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FAST-MOVING PATTERN INTERFACES CLOSE TO A TURING INSTABILITY IN AN ASYMPTOTIC MODEL FOR THE THREE-DIMENSIONAL BÉNARD-MARANGONI PROBLEM

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arXiv 2024年

作者： Hilder, Bastian Jansen, Jonas Department of Mathematics Technische Universität München Boltzmannstrasse 3 Garching B. München 85748 Germany Fraunhofer Institute for Algorithms and Scientific Computing SCAI Schloss Birlinghoven Sankt Augustin53757 Germany

We study the bifurcation of planar patterns and fast-moving pattern interfaces in an asymptotic longwave model for the three-dimensional Bénard–Marangoni problem, which is close to a Turing instability. We derive the model from the full free-boundary Bénard–Marangoni problem for a thin liquid film on a heated substrate of low thermal conductivity via a lubrication approximation. This yields a quasilinear, fully coupled, mixed-order degenerate-parabolic system for the film height and temperature. As the Marangoni number M increases beyond a critical value M∗, the pure conduction state destabilises via a Turing(–Hopf) instability. Close to this critical value, we formally derive a system of amplitude equations which govern the slow modulation dynamics of square or hexagonal patterns. Using center manifold theory, we then study the bifurcation of square and hexagonal planar patterns. Finally, we construct planar fast-moving modulating travelling front solutions that model the transition between two planar patterns. The proof uses a spatial dynamics formulation and a center manifold reduction to a finite-dimensional invariant manifold, where modulating fronts appear as heteroclinic orbits. These modulating fronts facilitate a possible mechanism for pattern formation, as previously observed in *** Codes 35B36, 70K50, 35B32, 35Q35, 35K41, 35K59, 35K65, 35Q79, 76A20, 35B06, 34C37, 37L10 Copyright © 2024, The Authors. All rights reserved.

关键词： Thermal conductivity of liquids

A Framework for Synthetic Power System Dynamics

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arXiv 2023年

作者： Büttner, Anna Plietzsch, Anton Anvari, Mehrnaz Hellmann, Frank Potsdam-Institute for Climate Impact Research Germany Fraunhofer Research Institution for Energy Infrastructures and Geothermal Systems Germany Fraunhofer Institute for Algorithms and Scientific Computing Germany

We present a modular framework for generating synthetic power grids that considers the heterogeneity of real power grid dynamics but remains simple and tractable. This enables the generation of large sets of synthetic grids for a wide range of applications. For the first time, our synthetic model also includes the major drivers of fluctuations on short-time scales and a set of validators that ensure the resulting system dynamics are plausible. The synthetic grids generated are robust and show good synchronization under all evaluated scenarios, as should be expected for realistic power grids. A software package that includes an efficient Julia implementation of the framework is released as a companion to the paper. © 2023, CC BY.

关键词： System theory

NFDI4Health Workflow and Service for Synthetic Data Generation, Assessment and Risk Management

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NFDI4Health Workflow and Service for Synthetic Data Generati...

69th Annual Meeting of the German Association of Medical Informatics, Biometry and Epidemiology, GMDS 2024

作者： Moazemi, Sobhan Adams, Tim Ng, Hwei Geok Kühnel, Lisa Schneider, Julian Näher, Anatol-Fiete Fluck, Juliane Fröhlich, Holger Department of Bioinformatics Fraunhofer Institute for Algorithms and Scientific Computing SCAI Sankt Augustin Germany Knowledge Management ZB MED - Information Centre for Life Sciences Cologne Germany Faculty of Technology Bielefeld University Bielefeld Germany Digital Global Public Health Hasso Plattner Institute for Digital Engineering University of Potsdam Potsdam Germany Institute of Medical Informatics Charité-Universitätsmedizin Germany Method Development Research Infrastructure and Information Technology Robert Koch Institute Berlin Germany The Agricultural Faculty University of Bonn Bonn Germany Institute for Geodesy and Geoinformation University of Bonn Bonn Germany University of Bonn Bonn Germany

ISBN: (纸本)9781643685366

Individual health data is crucial for scientific advancements, particularly in developing Artificial Intelligence (AI);however, sharing real patient information is often restricted due to privacy concerns. A promising solution to this challenge is synthetic data generation. This technique creates entirely new datasets that mimic the statistical properties of real data, while preserving confidential patient information. In this paper, we present the workflow and different services developed in the context of Germany's National Data Infrastructure project NFDI4Health. First, two state-of-the-art AI tools (namely, VAMBN and MultiNODEs) for generating synthetic health data are outlined. Further, we introduce SYNDAT (a public web-based tool) which allows users to visualize and assess the quality and risk of synthetic data provided by desired generative models. Additionally, the utility of the proposed methods and the web-based tool is showcased using data from Alzheimer's Disease Neuroimaging Initiative (ADNI) and the Center for Cancer Registry Data of the Robert Koch institute (RKI). © 2024 The Authors.

