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The white rat of numerical reproducibility

AIP Conference Proceedings 2021年第1期2365卷

作者： Michael Mascagni Departments of Computer Science Mathematics and Scientific Computing Florida State University Tallahassee FL 32306-4530 USA Applied and Computational Mathematics Division National Institute of Standards and Technology (NIST) Gaithersburg MD 20899-8910 USA

We explore an application from the author’s work in neuroscience. A code used to investigate neural development modeled 100 neurons with all-to-all excitatory connectivity. We used a simple ordinary differential equation system to model each neuron, and this 100-neuron model was used to produce a paper published in the Journal of Neurophysiology. Later a colleague used our code to continue this work, and found he could not reproduce our results. This lead us to thoroughly investigate this code and we discovered that it offered many different ways to thwart reproducibility that could be explained by round-off error arising from floating-point *** reproducibility is considered a task that directly follows from the determinism in computations. However, reproducibility has become an intense concern and and issue for research. In fact, the author developed an series of international workshops on numerical reproducibility and computational reproducibility that is now a regular offering at the annual international supercomputing conferences. We will show how this particular code provides a lack of reproducibility from the following three mechanisms: (i) the introduction of floating-point errors in an inner product; (ii) introduction of floating-point errors at each an increasing number of time steps during temporal refinement (ii); and (iii) differences in the output of library mathematical functions at the level of round-off error. This code’s sensitivity makes it a very powerful tool to explore many different manifestations of numerical reproducibility. However, this code is by no means exceptional, as in neuroscience these types of models are used extensively to gain insights on the functioning of the nervous system. In addition, these types of models are widely used in many other fields of study as they just nonlinear evolution equations.

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Democratizing Uncertainty Quantification

arXiv

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arXiv 2024年

作者： Seelinger, Linus Reinarz, Anne Lykkegaard, Mikkel B. Akers, Robert Alghamdi, Amal M.A. Aristoff, David Bangerth, Wolfgang Bénézech, Jean Diez, Matteo Frey, Kurt Jakeman, John D. Jørgensen, Jakob S. Kim, Ki-Tae Kent, Benjamin M. Martinelli, Massimiliano Parno, Matthew Pellegrini, Riccardo Petra, Noemi Riis, Nicolai A.B. Rosenfeld, Katherine Serani, Andrea Tamellini, Lorenzo Villa, Umberto Dodwell, Tim J. Scheichl, Robert Scientific Computing Center Karlsruhe Institute of Technology Karlsruhe Germany Department of Computer Science Durham University Durham United Kingdom digiLab Exeter United Kingdom UK Atomic Energy Authority Oxford United Kingdom Lyngby Denmark Department of Mathematics Colorado State University Fort CollinsCO United States Department of Mathematics Department of Geosciences Colorado State University Fort CollinsCO United States Centre for Integrated Materials Processes and Structures Department of Mechanical Engineering University of Bath Bath United Kingdom National Research Council Institute of Marine Engineering Rome Italy Institute for Disease Modeling Global Health Division Bill & Melinda Gates Foundation United States Optimization and Uncertainty Quantification Sandia National Laboratories AlbuquerqueNM United States University of California Merced United States National Research Council-Institute for Applied Mathematics and Information Technologies "E. Magenes" Pavia Italy Solea Energy ThetfordVT United States Copenhagen Imaging ApS Herlev Denmark The University of Texas Austin United States Heidelberg University Germany

Uncertainty Quantification (UQ) is vital to safety-critical model-based analyses, but the widespread adoption of sophisticated UQ methods is limited by technical complexity. In this paper, we introduce UM-Bridge (the UQ and Modeling Bridge), a high-level abstraction and software protocol that facilitates universal interoperability of UQ software with simulation codes. It breaks down the technical complexity of advanced UQ applications and enables separation of concerns between experts. UM-Bridge democratizes UQ by allowing effective interdisciplinary collaboration, accelerating the development of advanced UQ methods, and making it easy to perform UQ analyses from prototype to High Performance computing (HPC) scale. In addition, we present a library of ready-to-run UQ benchmark problems, all easily accessible through UM-Bridge. These benchmarks support UQ methodology research, enabling reproducible performance comparisons. We demonstrate UM-Bridge with several scientific applications, harnessing HPC resources even using UQ codes not designed with HPC support. © 2024, CC BY-NC-ND.

