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13th International Conference on Spectral and High Order Methods, ICOSAHOM 2021

作者： Field, Scott E. Gottlieb, Sigal Khanna, Gaurav McClain, Ed Department of Mathematics Center for Scientific Computing & Visualization Research University of Massachusetts DartmouthMA United States Department of Physics University of Rhode Island KingstonRI United States

ISBN: (纸本)9783031204319

Linear wave equations sourced by a dirac delta distribution δ(x) and its derivative(s) can serve as a model for many different phenomena. We describe a discontinuous Galerkin (DG) method to numerically solve such equations with source terms proportional to ∂nδ∕∂xn. Despite the presence of singular source terms, which imply discontinuous or potentially singular solutions, our DG method achieves global spectral accuracy even at the source’s location. Our DG method is developed for the wave equation written in fully first-order form. The first-order reduction is carried out using a distributional auxiliary variable that removes some of the source term’s singular behavior. While this is helpful numerically, it gives rise to a distributional constraint. We show that a time-independent spurious solution can develop if the initial constraint violation is proportional to δ(x). Numerical experiments verify this behavior and our scheme’s convergence properties by comparing against exact solutions. © 2023, The Author(s), under exclusive license to Springer Nature Switzerland AG.

关键词： Wave equations

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Toward exponentially-convergent simulations of extreme-mass-ratio inspirals: A time-domain solver for the scalar Teukolsky equation with singular source terms

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Physical Review D 2024年第10期110卷 104009页

作者： Manas Vishal Scott E. Field Katie Rink Sigal Gottlieb Gaurav Khanna Department of Mathematics Center for Scientific Computing and Data Science Research Department of Physics Center for Gravitational Physics Department of Physics and Center for Computational Research

Gravitational wave signals from extreme mass ratio inspirals are a key target for upcoming, space-based gravitational wave detectors. These systems are typically modeled as a distributionally forced Teukolsky equation, where the smaller black hole is treated as a Dirac delta distribution (i.e., a point-particle). Time-domain solvers often use regularization approaches that approximate the Dirac distribution. Unfortunately, such approaches often introduce small length scales (e.g., when the approximation is by a narrow Gaussian) and are a source of systematic error, especially near the smaller black hole. We describe a multidomain discontinuous Galerkin (DG) method for solving the distributionally forced s=0 Teukolsky equation that describes scalar fields evolving on a Kerr spacetime. To handle the Dirac delta, we expand the solution in spherical harmonics and recast the sourced Teukolsky equation as a first-order, one-dimensional symmetric hyperbolic system. This allows us to derive the method’s numerical flux to correctly account for the Dirac delta. As a result, our method achieves global spectral accuracy even at the source’s location. To connect the near field to future null infinity, we use the hyperboloidal layer method, allowing us to supply trivial outer boundary conditions and providing direct access to the far-field waveform. We document several numerical experiments where we test our method, including convergence tests against exact solutions, energy luminosities for circular orbits, the scheme’s superconvergence properties at future null infinity, and the late-time tail behavior of the scalar field. We also compare two systems that arise from different choices of the first-order reduction variables, finding that certain reasonable choices are numerically problematic in practice. The methods developed here may be beneficial when computing gravitational self-force effects, where the regularization procedure has been developed for the spherical harmonic mod

关键词： General relativity Numerical relativity Numerical simulations in gravitation & astrophysics

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POSTER: Learning to Parallelize in a Shared-Memory Environment with Transformers 28

POSTER: Learning to Parallelize in a Shared-Memory Environme...

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28th ACM SIGPLAN Annual Symposium on Principles and Practice of Parallel Programming, PPoPP 2023

作者： Harel, Re'Em Pinter, Yuval Oren, Gal Department of Computer Science Ben-Gurion University of the Negev Department of Physics Scientific Computing Center Nuclear Research Center Negev Israel Department of Computer Science Ben-Gurion University of the Negev Israel Department of Computer Science Technion - Israel Institute of Technology Scientific Computing Center Nuclear Research Center Negev Israel

ISBN: (纸本)9798400700156

In past years, the world has switched to multi and many core shared memory architectures. As a result, there is a growing need to utilize these architectures by introducing shared memory parallelization schemes, such as OpenMP, to applications. Nevertheless, introducing OpenMP work-sharing loop construct into code, especially legacy code, is challenging due to pervasive pitfalls in management of parallel shared memory. To facilitate the performance of this task, many source-to-source (S2S) compilers have been created over the years, tasked with inserting OpenMP directives into code automatically. In addition to having limited robustness to their input format, these compilers still do not achieve satisfactory coverage and precision in locating parallelizable code and generating appropriate directives. In this work, we propose leveraging recent advances in machine learning techniques, specifically in natural language processing (NLP), to suggest the need for an OpenMP work-sharing loop directive and data-sharing attributes clauses - the building blocks of concurrent programming. We train several transformer models, named PragFormer, for these tasks and show that they outperform statistically-trained baselines and automatic source-to-source (S2S) parallelization compilers in both classifying the overall need for an parallel for directive and the introduction of private and reduction clauses. In the future, our corpus can be used for additional tasks, up to generating entire OpenMP directives. The source code and database for our project can be accessed on GitHub 1 and HuggingFace 2. © 2023 Owner/Author.

