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arXiv 2023年

作者： Caforio, Federica Regazzoni, Francesco Pagani, Stefano Karabelas, Elias Augustin, Christoph Haase, Gundolf Plank, Gernot Quarteroni, Alfio Department of Mathematics & Scientific Computing NAWI Graz University of Graz Austria Gottfried Schatz Research Center Division of Biophysics Medical University of Graz Austria BioTechMed-Graz Austria MOX Department of Mathematics Politecnico di Milano Italy Institute of Mathematics EPFL Switzerland

The development of biophysical models for clinical applications is rapidly advancing in the research community, thanks to their predictive nature and their ability to assist the interpretation of clinical data. However, high-resolution and accurate multi-physics computational models are computationally expensive and their personalisation involves fine calibration of a large number of parameters, which may be space-dependent, challenging their clinical translation. In this work, we propose a new approach, which relies on the combination of physics-informed neural networks (PINNs) with three-dimensional soft tissue nonlinear biomechanical models, capable of reconstructing displacement fields and estimating heterogeneous patient-specific biophysical properties and secondary variables such as stresses and strains. The proposed learning algorithm encodes information from a limited amount of displacement and, in some cases, strain data, that can be routinely acquired in the clinical setting, and combines it with the physics of the problem, represented by a mathematical model based on partial differential equations, to regularise the problem and improve its convergence properties. Several benchmarks are presented to show the accuracy and robustness of the proposed method with respect to noise and model uncertainty and its great potential to enable the effective identification of patient-specific, heterogeneous physical properties, e.g. tissue stiffness properties. In particular, we demonstrate the capability of PINNs to detect the presence, location and severity of scar tissue, which is beneficial to develop personalised simulation models for disease diagnosis, especially for cardiac applications. © 2023, CC BY-NC-ND.

关键词： Biomechanics

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Optimizing post-Newtonian parameters and fixing the BMS frame for numerical-relativity waveform hybridizations

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Physical Review D 2024年第10期110卷 104076-104076页

作者： Dongze Sun Michael Boyle Keefe Mitman Mark A. Scheel Leo C. Stein Saul A. Teukolsky Vijay Varma Theoretical Astrophysics 350-17 California Institute of Technology 1200 E California Boulevard Pasadena California 91125 USA Cornell Center for Astrophysics and Planetary Science Cornell University Ithaca New York 14853 USA Department of Physics and Astronomy University of Mississippi University Mississippi 38677 USA Department of Mathematics Center for Scientific Computing and Visualization Research University of Massachusetts Dartmouth Dartmouth Massachusetts 02747 USA Max Planck Institute for Gravitational Physics (Albert Einstein Institute) D-14476 Potsdam Germany

Numerical relativity (NR) simulations of binary black holes provide precise waveforms, but are typically too computationally expensive to produce waveforms with enough orbits to cover the whole frequency band of gravitational-wave observatories. Accordingly, it is important to be able to hybridize NR waveforms with analytic, post-Newtonian (PN) waveforms, which are accurate during the early inspiral phase. We show that to build such hybrids, it is crucial to both fix the Bondi-Metzner-Sachs (BMS) frame of the NR waveforms to match that of PN theory, and optimize over the PN parameters to mitigate the error caused by the discrepancy between NR and PN parameters. We test such a hybridization procedure including all spin-weighted spherical harmonic modes with |m|≤ℓ for ℓ≤8, using 29 NR waveforms with mass ratios q≤10 and spin magnitudes |χ1|,|χ2|≤0.8. We find that for spin-aligned systems, the PN and NR waveforms agree very well. The difference is limited by the small nonzero orbital eccentricity of the NR waveforms, or equivalently by the lack of eccentric terms in the PN waveforms. To maintain full accuracy of the simulations, the matching window for spin-aligned systems should be at least 5 orbits long and end at least 15 orbits before merger. For precessing systems, the errors are larger than for spin-aligned cases. The errors are likely limited by the absence of precession-related spin-spin PN terms. Using 105M long NR waveforms, we find that there is no optimal choice of the matching window within this time span, because the hybridization result for precessing cases is always better if using earlier or longer matching windows. We provide the mean orbital frequency of the smallest acceptable matching window as a function of the target error between the PN and NR waveforms and the black hole spins.