关键词： Application programs

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GPU algorithms for efficient exascale discretizations

arXiv

引用

arXiv 2021年

作者： Abdelfattah, Ahmad Barra, Valeria Beams, Natalie Bleile, Ryan Brown, Jed Camier, Jean-Sylvain Carson, Robert Chalmers, Noel Dobrev, Veselin Dudouit, Yohann Fischer, Paul Karakus, Ali Kerkemeier, Stefan Kolev, Tzanio Lan, Yu-Hsiang Merzari, Elia Min, Misun Phillips, Malachi Rathnayake, Thilina Rieben, Robert Stitt, Thomas Tomboulides, Ananias Tomov, Stanimire Tomov, Vladimir Vargas, Arturo Warburton, Tim Weiss, Kenneth Center for Applied Scientific Computing Lawrence Livermore National Laboratory LivermoreCA94550 United States Mathematics and Computer Science Argonne National Laboratory LemontIL60439 United States Department of Computer Science University of Illinois at Urbana-Champaign UrbanaIL61801 United States Department of Mechanical Science and Engineering University of Illinois at Urbana-Champaign UrbanaIL61801 United States Innovative Computing Laboratory University of Tennessee KnoxvilleTN37996 United States Department of Computer Science University of Colorado BoulderCO80309 United States Department of Mathematics Virginia Tech BlacksburgVA24061 United States AMD Research Advanced Micro Devices Inc. AustinTX78735 United States Weapons and Complex Integration Lawrence Livermore National Laboratory LivermoreCA94550 United States Computational Engineering Division Lawrence Livermore National Laboratory LivermoreCA94550 United States Department of Nuclear Engineering Penn State PA16802 United States Department of Mechanical Engineering Aristotle University of Thessaloniki 54124 Greece Mechanical Engineering Department Middle East Technical University Ankara06800 Turkey

In this paper we describe the research and development activities in the Center for Efficient Exascale Dis-cretization within the US Exascale computing Project, targeting state-of-the-art high-order finite-element algorithms for high-order applications on GPU-accelerated platforms. We discuss the GPU developments in several components of the CEED software stack, including the libCEED, MAGMA, MFEM, libParanumal, and Nek projects. We report performance and capability improvements in several CEED-enabled applications on both NVIDIA and AMD GPU systems. © 2021, CC BY-NC-ND.

关键词： Finite element method

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Jamming and force distribution in growing epithelial tissue

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Physical Review Research 2021年第2期3卷 023129-023129页

作者： Pranav Madhikar Jan Åström Björn Baumeier Mikko Karttunen Department of Mathematics and Computer Science & Institute for Complex Molecular Systems Eindhoven University of Technology 5600 MB Eindhoven The Netherlands CSC Scientific Computing Ltd Kägelstranden 14 02150 Esbo Finland Department of Chemistry The University of Western Ontario 1151 Richmond Street London Ontario Canada N6A 5B7 Department of Applied Mathematics The University of Western Ontario 1151 Richmond Street London Ontario Canada N6A 5B7 The Centre for Advanced Materials and Biomaterials Research The University of Western Ontario 1151 Richmond Street London Ontario Canada N6A 3K7

