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Advances concerning multiscale methods and uncertainty quantification in EXA-DUNE

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Advances concerning multiscale methods and uncertainty quant...

International Conference on Software for Exascale computing, SPPEXA 2015

作者： Bastian, Peter Engwer, Christian Fahlke, Jorrit Geveler, Markus Göddeke, Dominik Iliev, Oleg Ippisch, Olaf Milk, René Mohring, Jan Müthing, Steffen Ohlberger, Mario Ribbrock, Dirk Turek, Stefan Interdisciplinary Center for Scientific Computing Heidelberg University Heidelberg Germany Institute for Computational and Applied Mathematics University of Münster Münster Germany Institute of Applied Analysis and Numerical Simulation University of Stuttgart Stuttgart Germany Institute for Applied Mathematics TU Dortmund Dortmund Germany Fraunhofer Institute for Industrial Mathematics ITWM Kaiserslautern Germany Institut für Mathematik TU Clausthal-Zellerfeld Clausthal-Zellerfeld Germany

ISBN: (纸本)9783319405261

In this contribution we present advances concerning efficient parallel multiscale methods and uncertainty quantification that have been obtained in the frame of the DFG priority program 1648 Software for Exascale computing (SPPEXA) within the funded project EXA-DUNE. This project aims at the development of flexible but nevertheless hardware-specific software components and scalable high-level algorithms for the solution of partial differential equations based on the DUNE platform. While the development of hardware-based concepts and software components is detailed in the companion paper (Bastian et al., Hardware-based efficiency advances in the EXA-DUNE project. In: Proceedings of the SPPEXA Symposium 2016, Munich, 25–27 Jan 2016), we focus here on the development of scalable multiscale methods in the context of uncertainty. © Springer International Publishing Switzerland 2016.

关键词： Uncertainty analysis

Deep neural networks on diffeomorphism groups for optimal shape reparameterization

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arXiv 2022年

作者： Celledoni, Elena Glöckner, Helge Riseth, Jørgen Schmeding, Alexander Department of Mathematics NTNU Trondheim Norway Institut für Mathematik Universität Paderborn Germany Department of Numerical Analysis and Scientific Computing Simula Research Laboratory Norway Department of Mathematics University of Oslo Norway

One of the fundamental problems in shape analysis is to align curves or surfaces before computing geodesic distances between their shapes. Finding the optimal reparametrization realizing this alignment is a computationally demanding task, typically done by solving an optimization problem on the diffeomorphism group. In this paper, we propose an algorithm for constructing approximations of orientation-preserving diffeomorphisms by composition of elementary diffeomorphisms. The algorithm is implemented using PyTorch, and is applicable for both unparametrized curves and surfaces. Moreover, we show universal approximation properties for the constructed architectures, and obtain bounds for the Lipschitz constants of the resulting *** Codes 65K10, 58D05, 46T10 © 2022, CC BY.

关键词： Deep neural networks

On The Importance of Fundamental Computational Fluid Dynamics Towards a Robust and Reliable Model of Left Atrial Flows: Is There More Than Meets the Eye?

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arXiv 2023年

作者： Khalili, Ehsan Daversin-Catty, Cécile Olivares, Andy L. Mill, Jordi Camara, Oscar Valen-Sendstad, Kristian Department of Computational Physiology Simula Research Laboratory Oslo Norway Department of Numerical Analysis and Scientific Computing Simula Research Laboratory Oslo Norway Department of Information and Communication Technologies Universitat Pompeu Fabra Barcelona Spain

Computational fluid dynamics (CFD) studies of left atrial flows have reached a sophisticated level, e.g., revealing plausible relationships between hemodynamics and stresses with atrial fibrillation. However, little focus has been on fundamental fluid modelling of LA flows. The purpose of this study was to investigate the spatiotemporal convergence, along with the differences between high- (HR) versus normal-resolution/accuracy (NR) solution strategies, respectively. CFD simulations on 12 patient-specific left atrial geometries, obtained from computed tomography scans, were performed by using a second-order accurate and space/time centered solver. The convergence studies showed an average variability of around 30% and 55% for time averaged wall shear stress (WSS), oscillatory shear index (OSI), relative residence time (RRT), and endothelial cell activation potential (ECAP), even between intermediate spatial and temporal resolutions, in the left atrium (LA) and left atrial appendage (LAA), respectively. The comparison between HR and NR simulations showed good correlation in the LA for WSS, RRT, and ECAP (R2 > 0.9), but not for OSI (R2 = 0.63). However, there were poor correlations in the LAA especially for OSI, RRT, and ECAP (R2 = 0.55, 0.63, and 0.61, respectively), except for WSS (R2 = 0.81). The errors are comparable to differences previously reported with disease correlations. To robustly predict atrial hemodynamics and stresses, numerical resolutions of 10M elements and 10k time-steps per cycle seem necessary (i.e., one order of magnitude higher than normally used in both space and time). In conclusion, attention to fundamental numerical aspects is essential towards establishing a plausible, robust, and reliable model of LA flows. Copyright © 2023, The Authors. All rights reserved.

