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:

Amin Jafarimoghaddam, Department of Aerospace Engineering, Universidad Carlos III, Madrid, Spain

Title: From Residual Neural Networks to Neural ODEs – theory and applications

Abstract:

This talk explores key developments in neural network architectures. The discussion begins with an examination of Residual Neural Networks and their relation to Neural Ordinary Differential Equations (Neural ODEs). We briefly review some of the advantages, and limitations of Neural ODEs. We also consider possible variations of Residual Neural Networks and their higher-order Neural ODE representation. Furthermore, we explore the possibility of networks equipped with average nonlinear programming techniques, which might be alternatives to addressing the deep learning issues. Finally, we highlight some potential practical applications.

How to join online

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

Lukas Baumgärtner, Department of Mathematics, Humboldt University Berlin
and
PD Dr. Stephan Schmidt, Department of Mathematics, University of Trier

Title: Using Transport Equations for Image Processing and Mesh Generation in Medical Applications

Abstract:

We consider the use of transport equations for solving medical image registration problem by determining the best optical flow between different brain MRI scans. In a follow-up procedure, this registration data is used to make a default generic brain mesh patient specific.
In the ensuing optimal control problem, the transport equation is solved via an upwind scheme in a DG discretization, which usually introduces non-smoothness due to absolute values. To avoid this, we propose a smoothed version of the upwind scheme which is by construction consistent with the transport equation. Its L2-stability can be shown similarly to the regular upwind scheme by a von Neumann stability analysis, however, under a slightly different CFL-condition. For the linear transport equation, this yields a reasonable scheme by the Lax equivalence theorem.
Numerical results are presented for the image registration problem. The corresponding mesh deformations are compared to state-of-the-art brain meshing software FreeSurfer. Towards the end of this talk, non-smoothness of the regular upwind scheme is discussed in the context of the non-linear PDEs of fluid mechanics.

How to join online

You can join online via Jitsi, using the following link:
https://jitsi.rptu.de/scicomp_seminar

Ket Yee Lee, RHRZ@RPTU and University of Applied Sciences Kaiserslautern

Title: Data Preprocessing Using NLP for Ticket Dispatching with Classical Classification Methods

Abstract:

Writing a support request from a customer perspective can be challenging. From a data science point of view, processing them for machine learning can be challenging as well. In this master thesis, the methods from Natural Language Processing (NLP) are applied to prepare the assignment of service requests into the respective associated queues in a machine-understandable way. Texts are cleaned and qualified using tokenization and part-of-speech tagging (POS) with the German Stuttgart-Tübingen tag set (STTS).
The classical classification methods Naïve Bayes, Decision Tree, Logistic Regression, Super Vector Machine, k Nearest Neigbor and the ensemble methods Random Forest, Gradient Boosting and Tree Ensemble are contrasted.
Dispatching of customer queries written in natural language is possible using classical classification methods. The proof-of-concept shows that with Logistic Regression, for the available database, tickets can be assigned by machine with 64.5% accuracy for the top 10 queues.

Dr. Kazuki Hayashi , Assistant Professor, Department of Architecture and Architectural Engineering, Kyoto University, Japan

Title: Extracting meaningful features from data with irregular connectivity for structural optimization

Abstract:

The data handled by machine learning is not necessarily aligned in a rectangular array like raster images. In this case, the data can be represented as graphs consisting of vertices and edges. However, capturing important features from graphs is a challenging problem. This talk discuss graph embedding, a technique used to extract features from graphs, and explore case studies that demostrate the usefulness of graph embedding in solving structural optimization problems, including topology optimization of trusses, sizing optimization of steel frames, and assembly sequence optimization.

How to join online

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

Dr. Alexander Linke , Chair for Scientific Computing (SciComp), University of Kaiserslautern-Landau (RPTU)

Title: On the Discretization of the Incompressible Navier–Stokes Equations, an Elephant in the Room, and a Conceptual Update for Discretizing Constrained PDEs

Abstract:

The dynamics of the incompressible Navier-Stokes equations are closely related to equivalence classes of forces and an associated semi-norm, in the kernel of which all gradient fields lie. The corresponding numerical treatment of gradient fields in the momentum balance, which only change the pressure but not the velocity of an incompressible flow, has been repeatedly addressed in research since the 1980s, and a number of very different algorithmic approaches have been proposed to avoid this numerical source of error. For many years, however, the research question remained the proverbial ‘elephant in the room’, whose relevance for simulation practice was assessed very differently in the research community. The talk provides an overview of the historical development of the research question and discusses its practical relevance based on completely different physical regimes such as hydrostatics and high Reynolds number vortex flows. In particular, it discusses how recently developed pressure-robust methods using H(div)-conforming finite elements could solve the numerical challenge in a fundamental way and thus contribute to the solution of other previously unsolved problems. Furthermore, a conceptual update for the discretization of PDEs with constraints is proposed, which replaces the historical Stokes model problem of classical mixed finite element theory by a set of model problems from which the relevance of H(div)-conforming algorithms for the discretization of incompressible flows immediately emerges. Finally, considerations on the relevance of the obtained results for the numerical treatment of related problems, such as the compressible Navier–Stokes equations, are discussed.

How to join online

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

Timo Sonnenschein, Department of Computer Science, University of Kaiserslautern-Landau (RPTU)

Title: Introduction to Implicit Layers in the context of Deep Equilibrium Models

Abstract:

Training modern neural networks can be challenging with the limited memory of specialized hardware. Reusing parameters and storing only a few intermediate results for backward propagation can reduce memory consumption significantly.

Implicit layers offer a solution by iteratively applying the same function until convergence and calculating the gradients at the converged point without any intermediate results using implicit differentiation. Further, implicit layers allow for various sets of requirements. Due to the separation of problem definition and actual computation, they can utilize several solving methods and adapt the accuracy to the problem. One major shortcoming is the runtime, not only for training but also for inference. Further investigation might solve this problem.

One architectures using implicit layers are the Deep Equilibrium Models. They have comparable accuracy to state-of-the-art models in a variety of fields, including language processing and visual tasks.

In conclusion, this talk explores implicit layers, emphasizing their efficiency, adaptability, and potential contributions to neural network architectures. The discussions on DEQ models aim to unravel their applications in the field.

How to join online

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

Anuja Chakraborty, Department of Computer Science, University of Kaiserslautern-Landau (RPTU)

Title: On Compressed Sensing and Dynamic Mode Decomposition

Abstract:

This talk is focused on the discussion regarding the development and application of compressed
sensing strategies for computing the dynamic mode decomposition (DMD) from heavily subsampled
or compressed data. The review was mainly done based on the paper of Brunton’s COMPRESSED
SENSING AND DYNAMIC MODE DECOMPOSITION [1]. The compressed sensing techniques developed
in this work result in DMD eigenvalues that are equivalent to those obtained from full-state data.
This is significant as it enables a consistent representation of system dynamics even with highly
reduced data. Using l1-minimization or greedy algorithms, the study demonstrates the possibility of
reconstructing full-state DMD eigenvectors from the compressed DMD eigenvalues. This
reconstruction allows for the recovery of detailed information about the system’s modes. These
results rely on a number of theoretical advances which is covered in this report. Also, effectiveness of
the proposed compressed sensing architecture is illustrated through two model systems where the
first example is on designing a spatial signal from a sparse vector of Fourier coefficients with a linear
dynamical system driving the coefficients and the second example is on a double gyre flow field,
which is a model for chaotic mixing in the ocean. So, the theoretical insights and practical
demonstrations enhance the understanding and applicability of DMD methodologies in diverse
scenarios.

[1] Steven L. Brunton, Joshua L. Proctor, Jonathan H. Tu, J. Nathan Kutz COMPRESSED SENSING AND
DYNAMIC MODE DECOMPOSITION, Journal of Computational Dynamics American Institute of
Mathematical Sciences, Volume 2, Number 2, December 2015

How to join online

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

Johannes Schoder, Institute for Computer Science, University of Jena

Title: First Steps Towards Bringing Automatic Differentiation to Scale with RISC-V

Abstract:

Small adaptions to the control unit and datapath of a RISC-V processor enable us to apply forward-mode automatic differentiation in hardware to arithmetic instructions. The presented processor design extends an existing implementation of the RISC-V ISA, written for high-level synthesis in C. With some adaptions to the existing architecture, we enable automatic differentiation in hardware. To that extent, we introduce custom RISC-V instructions. The synthesized design runs on an FPGA.

How to join online

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