We investigate morphologies of proliferating cellular tissues using a numerical simulation model for mechanical cell division and migration in two dimensions. The model is applied to a bimodal mixture consisting of stiff cells with a low growth potential and soft cells with a high growth potential; cancer cells are typically considered to be softer than healthy cells. In an even mixture, the soft cells develop into a tissue matrix and the stiff cells into a dendritelike network structure. When soft cells are placed inside a tissue consisting of stiff cells (to model cancer growth), the soft cells develop into a fast-growing tumorlike structure that gradually evacuates the stiff cell matrix. The model also demonstrates (1) how soft cells orient themselves in the direction of the largest effective stiffness as predicted by the theory of Bischofs and Schwarz [Proc. Natl. Acad. Sci. USA 100, 9274 (2003)] and (2) that the orientation and force generation continue a few cell rows behind the soft-stiff interface. With increasing intercell friction, tumor growth slows down, and cell death occurs. The contact force distribution between cells is demonstrated to be highly sensitive to cell type mixtures and cell-cell interactions, which indicates that local mechanical forces can be useful as a regulator of tissue formation. The results shed light on established experimental data.

关键词： Biological movement Cell aggregation Cell division Cell mechanics Jamming

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Enhanced hyperspectral tomography for bioimaging by spatiospectral reconstruction

arXiv

引用

arXiv 2021年

作者： Warr, Ryan Ametova, Evelina Cernik, Robert J. Fardell, Gemma Handschuh, Stephan Jørgensen, Jakob S. Papoutsellis, Evangelos Pasca, Edoardo Withers, Philip J. Henry Royce Institute Department of Materials The University of Manchester ManchesterM13 9PL United Kingdom Laboratory for Applications of Synchrotron Radiation Karlsruhe Institute of Technology Kaiserstr. 12 KarlsruheD-76131 Germany Scientific Computing Department Science Technology Facilities Council UK Research and Innovation Rutherford Appleton Laboratory Chilton DidcotOX11 0QX United Kingdom VetCore Facility for Research University of Veterinary Medicine Vienna Vienna Austria Department of Applied Mathematics and Computer Science Technical University of Denmark Denmark Department of Mathematics The University of Manchester ManchesterM13 9PL United Kingdom

Here we apply hyperspectral bright field imaging to collect computed tomographic images with excellent energy resolution (800 eV), applying it for the first time to map the distribution of stain in a fixed biological sample through its characteristic K-edge. Conventionally, because the photons detected at each pixel are distributed across as many as 200 energy channels, energy-selective images are characterised by low count-rates and poor signal-to-noise ratio. This means high X-ray exposures, long scan times and high doses are required to image unique spectral markers. Here, we achieve high quality energy-dispersive tomograms from low dose, noisy datasets using a dedicated iterative reconstruction algorithm. This exploits the spatial smoothness and inter-channel structural correlation in the spectral domain using two carefully chosen regularisation terms. For a multi-phase phantom, a reduction in scan time of 36 times is demonstrated. Spectral analysis methods including K-edge subtraction and absorption step-size fitting are evaluated for an ex vivo, single (iodine)-stained biological sample, where low chemical concentration and inhomogeneous distribution can affect soft tissue segmentation and visualisation. The reconstruction algorithms are available through the open-source Core Imaging Library. Taken together, these tools offer new capabilities for visualisation and elemental mapping, with promising applications for multiply-stained biological specimens. © 2021, CC BY.

关键词： Tomography

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Scalability of high-performance PDE solvers

arXiv

引用

arXiv 2020年

作者： Fischer, Paul Min, Misun Rathnayake, Thilina Dutta, Som Kolev, Tzanio Dobrev, Veselin Camier, Jean-Sylvain Kronbichler, Martin Warburton, Tim Swirydowicz, Kasia Brown, Jed Mathematics and Computer Science Argonne National Laboratory LemontIL60439 Department of Computer Science University of Illinois at Urbana-Champaign UrbanaIL61801 Department of Mechanical Science and Engineering University of Illinois at Urbana-Champaign UrbanaIL61801 Center for Applied Scientific Computing Lawrence Livermore National Laboratory LivermoreCA94550 Institute for Computational Mechanics Technical University of Munich Garching b. Muenchen85748 Germany Department of Computer Science University of Colorado BoulderCO80309 National Renewable Energy Laboratory LakewoodCO80401 Department of Mathematics Virginia Tech BlacksburgVA24061 Mechanical & Aerospace Engineering Utah State University UT84322

