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Exploration of core concepts required for mid- and domain-level ontology development to facilitate explainable-AI-readiness of data and models 4

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Exploration of core concepts required for mid- and domain-le...

4th International Workshop on Data meets Ontologies in Explainable AI, DAO-XAI 2024

作者： Horsch, Martin T. Chiacchiera, Silvia Todorov, Ilian T. Correia, Ana Teresa Dey, Aditya Konchakova, Natalia A. Scholze, Sebastian Stephan, Simon Tøndel, Kristin Sarkar, Arkopaul Karray, M. Hedi Al Machot, Fadi Schembera, Björn Norwegian University of Life Sciences Department of Data Science Postboks 5003 Ås1432 Norway UKRI Science and Technology Facilities Council Scientific Computing Department DaresburyWA4 4AD United Kingdom ATB Institut für Angewandte Systemtechnik Bremen GmbH Wiener Str. 1 Bremen28359 Germany Helmholtz-Zentrum Hereon Institute of Surface Science Max-Planck-Str. 1 Geesthacht21502 Germany RPTU Kaiserslautern Laboratory of Engineering Thermodynamics Kaiserslautern67663 Germany University of Technology Tarbes Occitanie Pyrénées Production Engineering Lab. 47 av. d’Azereix Tarbes France University of Stuttgart Institute of Applied Analysis and Numerical Simulation Stuttgart70569 Germany

This position paper reports on the initial discussions within the Knowledge Graph Alliance’s working group on explainable-AI-ready data and metadata principles, which was created in March 2024. At present, we are taking initial steps toward capturing core concepts related to explanation, grounding, reliance, and trust;the scope also extends to potential dual notions such as explainability, verifiability/reproducibility, reliability, and trustworthiness. These initial steps consist in reviewing core concepts as they are discussed in the literature and exploring what could be practically useful definitions of these most central concepts. One of the conclusions is that the metadata standards will need to be suitable for documenting three kinds of grounding: Grounding of knowledge, grounding of reliance, and grounding of trust. Pre-existing metadata standards at the mid and domain level are presently undergoing a redesign in order to become more modular, computationally tractable, intelligible to humans, and adjustable, which will be needed as we continue our work toward actionable recommendations. The development of this system of lite (OWL 2 EL) ontologies, called MSO-EM: Ontologies for modelling, simulation, optimization (MSO) and epistemic metadata (EM), is carried out on a public repository. © 2024 Copyright for this paper by its authors.

关键词： applied ontology epistemic metadata explainable-AI-ready (XAIR) ontology redesign reliability reproducibility

GRADIENT FLOW FINITE ELEMENT DISCRETISATIONS WITH ENERGY-BASED hp-ADAPTIVITY FOR THE GROSS-PITAEVSKII EQUATION WITH ANGULAR MOMENTUM ROTATION

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arXiv 2024年

作者： Heid, Pascal Houston, Paul Stamm, Benjamin Wihler, Thomas P. TUM School of Computation Information Technlogy - Department of Mathematics Boltzmannstrasse 3 Garching bei München85748 Germany University of Applied Sciences and Arts Northwestern Bahnhofstrasse 6 Windisch5210 Switzerland School of Mathematical Sciences University of Nottingham University Park NottinghamNG7 2RD United Kingdom Institute of Applied Analysis and Numerical Simulation University of Stuttgart StuttgartD-70569 Germany Mathematics Institute University of Bern BernCH-3012 Switzerland

This article deals with the stationary Gross-Pitaevskii non-linear eigenvalue problem in the presence of a rotating magnetic field that is used to model macroscopic quantum effects such as Bose-Einstein condensates (BECs). In this regime, the ground-state wave-function can exhibit an a priori unknown number of quantum vortices at unknown locations, which necessitates the exploitation of adaptive numerical strategies. To this end, we consider the conforming finite element method and introduce a combination of a Sobolev gradient descent that respects the energy-topology of the problem to solve the non-linearity and an hp-adaptive strategy that is solely based on energy decay rather than a posteriori error estimators for the refinement process. numerical results demonstrate that the hp-adaptive strategy is highly efficient in terms of accuracy to compute the ground-state wave function and energy for several test problems where we observe exponential convergence. Copyright © 2024, The Authors. All rights reserved.