关键词： Electronic health record

A Dimension-adaptive Combination Technique for Uncertainty Quantification

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arXiv 2022年

作者： Seidler, Uta Griebel, Michael Institute for Numerical Simulation University of Bonn Friedrich-Hirzebruch-Allee 7 Bonn53115 Germany Fraunhofer Institute for Algorithms and Scientific Computing SCAI Schloss Birlinghoven Sankt Augustin53754 Germany

We present an adaptive algorithm for the computation of quantities of interest involving the solution of a stochastic elliptic PDE where the diffusion coefficient is parametrized by means of a Karhunen-Loève expansion. The approximation of the equivalent parametric problem requires a restriction of the countably infinite-dimensional parameter space to a finite-dimensional parameter set, a spatial discretization and an approximation in the parametric variables. We consider a sparse grid approach between these approximation directions in order to reduce the computational effort and propose a dimension-adaptive combination technique. In addition, a sparse grid quadrature for the high-dimensional parametric approximation is employed and simultaneously balanced with the spatial and stochastic approximation. Our adaptive algorithm constructs a sparse grid approximation based on the benefit-cost ratio such that the regularity and thus the decay of the Karhunen-Loève coefficients is not required beforehand. The decay is detected and exploited as the algorithm adjusts to the anisotropy in the parametric variables. We include numerical examples for the Darcy problem with a lognormal permeability field, which illustrate a good performance of the algorithm: For sufficiently smooth random fields, we essentially recover the spatial order of convergence as asymptotic convergence rate with respect to the computational *** Codes 65N35, 65C20, 65D30, 65N30, 60H35 © 2022, CC BY.

关键词： Diffusion

algorithms in the Orchard: An Embedding-Based Expert Answering System for Apple Rust

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SSRN

SSRN 2025年

作者： Anand, Astha Shen, Jian Cremers, Armin Bernd Jacobs, Marc Fraunhofer Institute for Algorithms and Scientific Computing SCAI Schloss Birlinghoven 1 North Rhine-Westphalia Sankt Augustin53757 Germany RPU Rhenish Plant Power Envirotech Co. Ltd. Bonn-Aachen International Center for Information Technology Friedrich-Hirzebruch-Allee 5 North Rhine-Westphalia Bonn53115 Germany

As sustainable agricultural practices gain importance, the need for intelligent pest control decision-making has grown. This paper introduces SEEDS: Similarity-based Expert Embedding Decision System, a Retrieval-Augmented Generation (RAG) based agricultural question-answering (QA) system. It is built upon a domain-specific knowledge graph (KG), representing Cedar Apple Rust disease, its host and causative agents, plant defense molecules against apple rust infection, and various pesticides. Utilizing the OpenAI embedding model, the system generates embeddings for user queries and KG data, employing similarity metrics to rank KG entries, facilitating accurate and relevant pest control recommendations. SEEDS is a promising niche AI tool in plant protection, setting the stage for scalable, extensible QA frameworks in precision agriculture. The results signify not only a step forward in agricultural expert systems but also highlight the potential for expanding this approach to other crops and pests, marking a substantial advancement in the use of AI for agricultural pest control. © 2025, The Authors. All rights reserved.

关键词： Fruits

Proposal of an achitecture for terminology management in a research project 30

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Proposal of an achitecture for terminology management in a r...

30th Medical Informatics Europe Conference, MIE 2020

作者： Mora, Sara Madan, Sumit Gebel, Stephan Giacomini, Mauro University of Genoa Italy Fraunhofer Institute for Algorithms and Scientific Computing SCAI Department of Bioinformatics Schloss Birlinghoven Sankt Augustin Germany

ISBN: (纸本)9781643680828

Clinical and medical knowledge evolve and this causes changes in concepts and terms that describe them. The objective of this work is to formally present an ontology-based standard architecture that will be used in the scenario of neurodegeneration research to maintain terminologies and their relations updated and coherent over the time. The proposed structure is composed by three elements that will allow the user to do a list of operations on the terminology resources explicitly contemplated by the Common Terminology Service Release 2 (CTS2). © 2020 European Federation for Medical Informatics (EFMI) and IOS Press.