关键词： Sensitivity analysis

A Hybrid Discontinuous Galerkin Method for Darcy-Stokes Problems

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Lecture Notes in Computational Science and Engineering

Lecture Notes in Computational Science and Engineering 2013年 91卷 663-670页

作者： Egger, Herbert Waluga, Christian Department of Mathematics Numerical Analysis and Scientific Computing Technische Universität Darmstadt Dolivostraße 15 64293 Darmstadt Germany Center of Mathematics Technische Universität München Boltzmannstraße 3 85748 Garching bei München Germany

We propose and analyze a hybrid discontinuous Galerkin method for the solution of incompressible flow problems, which allows to deal with pure Stokes, pure Darcy, and coupled Darcy-Stokes flow in a unified manner. The... 详细信息

ISBN: (纸本)9783642352744

关键词： Incompressible flow

Hardware-Based efficiency advances in the EXA-DUNE project

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Hardware-Based efficiency advances in the EXA-DUNE project

International Conference on Software for Exascale computing, SPPEXA 2015

作者： Bastian, Peter Engwer, Christian Fahlke, Jorrit Geveler, Markus Göddeke, Dominik Iliev, Oleg Ippisch, Olaf Milk, René Mohring, Jan Müthing, Steffen Ohlberger, Mario Ribbrock, Dirk Turek, Stefan Interdisciplinary Center for Scientific Computing Heidelberg University Heidelberg Germany Institute for Computational and Applied Mathematics University of Münster Münster Germany Institute of Applied Analysis and Numerical Simulation University of Stuttgart Stuttgart Germany Institute of Applied Mathematics TU Dortmund Dortmund Germany Fraunhofer Institute for Industrial Mathematics ITWM Kaiserslautern Germany Institut für Mathematik TU Clausthal-Zellerfeld Clausthal-Zellerfeld Germany

ISBN: (纸本)9783319405261

We present advances concerning efficient finite element assembly and linear solvers on current and upcoming HPC architectures obtained in the frame of the EXA-DUNE project, part of the DFG priority program 1648 Software for Exascale computing (SPPEXA). In this project, we aim at the development of both flexible and efficient hardware-aware software components for the solution of PDEs based on the DUNE platform and the FEAST library. In this contribution, we focus on node-level performance and accelerator integration, which will complement the provenMPI-level scalability of the framework. The higher-level aspects of the EXADUNE project, in particular multiscale methods and uncertainty quantification, are detailed in the companion paper (Bastian et al., Advances concerning multiscale methods and uncertainty quantification in EXA-DUNE. In: Proceedings of the SPPEXA Symposium, 2016). © Springer International Publishing Switzerland 2016.

关键词： Uncertainty analysis

The directional flow generated by peristalsis in perivascular networks – theoretical and numerical reduced-order descriptions

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arXiv 2023年

作者： Gjerde, Ingeborg G. Rognes, Marie E. Sánchez, Antonio L. Department of Numerical Analysis and Scientific Computing Simula Research Laboratory Kristian Augusts gate 23 Oslo0164 Norway Department of Mechanical and Aerospace Engineering University of California San Diego La Jolla United States

Directional fluid flow in perivascular spaces surrounding cerebral arteries is hypothesized to play a key role in brain solute transport and clearance. While various drivers for pulsatile flow, such as cardiac or respiratory pulsations, are well quantified, the question remains as to which mechanisms could induce directional flow within physiological regimes. To address this question, we develop theoretical and numerical reduced-order models to quantify the directional (net) flow induceable by peristaltic pumping in periarterial networks. Each periarterial element is modeled as a slender annular space bounded internally by a circular tube supporting a periodic traveling (peristaltic) wave. Under the reasonable assumptions of small Reynolds number flow, small radii, and small-amplitude peristaltic waves, we use lubrication theory and regular perturbation methods to derive theoretical expressions for the directional net flow and pressure distribution in the perivascular network. The reduced model is used to derive closed-form analytical expressions for the net flow for simple network configurations of interest, including single elements, two elements in tandem, and a three element bifurcation, with results compared with numerical predictions. In particular, we provide a computable theoretical estimate of the net flow induced by peristaltic motion in perivascular networks as a function of physiological parameters, notably wave length, frequency, amplitude and perivascular dimensions. Quantifying the maximal net flow for specific physiological regimes, we find that vasomotion may induce net pial periarterial flow velocities on the order of a few to tens of µm/s and that sleep-related changes in vasomotion pulsatility may drive a threefold flow *** Codes 76M45, 76Z05, 76D08, 76M10, © 2023, CC BY-NC-ND.