关键词： Wave functions

Adaptive Piecewise Poly-Sinc Methods for Ordinary Differential Equations

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arXiv 2022年

作者： Khalil, Omar El-Sharkawy, Hany Youssef, Maha Baumann, Gerd Mathematics Department German University in Cairo New Cairo City Cairo11835 Egypt Department of Mathematics Faculty of Science Ain Shams University Abbassia Cairo11566 Egypt Institute of Applied Analysis and Numerical Simulation University of Stuttgart Pfaffenwaldring 57 StuttgartD-70569 Germany Faculty of Natural Sciences University of Ulm Albert-Einstein-Allee 11 UlmD-89069 Germany

We propose a new method of adaptive piecewise approximation based on Sinc points for ordinary differential equations. The adaptive method is a piecewise collocation method which utilizes Poly-Sinc interpolation to reach a preset level of accuracy for the approximation. Our work extends the adaptive piecewise Poly-Sinc method to function approximation, for which we derived an a priori error estimate for our adaptive method and showed its exponential convergence in the number of iterations. In this work, we show the exponential convergence in the number of iterations of the a priori error estimate obtained from the piecewise collocation method, provided that a good estimate of the exact solution of the ordinary differential equation at the Sinc points exists. We use a statistical approach for partition refinement. The adaptive greedy piecewise Poly-Sinc algorithm is validated on regular and stiff ordinary differential equations. © 2022, CC BY.

关键词： Initial value problems

Error Estimation for the simulation of Elastic Multibody Systems

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PAMM 2018年第1期18卷

作者： Jörg Fehr Dennis Grunert Ashish Bhatt Bernard Haasdonk Institute of Engineering and Computational Mechanics University of Stuttgart Pfaffenwaldring 9 70569 Stuttgart Institute of Applied Analysis and Numerical Simulation University of Stuttgart Pfaffenwaldring 57 70569 Stuttgart

One important issue in the development of complex technical system is the use of rapid simulations to evaluate substructures / surrogate models for system level simulations. For safety-critical simulations, it is essential to know the error introduced by model order reduction (MOR) used to create the surrogate models to decide whether the simulation can be trusted or not. Typically, a-priori error estimates, e.g., the sum of neglected singular values in balanced truncation are used. They deliver upper bounds for the error – independently of the applied excitation. By contrast, the error estimates from the reduced basis community deliver a-posteriori error bounds, which account for the current excitation. These error bounds use the residual between the reduced and original model to derive an error bound. In this work, we review the error bounds used in elastic multibody system (EMBS) described in the floating frame of reference formulation.

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Exa-Dune - Flexible PDE solvers, numerical methods and applications

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arXiv 2019年

作者： Bastian, Peter Altenbernd, Mirco Dreier, Nils-Arne Engwer, Christian Fahlke, Jorrit Fritze, René Geveler, Markus Göddeke, Dominik Iliev, Oleg Ippisch, Olaf Mohring, Jan Müthing, Steffen Ohlberger, Mario Ribbrock, Dirk Shegunov, Nikolay Turek, Stefan Interdisciplinary Center for Scientific Computing Heidelberg University Im Neuenheimer Feld 368 HeidelbergD-69120 Institute for Analysis and Numerics University of Münster Orleans-Ring 10 MünsterD-48149 Institute for Applied Analysis and Numerical Simulation University of Stuttgart Allmandring 5b StuttgartD-70569 Inst. f. Applied Mathematics TU Dortmund Vogelpothsweg 87 DortmundD-44227 Germany Fraunhofer Institute for Industrial Mathematics ITWM Fraunhofer-Platz 1 KaiserslauterD-67663 Germany Institut für Mathematik TU Clausthal-Zellerfeld Erzstr. 1 Clausthal-ZellerfeldD-38678 Germany