关键词： Ontology

A Partition of Unity Construction of the Stabilization Function in Nitsche's Method for Variational Problems

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SSRN

SSRN 2024年

作者： Jiménez Recio, Pablo Schweitzer, Marc Alexander Institut für Numerische Simulation Universität Bonn Friedrich-Hirzebruch-Allee 7 Bonn53115 Germany Fraunhofer Institute for Algorithms and Scientific Computing Schloss Birlinghoven Sankt Augustin53757 Germany

In this paper we develop a partition-of-unity construction of the stabilization function needed in Nitsche’s method, which can be seen as a generalization of the element-wise construction that is widely used in finite element methods. This allows for the use of Nitsche’s method within the Partition of Unity Method with a stabilization function that is not simply a constant over the whole boundary. In addition to that, we introduce a patch-aggregation approach designed to avoid arbitrarily large values of the stabilization function and the associated ill-conditioned systems and deteriorated convergence rates. We present numerical results to validate the proposed methods, covering Dirichlet boundary conditions, interface constraints and higher- order problems. These results clearly show that our approach leads to optimal convergence rates. © 2024, The Authors. All rights reserved.

关键词： Boundary conditions

Efficient solution of ill-posed integral equations through averaging

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arXiv 2024年

作者： Griebel, Michael Jahn, Tim Institut für Numerische Simulation Universität Bonn Friedrich-Hirzebruch-Allee 7 Bonn53115 Germany Fraunhofer Institute for Algorithms and Scientific Computing SCAI Schloss Birlinghoven Sankt Augustin53754 Germany Institut für Mathematik TU Berlin Straße des 17. Juni 135 Berlin10623 Germany

This paper discusses the error and cost aspects of ill-posed integral equations when given discrete noisy point evaluations on a fine grid. Standard solution methods usually employ discretization schemes that are directly induced by the measurement points. Thus, they may scale unfavorably with the number of evaluation points, which can result in computational inefficiency. To address this issue, we propose an algorithm that achieves the same level of accuracy while significantly reducing computational costs. Our approach involves an initial averaging procedure to sparsify the underlying grid. To keep the exposition simple, we focus on regularization via the truncated singular value decomposition of one-dimensional ill-posed integral equations that have sufficient smoothness. However, the approach can be generalized to other popular regularization methods and more complicated two- and three-dimensional problems with appropriate *** Codes 65, 65R32, 65R20 © 2024, CC BY.

关键词： Integral equations

Predicting Properties of Oxide Glasses Using Informed Neural Networks

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arXiv 2023年

作者： Maier, Gregor Hamaekers, Jan Martilotti, Dominik-Sergio Ziebarth, Benedikt Fraunhofer Institute for Algorithms and Scientific Computing SCAI Schloss Birlinghoven Sankt Augustin53757 Germany Institut für Numerische Simulation Universität Bonn Friedrich-Hirzebruch-Allee 7 Bonn53115 Germany Fraunhofer Center for Machine Learning Schloss Birlinghoven Sankt Augustin53757 Germany Schott AG Hattenbergstrasse 10 Mainz55122 Germany

Many modern-day applications require the development of new materials with specific properties. In particular, the design of new glass compositions is of great industrial interest. Current machine learning methods for learning the composition-property relationship of glasses promise to save on expensive trial-and-error approaches. Even though quite large datasets on the composition of glasses and their properties already exist (i.e., with more than 350,000 samples), they cover only a very small fraction of the space of all possible glass compositions. This limits the applicability of purely data-driven models for property prediction purposes and necessitates the development of models with high extrapolation power. In this paper, we propose a neural network model which incorporates prior scientific and expert knowledge in its learning pipeline. This informed learning approach leads to an improved extrapolation power compared to blind (uninformed) neural network models. To demonstrate this, we train our models to predict three different material properties, that is, the glass transition temperature, the Young’s modulus (at room temperature), and the shear modulus of binary oxide glasses which do not contain sodium. As representatives for conventional blind neural network approaches we use five different feed-forward neural networks of varying widths and depths. For each property, we set up model ensembles of multiple trained models and show that, on average, our proposed informed model performs better in extrapolating the three properties of previously unseen sodium borate glass samples than all five conventional blind models. © 2023, CC BY-SA.

关键词： Extrapolation