Performance tests and analyses are critical to effective HPC software development and are central components in the design and implementation of computational algorithms for achieving faster simulations on existing and future computing architectures for large-scale application problems. In this paper, we explore performance and space-time trade-offs for important compute-intensive kernels of large-scale numerical solvers for PDEs that govern a wide range of physical applications. We consider a sequence of PDE-motivated bake-off problems designed to establish best practices for efficient high-order simulations across a variety of codes and platforms. We measure peak performance (degrees of freedom per second) on a fixed number of nodes and identify effective code optimization strategies for each architecture. In addition to peak performance, we identify the minimum time to solution at 80% parallel efficiency. The performance analysis is based on spectral and p-type finite elements but is equally applicable to a broad spectrum of numerical PDE discretizations, including finite difference, finite volume, and h-type finite *** Codes 35-04 Copyright © 2020, The Authors. All rights reserved.

关键词： computer architecture

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Numerical study of heat transfer in Rayleigh-Bénard convection under rarefied gas conditions

引用

Physical Review E 2020年第1期102卷 013102-013102页

作者： B. Goshayeshi G. Di Staso F. Toschi H. J. H. Clercx Fluid Dynamics Laboratory and J.M. Burgers Center for Fluid Dynamics Department of Applied Physics Eindhoven University of Technology P. O. Box 513 5600 MB Eindhoven The Netherlands Centre of Analysis Scientific Computing and Applications W&I Department of Mathematics and Computer Science Eindhoven University of Technology P. O. Box 513 5600 MB Eindhoven The Netherlands Istituto per le Applicazioni del Calcolo Consiglio Nazionale delle Ricerche 00185 Rome Italy

The focus of this research is to delineate the thermal behavior of a rarefied monatomic gas confined between horizontal hot and cold walls, physically known as rarefied Rayleigh-Bénard (RB) convection. Convection in a rarefied gas appears only for high temperature differences between the horizontal boundaries, where nonlinear distributions of temperature and density make it different from the classical RB problem. Numerical simulations adopting the direct simulation Monte Carlo approach are performed to study the rarefied RB problem for a cold to hot wall temperature ratio equal to r=0.1 and different rarefaction conditions. Rarefaction is quantified by the Knudsen number, Kn. To investigate the long-time thermal behavior of the system two ways are followed to measure the heat transfer: (i) measurements of macroscopic hydrodynamic variables in the bulk of the flow and (ii) measurements at the microscopic scale based on the molecular evaluation of the energy exchange between the isothermal wall and the fluid. The measurements based on the bulk and molecular scales agreed well. Hence, both approaches are considered in evaluations of the heat transfer in terms of the Nusselt number, Nu. To characterize the flow properly, a modified Rayleigh number (Ram) is defined to take into account the nonlinear temperature and density distributions at the pure conduction state. Then the limits of instability, indicating the transition of the conduction state into a convection state, at the low and large Froude asymptotes are determined based on Ram. At the large Froude asymptote, simulations following the onset of convection showed a relatively small range for the critical Rayleigh (Ram=1770±15) that flow instability occurs at each investigated rarefaction degree. Moreover, we measured the maximum Nusselt values Numax at each investigated Kn. It was observed that for Kn≥0.02, Numax decreases linearly until the transition to conduction at Kn≈0.03, known as the rarefaction limit for