In the Exa-Dune project we have developed, implemented and optimised numerical algorithms and software for the scalable solution of partial differential equations (PDEs) on future exascale systems exhibiting a heterogeneous massively parallel architecture. In order to cope with the increased probability of hardware failures, one aim of the project was to add flexible, application-oriented resilience capabilities into the framework. Continuous improvement of the underlying hardware-oriented numerical methods have included GPU-based sparse approximate inverses, matrix-free sum-factorisation for high-order discontinuous Galerkin discretisations as well as partially matrix-free preconditioners. On top of that, additional scalability is facilitated by exploiting massive coarse grained parallelism offered by multiscale and uncertainty quantification methods where we have focused on the adaptive choice of the coarse/fine scale and the overlap region as well as the combination of local reduced basis multiscale methods and the multilevel Monte-Carlo algorithm. Finally, some of the concepts are applied in a land-surface model including subsurface flow and surface runoff. Copyright © 2019, The Authors. All rights reserved.

关键词： numerical methods

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Preface

International Journal of Mineral Processing 2004年第2期73卷 63-63页

作者： B.K. Parekh Raimund Bürger Karsten Keller Center for Applied Energy Research University of Kentucky 2540 Research Park Drive Lexington KY 40511 USA Institute of Applied Analysis and Numerical Simulation University of Stuttgart Germany DuPont Research and Development Wilmington DE USA

A Quasi Time-Reversible scheme based on density matrix extrapolation on the Grassmann manifold for Born-Oppenheimer Molecular Dynamics

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arXiv 2023年

作者： Pes, Federica Polack, Étienne Mazzeo, Patrizia Dusson, Geneviève Stamm, Benjamin Lipparini, Filippo Dipartimento di Chimica e Chimica Industriale Università di Pisa Via G. Moruzzi 13 Pisa56124 Italy CERMICS École des Ponts and Inria Paris 6 & 8 avenue Blaise Pascal Marne-la-Vallé 77455 France Laboratoire de Mathématiques de Besançon UMR CNRS 6623 Université de Franche-Comté 16 route de Gray Besançon25030 France Institute of Applied Analysis and Numerical Simulation University of Stuttgart Stuttgart70569 Germany

This article proposes a so-called Quasi Time-Reversible (QTR G-Ext) scheme based on Grassmann extrapolation of density matrices for an accurate calculation of initial guesses in Born-Oppenheimer Molecular Dynamics simulations. The method shows excellent results on four large molecular systems, ranging from 21 to 94 atoms simulated with Kohn-Sham density functional theory surrounded with a classical environment with 6k to 16k atoms. Namely, it clearly reduces the number of self-consistent field iterations, while keeping a similar energy drift as in the extended Lagrangian Born-Oppenheimer method. © 2023, CC BY-NC-SA.

关键词： Extrapolation

Correction to: modelling sediment transport in three-phase surface water systems

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Journal of Hydraulic Research 2023年第1期61卷 168-171页

作者： Cass T. Miller William G. Gray Christopher E. Kees Iryna V. Rybak Brittany J. Shepherd a Okun Distinguished Professor Department of Environmental Sciences and Engineering University of North Carolina Chapel Hill North Carolina 27599-7431 USA b Professor Department of Environmental Sciences and Engineering University of North Carolina Chapel Hill North Carolina 27599-7431 USA Email: graywg@*** c CSRS Distinguished Professor Louisiana State University Baton Rouge Louisiana 70803 USA Email: cekees@lsu.edu d Research Engineer Institute of Applied Analysis and Numerical Simulation University of Stuttgart Germany Email: rybak@ians.uni-stuttgart.de e PhD Student Department of Mathematics University of North Carolina Chapel Hill North Carolina 27599-3250 USA Email: breizh@live.unc.edu