关键词： Solute transport

A perfectly matched layer approach for radiative transfer in highly scattering regimeS

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arXiv 2018年

作者： Egger, Herbert Schlottbom, Matthias Department of Mathematics Numerical Analysis and Scientific Computing TU Darmstadt Dolivostr. 15 Darmstadt64293 Germany ZDepartment of Applied Mathematics University of Twente P.O. Box 217 Enschede7500 AE Netherlands

We consider the numerical approximation of boundary conditions in radiative transfer problems by a perfectly matched layer approach. The main idea is to extend the computational domain by an absorbing layer and to use an appropriate reection boundary condition at the boundary of the extended domain. A careful analysis shows that the consistency error introduced by this approach can be made arbitrarily small by increasing the size of the extension domain or the magnitude of the artificial absorption in the surrounding layer. A particular choice of the reection boundary condition allows us to circumvent the half-space integrals that arise in the variational treatment of the original vacuum boundary conditions and which destroy the sparse coupling observed in numerical approximation schemes based on truncated spherical harmonics expansions. A combination of the perfectly matched layer approach with a mixed variational formulation and a PN- finite element approximation leads to discretization schemes with optimal sparsity pattern and provable quasi-optimal convergence properties. As demonstrated in numerical tests these methods are accurate and very eficient for radiative transfer in the scattering regime.65N12, 65N15, 65N30, 65N35 Copyright © 2018, The Authors. All rights reserved.

关键词： numerical methods

Feasibility of Acousto-Electric Tomography

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arXiv 2019年

作者： Jensen, Bjørn Kirkeby, Adrian Knudsen, Kim Faculty of Information Technology University of Jyväskylä Finland Department of Numerical Analysis and Scientific Computing Simula Research Laboratory Oslo Norway Department of Applied Mathematics and Computer Science Technical University of Denmark Kgs Lyngby Denmark

In acousto-electric tomography the goal is to reconstruct the electric conductivity in a domain from electrostatic boundary measurements of corresponding currents and voltages, while the domain is penetrated by a time-dependent acoustic wave. In this paper we provide an in-silico model of the entire coupled physics scenario and perform computational experiments. We propose a complete inversion framework for acousto-electric tomography in two steps: First the interior power density is obtained from boundary measurements by solving a linear inverse problem;second the interior conductivity is reconstructed from the power density by solving a non-linear, fairly well-posed problem. We develop a numerical model with realistically chosen parameters inspired by medical imaging. The critical signal strength is analyzed and the omnipresent Johnson-Nyquist noise is estimated. With this setup we perform numerical experiments on synthetic data with noise and demonstrate the feasibility of the method. However, our findings are a mix of positive and negative. We reconstruct features even under severe noise conditions, but we also find that the required Signal-to-Noise ratio yet remains infeasible for practical *** Codes 35R30, 65N21 Copyright © 2019, The Authors. All rights reserved.

关键词： Inverse problems

Exploring Biologically Inspired Mechanisms of Adversarial Robustness

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arXiv 2024年

作者： Holzhausen, Konstantin Merlid, Mia Torvik, Håkon Olav Malthe-Sørenssen, Anders Lepperød, Mikkel Elle Department of Physics University of Oslo Sem Sælands vei 24 Fysikkbygningen Oslo0371 Norway Department of Numerical Analysis and Scientific Computing Simula Reserach Laboratory Kristian Augusts gate 23 Oslo0164 Norway

Backpropagation-optimized artificial neural networks, while precise, lack robustness, leading to unforeseen behaviors that affect their safety. Biological neural systems do solve some of these issues already. Unlike artificial models, biological neurons adjust connectivity based on neighboring cell activity. Understanding the biological mechanisms of robustness can pave the way towards building trustworthy and safe systems. Robustness in neural representations is hypothesized to correlate with the smoothness of the encoding manifold. Recent work suggests power law covariance spectra, which were observed studying the primary visual cortex of mice, to be indicative of a balanced trade-off between accuracy and robustness in representations. Here, we show that unsupervised local learning models with winner takes all dynamics learn such power law representations, providing upcoming studies a mechanistic model with that characteristic. Our research aims to understand the interplay between geometry, spectral properties, robustness, and expressivity in neural representations. Hence, we study the link between representation smoothness and spectrum by using weight, Jacobian and spectral regularization while assessing performance and adversarial robustness. Our work serves as a foundation for future research into the mechanisms underlying power law spectra and optimally smooth encodings in both biological and artificial systems. The insights gained may elucidate the mechanisms that realize robust neural networks in mammalian brains and inform the development of more stable and reliable artificial systems. © 2024, CC BY-NC-ND.

关键词： Adversarial machine learning