关键词： Flow instability Rarefied flows Rayleigh-Bénard convection

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Exploration of Differentiability in a Proton Computed Tomography Simulation Framework

arXiv

引用

arXiv 2022年

作者： Aehle, Max Alme, Johan Barnaföldi, Gergely Gábor Blühdorn, Johannes Bodova, Tea Borshchov, Vyacheslav van den Brink, Anthony Eikeland, Viljar Feofilov, Gregory Garth, Christoph Gauger, Nicolas R. Grøttvik, Ola Helstrup, Håvard Igolkin, Sergey Keidel, Ralf Kobdaj, Chinorat Kortus, Tobias Kusch, Lisa Leonhardt, Viktor Mehendale, Shruti Mulawade, Raju Ningappa Odland, Odd Harald O’Neill, George Papp, Gábor Peitzmann, Thomas Pettersen, Helge Egil Seime Piersimoni, Pierluigi Pochampalli, Rohit Protsenko, Maksym Rauch, Max Rehman, Attiq Ur Richter, Matthias Röhrich, Dieter Sagebaum, Max Santana, Joshua Schilling, Alexander Seco, Joao Songmoolnak, Arnon Sudár, Ákos Tambave, Ganesh Tymchuk, Ihor Ullaland, Kjetil Varga-Kofarago, Monika Volz, Lennart Wagner, Boris Wendzel, Steffen Wiebel, Alexander Xiao, RenZheng Yang, Shiming Zillien, Sebastian Chair for Scientific Computing University of Kaiserslautern-Landau Kaiserslautern67663 Germany Department of Physics and Technology University of Bergen Bergen5007 Norway Wigner Research Centre for Physics Budapest Hungary Kharkiv Ukraine Institute for Subatomic Physics Utrecht University/Nikhef Utrecht Netherlands St. Petersburg University St. Petersburg Russia Scientific Visualization Lab University of Kaiserslautern-Landau Kaiserslautern67663 Germany Department of Computer Science Electrical Engineering and Mathematical Sciences Western Norway University of Applied Sciences Bergen5020 Norway University of Applied Sciences Worms Worms Germany Institute of Science Suranaree University of Technology Nakhon Ratchasima Thailand Department of Oncology and Medical Physics Haukeland University Hospital Bergen5021 Norway Institute for Physics Eötvös Loránd University 1/A Pázmány P. Sétány BudapestH-1117 Hungary FSN Department ENEA Frascati Research Center Frascati00044 Italy Department of Physics University of Oslo Oslo0371 Norway Department of Biomedical Physics in Radiation Oncology DKFZ—German Cancer Research Center Heidelberg Germany Department of Physics and Astronomy Heidelberg University Heidelberg Germany Bhubaneswar India Biophysics GSI Helmholtz Center for Heavy Ion Research GmbH Darmstadt Germany Department of Medical Physics and Biomedical Engineering University College London London United Kingdom College of Mechanical & Power Engineering China Three Gorges University Yichang China

Objective. Algorithmic differentiation (AD) can be a useful technique to numerically optimize design and algorithmic parameters by, and quantify uncertainties in, computer simulations. However, the effectiveness of AD depends on how "well-linearizable" the software is. In this study, we assess how promising derivative information of a typical proton computed tomography (pCT) scan computer simulation is for the aforementioned applications. Approach. This study is mainly based on numerical experiments, in which we repeatedly evaluate three representative computational steps with perturbed input values. We support our observations with a review of the algorithmic steps and arithmetic operations performed by the software, using debugging techniques. Main results. The model-based iterative reconstruction (MBIR) subprocedure (at the end of the software pipeline) and the Monte Carlo (MC) simulation (at the beginning) were piecewise differentiable. Jumps in the MBIR function arose from the discrete computation of the set of voxels intersected by a proton path. Jumps in the MC function likely arose from changes in the control flow that affect the amount of consumed random numbers. The tracking algorithm solves an inherently non-differentiable problem. Significance. The MC and MBIR codes are ready for the integration of AD, and further research on surrogate models for the tracking subprocedure is necessary. Copyright © 2022, The Authors. All rights reserved.