关键词： Machine learning

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Fast waveform generation for gravitational waves using evolutionary algorithms

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Physical Review D 2024年第4期110卷 043035页

作者： Quirijn Meijer Sarah Caudill Institute for Gravitational and Subatomic Physics (GRASP) Department of Physics Science Park 105 1098XG Amsterdam The Netherlands Department of Physics Center for Scientific Computing and Data Science Research

Gravitational-wave analyses depend heavily on waveforms that model the evolution of compact binary coalescences as seen by observing detectors. In many cases these waveforms are given by waveform approximants, models that approximate the amplitude and phase of the waveform at a set of frequencies. Because of their omnipresence, improving the speed at which approximants can generate waveforms is crucial to accelerating the overall analysis of gravitational-wave detections. An optimization algorithm is proposed that can select at which frequencies in the spectrum an approximant should compute the power of a waveform, and at which frequencies the power can be safely interpolated at a minor loss in accuracy. The algorithm used is an evolutionary algorithm modeled after the principle of natural selection, iterating frequency arrays that perform better at every iteration. As an application, the candidates proposed by the algorithm are used to reconstruct signal-to-noise ratios. It is shown that the imrphenomxphm approximant can be sped up by at least 30% at a loss of at most 2.87% on the drawn samples, measured by the accuracy of the reconstruction of signal-to-noise ratios. The behavior of the algorithm as well as lower bounds on both speedup and error are explored, leading to a proposed proof of concept candidate that obtains a speedup of 46% with a maximum error of 0.5% on a sample of the parameter space used.

关键词： General relativity Gravitational waves

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Novel signal-consistency test for gravitational-wave searches of generic black hole binaries

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Physical Review D 2024年第2期110卷 023042-023042页

作者： Stefano Schmidt Sarah Caudill Science Park 105 1098 XG Amsterdam The Netherlands Institute for Gravitational and Subatomic Physics (GRASP) Department of Physics Center for Scientific Computing and Data Science Research

We propose a novel signal-consistency test applicable to a broad search for gravitational waves emitted by generic binary black hole (BBH) systems. The test generalizes the time domain ξ2 signal-consistency test currently utilized by the gstlal pipeline, which quantifies the discrepancy between the expected signal-to-noise ratio time series with the measured one. While the traditional test is restricted to aligned-spin circular orbits and does not account for higher-order modes (HMs), our test does not make any assumption on the nature of the signal. After addressing the mathematical details of the new test, we quantify its advantages in the context of searching for precessing BBHs and/or BBHs with HM content. Our results reveal that, for precessing signals, the new test is optimal and has the potential to reduce the values of the ξ2 statistics by up to 2 orders of magnitude when compared to the standard test. However, in the case of signals with HM content, only a modest enhancement is observed. Recognizing the computational burden associated with the new test, we also derive an approximated signal-consistency test. This approximation maintains the same computational cost as the standard test and can be easily implemented in any matched-filtering pipeline with minimal changes, sacrificing only a few percent of accuracy in the low-SNR regime. However, in the high-SNR regime, the approximated signal-consistency test does not bring any improvement as compared to the “standard” one. By introducing our new test and its approximation and understanding their validity and limitation, this work will benefit any matched-filtering pipeline aimed at searching for BBH signals with strong precession and/or HM content.

关键词： Gravitational waves Data analysis

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Surrogate model for gravitational wave signals from comparable and large-mass-ratio black hole binaries

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Physical Review D 2020年第8期101卷 081502(R)-081502(R)页

作者： Nur E. M. Rifat Scott E. Field Gaurav Khanna Vijay Varma Department of Physics and Center for Scientific Computing and Visualization Research University of Massachusetts Dartmouth Massachusetts 02747 USA Department of Mathematics and Center for Scientific Computing and Visualization Research University of Massachusetts Dartmouth Massachusetts 02747 USA Theoretical Astrophysics California Institute of Technology Pasadena California 91125 USA

