Prof. Dr. Nicolas Gauger, Chair for Scientific Computing (SciComp), TU Kaiserslautern

SciComp Seminar Series

Please contact Prof. Gauger, if you want to register for an online talk in our SciComp Seminar Series or just to register for the seminar.

A list of the already scheduled talks can be found –> here:

Dr. Marcella Bonazzoli, Inria Saclay Centre at Institut Polytechnique de Paris (Palaiseau, France)

Title: One-shot and domain decomposition methods for inverse problems

Abstract:

When an inverse problem is solved by a gradient-based optimization algorithm, the corresponding forward and adjoint problems, which are introduced to compute the gradient, can be also solved iteratively, for instance by domain decomposition methods. In this framework, one-shot inversion methods iterate at the same time on the inverse problem unknown and on the forward and adjoint problem solutions. We are especially interested in the case where the inner iterations for the direct and adjoint problems are incomplete, that is, stopped before achieving a high accuracy on their solutions.
We analyze the convergence of one-shot methods for general linear inverse problems and fixed-point iterations for the associated forward/adjoint problems. In particular, we establish sufficient conditions on the descent step for convergence, which are explicit in the number of inner iterations. We provide numerical experiments, for linear and non linear inverse problems, to illustrate the convergence of these methods in comparison with the classical gradient descent method, where the forward and adjoint problems are solved exactly by a direct solver instead.
This is joint work with Tuan Anh Vu and Houssem Haddar.

How to join online

You can join online via Zoom, using the following link:
https://uni-kl-de.zoom.us/j/63123116305?pwd=Yko3WU9ZblpGR3lGUkVTV1kzMCtUUT09

Lea Fischer, University of Göttingen

Title: Proximal Block Implicit-Explicit Algorithm for Near-field Ptychography

Abstract:

The talk explores the application of the Proximal Heterogeneous Block Input-Output Method (PHeBIE) algorithm to the blind near-field ptychography problem. The structure of the near-field ptychography problem uses lateral and longitudinal shifts of the object. The talk begins with an introduction to fundamental concepts of numerical analysis, focusing on the Fourier transform and the Fresnel near-field propagator. We present an approach to near-field ptychography using lateral and longitudinal shifts, as well as the PHeBIE algorithm. The core of this work lies in the application of the PHeBIE algorithm to near-field ptychography. The resulting new algorithm is implemented in Python and numerical results are presented.

Gururaj Bhat, RPTU

Title: Electricity market nodeling

Abstract:

Electricity is a unique and indispensable commodity that underpins nearly every aspect of
modern life. Electricity prices are affected by numerous factors like fuel sources for power
generation, infrastructure of the electricity grids, and weather, to name a few. Modelling
electricity prices is a complex process due to its non-storable property and the different
characteristics it exhibits, which are discussed in this work. Nonetheless, it is important
to have reliable price simulations to manage risks, keep the system operating smoothly,
and encourage investment in infrastructure and technology for the future. Acknowledging
the past work on anomaly detection in electricity price data, this thesis evaluates existing
methods on recent German market prices and addresses the challenges faced by them.
This work proposes a segmented anomaly detection approach for data processing before
the data is used for calibrating the spot price model. A two-factor electricity spot price
model with a diffusion factor and a jump factor is implemented. Analysis and inferences
drawn from studying the impact of the existing and new methods on the data quality are
presented first. The yield of the respective methods is then evaluated by the calibration
and simulation performance of the chosen two-factor model. The results support the
application of segmented approaches presented in this work as they identify jumps with
higher accuracy, and are able to capture more realised spot price observations in the
different quantile ranges of the simulated price paths.

Prof. Lisa Kusch, TU Eindhoven, The Netherlands

Title:
Design of optical systems: Extending inverse design strategies for imaging and using neural networks for the design of optical surfaces.

Abstract:

Optical systems are designed for various purposes: In non-imaging systems (e.g. lighting) optical surfaces shall guide the light to achieve a certain illuminance. For imaging systems (e.g. cameras, telescopes) light coming from a single point of the object shall also be focused on a single point of the image.

Inverse methods for optical design have been established in the past for designing illumination systems. The overall goal is to find freeform optical surfaces that convert a source distribution into a desired target distribution. With the help of laws for optics, it is possible to find the inverse solution of this problem. This involves solving the Monge-Ampere equation with a transport boundary condition. In this talk we extend the methodology to the design of imaging systems and propose an alternative process for finding the inverse solution.

Designing for imaging optics (cameras, scopes) aims at minimizing aberrations that are deviations from the perfect image on a given target surface. In the first part of this talk we derive an additional condition for inverse design to allow for the design of imaging systems. We apply this methodology for the design of a two-dimensional reflector system and compare the results to a classical design of a telescope system.

In the second part of this talk we will take a closer look at an alternative approach for solving the Monge-Ampere equation with transport boundary condition using a neural network. We impose properties of the underlying physical problem by formulating an appropriate loss function for training the network. The performance is compared to the classical solution strategy based on finite differences and the methodology is further analysed by performing a hyperparameter study.

Finally, we will see some future challenges for the design of imaging systems.

How to join online

You can join online via Zoom, using the following link:
https://uni-kl-de.zoom.us/j/63123116305?pwd=Yko3WU9ZblpGR3lGUkVTV1kzMCtUUT09