ABSTRACTABSTRACTThis note corrects an error made in Miller et al. (2019). Modelling sediment transport in three-phase surface water *** of Hydraulic Research,57(4), 439–463,https://***/10.1080/00221686.2019.1581... 详细信息

关键词： Averaging theory continuum mechanics entropy production rate mechanistic modeling porous medium flow TCAT

Verification benchmarks for single-phase flow in three-dimensional fractured porous media

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arXiv 2020年

作者： Berre, Inga Boon, Wietse M. Flemisch, Bernd Fumagalli, Alessio Gläser, Dennis Keilegavlen, Eirik Scotti, Anna Stefansson, Ivar Tatomir, Alexandru Brenner, Konstantin Burbulla, Samuel Devloo, Philippe Duran, Omar Favino, Marco Hennicker, Julian Lee, I-Hsien Lipnikov, Konstantin Masson, Roland Mosthaf, Klaus Chiara Nestola, Maria Giuseppina Ni, Chuen-Fa Nikitin, Kirill Schädle, Philipp Svyatskiy, Daniil Yanbarisov, Ruslan Zulianp, Patrick Department of Mathematics University of Bergen Allégaten 41 Bergen5007 Norway Department of Mathematics KTH Royal Institute of Technology Lindstedtsvägen 25 Stockholm11428 Sweden Department of Hydromechanics and Modelling of Hydrosystems University of Stuttgart Pfaffenwaldring 61 Stuttgart70569 Germany Laboratory for Modeling and Scientific Computing MOX Politecnico di Milano p.za Leonardo da Vinci 32 Milano20133 Italy Department of Applied Geology Geosciences Center University of Göttingen Goldschmidtstrasse 3 Göttingen37077 Germany Department of Earth Sciences Uppsala University Villavägen 16 UppsalaS-75236 Sweden University of Côte d’Azur CNRS INRIA LJAD Nice France Institute of Applied Analysis and Numerical Simulation University of Stuttgart Pfaffenwaldring 57 Stuttgart70569 Germany FEC Universidade Estadual de Campinas Cidade Universitária R. Josiah Willard Gibbs 85 Campinas-SPCEP 13083-839 Brazil Institute of Earth Sciences University of Lausanne Building Geopolis UNIL-Mouline Lausanne1015 Switzerland Section de Mathématiques Université de Genève 2-4 rue du Lièvre CP 64 Genève1211 Switzerland Graduate Institute of Applied Geology National Central University Taiwan Center for Environmental Studies National Central University Taiwan Los Alamos National Laboratory New Mexico United States Department of Environmental Engineering Technical University of Denmark Bygningstorvet Building 115 Kgs. Lyngby2800 Denmark Numerical Simulation in Science Medicine and Engineering Group Institute of Computational Science Università della Svizzera italiana. Via G. Buffi 13 Lugano Ticino6900 Switzerland Marchuk Institute of Numerical Mathematics of Russian Academy of Sciences Moscow Russia ETH Zürich Geothermal Energy and Geofluids Group Institute of Geophysics Zürich8092 Switzerland

Flow in fractured porous media occurs in the earth’s subsurface, in biological tissues, and in man-made materials. Fractures have a dominating influence on flow processes, and the last decade has seen an extensive development of models and numerical methods that explicitly account for their presence. To support these developments, we present a portfolio of four benchmark cases for single-phase flow in three-dimensional fractured porous media. The cases are specifically designed to test the methods’ capabilities in handling various complexities common to the geometrical structures of fracture networks. Based on an open call for participation, results obtained with 17 numerical methods were collected. This paper presents the underlying mathematical model, an overview of the features of the participating numerical methods, and their performance in solving the benchmark cases. Copyright © 2020, The Authors. All rights reserved.

关键词： numerical methods