Gravitational wave signals from compact astrophysical sources such as those observed by LIGO and Virgo require a high-accuracy, theory-based waveform model for the analysis of the recorded signal. Current inspiral-merger-ringdown models are calibrated only up to moderate mass ratios, thereby limiting their applicability to signals from high-mass-ratio binary systems. We present EMRISur1dq1e4, a reduced-order surrogate model for gravitational waveforms of 13 500 M in duration and including several harmonic modes for nonspinning black hole binary systems with mass ratios varying from 3 to 10000, thus vastly expanding the parameter range beyond the current models. This surrogate model is trained on waveform data generated by point-particle black hole perturbation theory (ppBHPT) both for large-mass-ratio and comparable mass-ratio binaries. We observe that the gravitational waveforms generated through a simple application of ppBHPT to the comparable mass-ratio cases agree surprisingly well with those from full numerical relativity after a rescaling of the ppBHPT’s total mass parameter. This observation and the EMRISur1dq1e4 surrogate model will enable data analysis studies in the high-mass-ratio regime, including potential intermediate-mass-ratio signals from LIGO/Virgo and extreme-mass-ratio events of interest to the future space-based observatory LISA.

关键词： Classical black holes General relativity equations & solutions Gravitational wave sources

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Discontinuous Galerkin method for linear wave equations involving derivatives of the Dirac delta distribution

arXiv

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arXiv 2022年

作者： Field, Scott E. Gottlieb, Sigal Khanna, Gaurav McClain, Ed. Department of Mathematics Center for Scientific Computing & Visualization Research University of Massachusetts DartmouthMA02747 United States Department of Physics Center for Scientific Computing & Visualization Research University of Massachusetts DartmouthMA02747 United States Department of Physics University of Rhode Island KingstonRI02881 United States

Linear wave equations sourced by a Dirac delta distribution δ(x) and its derivative(s) can serve as a model for many different phenomena. We describe a discontinuous Galerkin (DG) method to numerically solve such equations with source terms proportional to ∂nδ/∂xn. Despite the presence of singular source terms, which imply discontinuous or potentially singular solutions, our DG method achieves global spectral accuracy even at the source’s location. Our DG method is developed for the wave equation written in fully first-order form. The first-order reduction is carried out using a distributional auxiliary variable that removes some of the source term’s singular behavior. While this is helpful numerically, it gives rise to a distributional constraint. We show that a time-independent spurious solution can develop if the initial constraint violation is proportional to δ(x). Numerical experiments verify this behavior and our scheme’s convergence properties by comparing against exact solutions. Copyright © 2022, The Authors. All rights reserved.

关键词： Wave equations

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Remnant black hole properties from numerical-relativity-informed perturbation theory and implications for waveform modeling

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Physical Review D 2023年第6期108卷 064048-064048页

作者： Tousif Islam Scott E. Field Gaurav Khanna Department of Physics University of Massachusetts Dartmouth Massachusetts 02747 USA Department of Mathematics University of Massachusetts Dartmouth Massachusetts 02747 USA Center for Scientific Computing and Visualization Research University of Massachusetts Dartmouth Massachusetts 02747 USA Department of Physics and Center for Computational Research University of Rhode Island Kingston Rhode Island 02881 USA

During binary black hole (BBH) mergers, energy and momenta are carried away from the binary system as gravitational radiation. Access to the radiated energy and momenta allows us to predict the properties of the remnant black hole. We develop a Python package gw_remnant to extract the remnant mass, remnant spin, peak luminosity, and the final kick imparted on the remnant black hole from the gravitational waveforms. Using this package, we extract the remnant properties of the final black hole in case of nonspinning BBH mergers with mass ratios ranging from q=2.5 to q=1000 using waveform modes generated from BHPTNRSur1dq1e4, a recently developed numerical-relativity-informed surrogate model based on the black hole perturbation theory framework. We validate our results against the remnant properties estimated from numerical relativity (NR) surrogate models in the comparable mass-ratio regime and against recently available high-mass-ratio NR simulations at q=[15,32,64]. We find that our remnant property estimates computed from fluxes at future null infinity closely match the estimates obtained from the NR surrogate model of apparent horizon data. Using Gaussian process regression fitting methods, we train a surrogate model, BHPTNR_Remnant, for the properties of the remnant black hole arising from BBH mergers with mass ratios from q=2.5 to q=1000. Finally, we discuss potential improvements in the BHPTNRSur1dq1e4 waveform model when including remnant information. We make both the gw_remnant and BHPTNR_Remnant packages publicly available.