关键词： Monte Carlo methods

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A practical guide to machine learning interatomic potentials – Status and future

arXiv

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arXiv 2025年

作者： Jacobs, Ryan Morgan, Dane Attarian, Siamak Meng, Jun Shen, Chen Wu, Zhenghao Xie, Clare Yijia Yang, Julia H. Artrith, Nongnuch Blaiszik, Ben Ceder, Gerbrand Choudhary, Kamal Csanyi, Gabor Cubuk, Ekin Dogus Deng, Bowen Drautz, Ralf Fu, Xiang Godwin, Jonathan Honavar, Vasant Isayev, Olexandr Johansson, Anders Kozinsky, Boris Martiniani, Stefano Ong, Shyue Ping Poltavsky, Igor Schmidt, K.J. Takamoto, So Thompson, Aidan Westermayr, Julia Wood, Brandon M. Department of Materials Science and Engineering University of Wisconsin-Madison MadisonWI55705 United States Harvard University Center for the Environment Harvard University CambridgeMA02138 United States John A. Paulson School of Engineering and Applied Sciences Harvard University CambridgeMA02138 United States Materials Chemistry and Catalysis Debye Institute for Nanomaterials Science Utrecht University Utrecht3584 CG Netherlands Globus University of Chicago ChicagoIL United States Data Science and Learning Division Argonne National Laboratory LemontIL United States Department of Materials Science and Engineering University of California BerkeleyCA94720 United States Materials Sciences Division Lawrence Berkeley National Laboratory CA94720 United States Material Measurement Laboratory National Institute of Standards and Technology GaithersburgMD20899 United States Department of Engineering University of Cambridge CambridgeCB2 1PZ United Kingdom Google DeepMind Mountain ViewCA United States Ruhr-Universität Bochum Bochum44780 Germany Meta United States Orbital Materials London United Kingdom Department of Computer Science and Engineering The Pennsylvania State University University ParkPA United States College of Information Sciences and Technology The Pennsylvania State University University ParkPA United States Artificial Intelligence Research Laboratory The Pennsylvania State University University ParkPA United States Center for Artificial Intelligence Foundations and Scientific Applications The Pennsylvania State University University ParkPA United States Department of Chemistry Mellon College of Science Carnegie Mellon University PittsburghPA15213 United States Computational Biology Department School of Computer Science Carnegie Mellon University PittsburghPA15213 United States Courant Institute of Mathematical Sciences New York University New YorkNY10003 United States Center for Soft Matter Research Department of P

The rapid development and large body of literature on machine learning interatomic potentials (MLIPs) can make it difficult to know how to proceed for researchers who are not experts but wish to use these tools. The spirit of this review is to help such researchers by serving as a practical, accessible guide to the state-of-the-art in MLIPs. This review paper covers a broad range of topics related to MLIPs, including (i) central aspects of how and why MLIPs are enablers of many exciting advancements in molecular modeling, (ii) the main underpinnings of different types of MLIPs, including their basic structure and formalism, (iii) the potentially transformative impact of universal MLIPs for both organic and inorganic systems, including an overview of the most recent advances, capabilities, downsides, and potential applications of this nascent class of MLIPs, (iv) a practical guide for estimating and understanding the execution speed of MLIPs, including guidance for users based on hardware availability, type of MLIP used, and prospective simulation size and time, (v) a manual for what MLIP a user should choose for a given application by considering hardware resources, speed requirements, energy and force accuracy requirements, as well as guidance for choosing pre-trained potentials or fitting a new potential from scratch, (vi) discussion around MLIP infrastructure, including sources of training data, pre-trained potentials, and hardware resources for training, (vii) summary of some key limitations of present MLIPs and current approaches to mitigate such limitations, including methods of including long-range interactions, handling magnetic systems, and treatment of excited states, and finally (viii) we finish with some more speculative thoughts on what the future holds for the development and application of MLIPs over the next 3-10+ years. © 2025, CC BY.

关键词： Digital storage

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Feasibility of Acousto-Electric Tomography

arXiv

引用

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

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