arXiv subjects

Marcel Koch

Publications and source records attributed to Marcel Koch.

5 recordsLinked to original sources

arXiv2026

Risk-averse Optimization in Random Materials: Algorithmic Advances and HPC Acceleration

We summarize our advances in the algorithmic development and hardware utilization for risk-averse optimization problems in random materials. This includes risk-averse optimization using the entropic risk measure, as well as recently developed sampling techniques for random materials, that are interoperable with the optimization framework. Furthermore, we discuss recent progress in the efficient utilization of modern hybrid hardware architectures for these methods to solve three-dimensional partial differential equations.

math.NA↗

arXiv2025

Investigating Matrix Repartitioning to Address the Over- and Undersubscription Challenge for a GPU-based CFD Solver

Modern high-performance computing (HPC) increasingly relies on GPUs, but integrating GPU acceleration into complex scientific frameworks like OpenFOAM remains a challenge. Existing approaches either fully refactor the codebase or use plugin-based GPU solvers, each facing trade-offs between performance and development effort. In this work, we address the limitations of plugin-based GPU acceleration in OpenFOAM by proposing a repartitioning strategy that better balances CPU matrix assembly and GPU-based linear solves. We present a detailed computational model, describe a novel matrix repartitioning and update procedure, and evaluate its performance on large-scale CFD simulations. Our results show that the proposed method significantly mitigates oversubscription issues, improving solver performance and resource utilization in heterogeneous CPU-GPU environments.

cs.DC↗

arXiv2025

Software Development Aspects of Integrating Linear Algebra Libraries

Many scientific discoveries are made through, or aided by, the use of simulation software. These sophisticated software applications are not built from the ground up, instead they rely on smaller parts for specific use cases, usually from domains unfamiliar to the application scientists. The software library Ginkgo is one of these building blocks to handle sparse numerical linear algebra on different platforms. By using Ginkgo, applications are able to ease the transition to modern systems, and speed up their simulations through faster numerical linear algebra routines. This paper discusses the challenges and benefits for application software in adopting Ginkgo. It will present examples from different domains, such as CFD, power grid simulation, as well as electro-cardiophysiology. For these cases, the impact of the integrations on the application code is discussed from a software engineering standpoint, and in particular, the approaches taken by Ginkgo and the applications to enable sustainable software development are highlighted.

cs.SE↗

arXiv2024

Performance evaluation of mixed-precision Runge-Kutta methods for the solution of partial differential equations

This work focuses on the numerical study of a recently published class of Runge-Kutta methods designed for mixed-precision arithmetic. We employ the methods in solving partial differential equations on modern hardware. In particular we investigate what speedups are achievable by the use of mixed precision and the dependence of the methods algorithmic compatibility with the computational hardware. We use state-of-the-art software, utilizing the Ginkgo library, which is designed to incorporate mixed precision arithmetic, and perform numerical tests of 3D problems on both GPU and CPU architectures. We show that significant speedups can be achieved but that performance depends on solver parameters and performance of software kernels.

math.NA↗

arXiv2023

Why Capsule Neural Networks Do Not Scale: Challenging the Dynamic Parse-Tree Assumption

Capsule neural networks replace simple, scalar-valued neurons with vector-valued capsules. They are motivated by the pattern recognition system in the human brain, where complex objects are decomposed into a hierarchy of simpler object parts. Such a hierarchy is referred to as a parse-tree. Conceptually, capsule neural networks have been defined to realize such parse-trees. The capsule neural network (CapsNet), by Sabour, Frosst, and Hinton, is the first actual implementation of the conceptual idea of capsule neural networks. CapsNets achieved state-of-the-art performance on simple image recognition tasks with fewer parameters and greater robustness to affine transformations than comparable approaches. This sparked extensive follow-up research. However, despite major efforts, no work was able to scale the CapsNet architecture to more reasonable-sized datasets. Here, we provide a reason for this failure and argue that it is most likely not possible to scale CapsNets beyond toy examples. In particular, we show that the concept of a parse-tree, the main idea behind capsule neuronal networks, is not present in CapsNets. We also show theoretically and experimentally that CapsNets suffer from a vanishing gradient problem that results in the starvation of many capsules during training.

cs.CV↗