关键词： General relativity Gravitational waves

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Gravitational wave surrogate model for spinning, intermediate mass ratio binaries based on perturbation theory and numerical relativity

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Physical Review D 2024年第12期110卷 124069-124069页

作者： Katie Rink Ritesh Bachhar Tousif Islam Nur E. M. Rifat Kevin González-Quesada Scott E. Field Gaurav Khanna Scott A. Hughes Vijay Varma Department of Physics and Center for Scientific Computing and Visualization Research University of Massachusetts Dartmouth Massachusetts 02747 USA Department of Physics and Weinberg Institute for Theoretical Physics University of Texas at Austin Austin Texas 78712 USA Department of Physics and Center for Computational Research East Hall University of Rhode Island Kingston Rhode Island 02881 USA Kavli Institute for Theoretical Physics University of California Santa Barbara Kohn Hall Lagoon Road Santa Barbara California 93106 USA Kavli Institute for Theoretical Physics University of California Santa Barbara Santa Barbara California 93106 USA Department of Physics University of Virginia 1827 University Avenue Charlottesville Virginia 22903 USA Department of Physics and Center for Education and Research in Cosmology and Astrophysics (CERCA) Case Western Reserve University Cleveland Ohio 44106 USA Department of Mathematics and Center for Scientific Computing and Visualization Research University of Massachusetts Dartmouth Massachusetts 02747 USA Department of Physics Massachusetts Institute of Technology Cambridge Massachusetts 02139 USA

We present BHPTNRSur2dq1e3, a reduced order surrogate model of gravitational waves emitted from binary black hole (BBH) systems in the comparable to large mass ratio regime with aligned spin (χ1) on the heavier mass (m1). We trained this model on waveform data generated from point particle black hole perturbation theory (ppBHPT) with mass ratios varying from 3≤q≤1000 and spins from −0.8≤χ1≤0.8. The waveforms are 13,500 m1 long and include all ℓ≤4 spin-weighted spherical harmonic modes except the (4,1) and m=0 modes. We find that, for binaries with χ1≲−0.5, retrograde quasinormal modes are significantly excited, thereby complicating the modeling process. To overcome this issue, we introduce a domain decomposition approach to model the inspiral and merger-ringdown portion of the signal separately. The resulting model can faithfully reproduce ppBHPT waveforms with a median time-domain mismatch error of 8×10−5. We then calibrate our model with numerical relativity (NR) data in the comparable mass regime (3≤q≤10). By comparing with spin-aligned BBH NR simulations at q=15, we find that the dominant quadrupolar (subdominant) modes agree to better than ≈10−3 (≈10−2) when using a time-domain mismatch error, where the largest source of calibration error comes from the transition-to-plunge and ringdown approximations of perturbation theory. Mismatch errors are below ≈10−2 for systems with mass ratios between 6≤q≤15 and typically get smaller at larger mass ratio. Our two models—both the ppBHPT waveform model and the NR-calibrated ppBHPT model—will be publicly available through gwsurrogate and the black hole perturbation toolkit packages.

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Portability and Scalability of OpenMP Offloading on State-of-the-Art Accelerators 38th

Portability and Scalability of OpenMP Offloading on State...

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38th International Conference on High Performance computing, ISC High Performance 2023

作者： Fridman, Yehonatan Tamir, Guy Oren, Gal Department of Computer Science Ben-Gurion University of the Negev Be’er Sheva Israel Department of Physics Nuclear Research Center - Negev Be’er Sheva Israel Scientific Computing Center Nuclear Research Center - Negev Be’er Sheva Israel Intel Corporation Santa Clara United States Department of Computer Science Technion - Israel Institute of Technology Haifa Israel

ISBN: (纸本)9783031408427

Over the last decade, most of the increase in computing power has been gained by advances in accelerated many-core architectures, mainly in the form of GPGPUs. While accelerators achieve phenomenal performances in various computing tasks, their utilization requires code adaptations and transformations. Thus, OpenMP, the most common standard for multi-threading in scientific computing applications, introduced offloading capabilities between host (CPUs) and accelerators since v4.0, with increasing support in the successive v4.5, v5.0, v5.1, and the latest v5.2 versions. Recently, two state-of-the-art GPUs – the Intel Ponte Vecchio Max 1100 and the NVIDIA A100 GPUs – were released to the market, with the oneAPI and NVHPC compilers for offloading, correspondingly. In this work, we present early performance results of OpenMP offloading capabilities to these devices while specifically analyzing the portability of advanced directives (using SOLLVE’s OMPVV test suite) and the scalability of the hardware in representative scientific mini-app (the LULESH benchmark). Our results show that the coverage for version 4.5 is nearly complete in both latest NVHPC and oneAPI tools. However, we observed a lack of support in versions 5.0, 5.1, and 5.2, which is particularly noticeable when using NVHPC. From the performance perspective, we found that the PVC1100 and A100 are relatively comparable on the LULESH benchmark. While the A100 is slightly better due to faster memory bandwidth, the PVC1100 reaches the next problem size (4003 ) scalably due to the larger memory size. The results are available at: https://***/scientific-computing-Lab-NRCN/Accel-OpenMP-Portability-Scalability. © 2023, The Author(s), under exclusive license to Springer Nature Switzerland AG.

关键词： Scalability

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