling fatigue induced degradation of a metal film requires a consistent mathematical description of the physically relevant damage driving forces. In this work, a state space model, based on Itó stochastic processes to account for intrinsic stochastic effects, is followed. Parameter identification and uncertainty quantification are based on the system’s corresponding Fokker-Planck equation,...

12. Process Simulation at Linde Engineering

Stephania Hokenmaier

08/11/2019, 14:00

Building on its vast and unique experience, Linde has been developing and optimizing gas processing, separation and liquefaction technologies for 140 years. Through trusted, lasting business relationships, it collaborates closely with customers the world over to develop tailored solutions that maximize plant lifecycle productivity, efficiency and service life.
With the help of process...

9. Modelling and Machine Learning for industrial sensing applications

Romana Boiger

08/11/2019, 14:15

The Materials Center Leoben (MCL) is an internationally active research institution specialized in materials, production and processing engineering and innovative material applications. Besides a comprehensive range of services, the MCL carries out cooperative research and development projects in close collaboration with industry. The latter is the focus of my team, the embedded computing...

30. Brief introduction into the work as an actuary

Jonas Offtermatt

08/11/2019, 14:30

In this talk a short introduction into to work of a mathematician at an insurance company will be given. Starting with the one and only necessary equation for insurance mathematics, over working as data analyst, or in marketing, we will end with the work of a mathematician in IT-department.

6. A pattern identification problem in energy time series

Peter Steinhorst

Prognoses of energy yield and load profiles are an useful tool for optimization in dimensioning and operation management of renewable energy-storage-systems. Within part of a research project, time series with electric power data of a photovoltaics unit, some machines and overall consumption have been measured with high time resolution at an industrial company.
Caused by breakdowns in...

31. Closing Event