关键词： General relativity Gravitation Gravitational waves Astronomical black holes Numerical relativity Numerical simulations in gravitation & astrophysics

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Survey of gravitational wave memory in intermediate mass ratio binaries

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Physical Review D 2023年第2期108卷 024046-024046页

作者： Tousif Islam Scott E. Field Gaurav Khanna Niels Warburton 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 Kavli Institute for Theoretical Physics University of California Santa Barbara California 93106 USA Department of Physics University of Rhode Island Kingston Rhode Island 02881 USA School of Mathematics and Statistics University College Dublin Belfield Dublin 4 Ireland

The nonlinear gravitational wave (GW) memory effect is a distinct prediction in general relativity. While the effect has been well studied for comparable mass binaries, it has mostly been overlooked for intermediate mass ratio inspirals (IMRIs). We offer a comprehensive analysis of the phenomenology and detectability of memory effects, including contributions from subdominant harmonic modes, in heavy IMRIs consisting of a stellar mass black hole and an intermediate mass black hole. When formed through hierarchical mergers, for example when a GW190521-like remnant captures a stellar mass black hole, IMRI systems have a large total mass, large spin on the primary, and possibly residual eccentricity; features that potentially raise the prospect for memory detection. We compute both the displacement and spin nonlinear GW memory from the m≠0 gravitational waveforms computed within a black hole perturbation theory framework that is partially calibrated to numerical relativity waveforms. We probe the dependence of memory effects on mass ratio, spin, and eccentricity and consider the detectability of a memory signal from IMRIs using current and future GW detectors. We find that (i) while eccentricity introduces additional features in both displacement and spin memory, it does not appreciatively change the prospects of detectability, (ii) including higher modes into the memory computation can increase signal-to-noise (SNR) values by about 7% in some cases, (iii) the SNR from displacement memory dramatically increases as the spin approaches large, positive values, and (iv) spin memory from heavy IMRIs would, however, be difficult to detect with future generation detectors even from highly spinning systems. Our results suggest that hierarchical binary black hole mergers may be a promising source for detecting memory and could favorably impact memory forecasts.

关键词： Gravitational waves

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Approximate relation between black hole perturbation theory and numerical relativity

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Physical Review D 2023年第12期108卷 124046-124046页

作者： Tousif Islam 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 Data Science 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

We investigate the interplay between numerical relativity (NR) and adiabatic point-particle black hole perturbation theory (ppBHPT) in the comparable mass regime for quasicircular nonspinning binary black holes. Specifically, we reassess the α−β scaling technique, previously introduced by Islam et al. [Surrogate model for gravitational wave signals from nonspinning, comparable-to large-mass-ratio black hole binaries built on black hole perturbation theory waveforms calibrated to numerical relativity, Phys. Rev. D 106, 104025 (2022)], as a means to effectively match ppBHPT waveforms to NR waveforms within this regime. In particular, α rescales the amplitude and β rescales the time (and hence the phase). Utilizing publicly available long NR data (SXS:BBH:2265 [SXS Collaboration, Binary black-hole simulation SXS:BBH:2265 (2019)]) for a mass ratio of 1∶3, encompassing the final ∼65 orbital cycles of the binary evolution, we examine the range of applicability of such scalings. We observe that the scaling technique remains effective even during the earlier stages of the inspiral. Additionally, we provide commentary on the temporal evolution of the α and β parameters and discuss whether they can be approximated as constant values. Consequently, we derive the α−β scaling as a function of orbital frequencies and demonstrate that it is equivalent to a frequency-dependent correction. We further provide a brief comparison between post-Newtonian (PN) waveforms and the rescaled ppBHPT waveform at a mass ratio of 1∶3 and comment on their regime of validity. Finally, we explore the possibility of using PN theory to obtain the α−β calibration parameters and still provide a rescaled ppBHPT waveform that matches NR.

关键词： Gravitational waves

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Robustness of Deep Learning Models to Precession in Gravitational-Wave Searches for Intermediate-Mass Black Hole Binaries

arXiv

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arXiv 2024年

作者： Meijer, Quirijn van der Sluys, Marc Caudill, Sarah Department of Physics Utrecht University Princetonplein 1 Utrecht3584CC Netherlands Nikhef Science Park 105 Amsterdam1098XG Netherlands Department of Physics University of Massachusetts DartmouthMA02747 United States Center for Scientific Computing and Visualization Research University of Massachusetts DartmouthMA02747 United States

Gravitational-wave searches for signals of intermediate-mass black hole binaries are hindered by detector glitches, as the increased masses from stellar-mass systems hinder current generation detectors from observing the inspiral phase of the binary evolution. This causes the waveforms to strongly resemble glitches, which are of similar duration within a similar frequency band. Additionally, precession of the orbital plane of a binary black hole may further warp signal waveforms. In this work three neural network-based classifiers for the task of distinguishing between signals and glitches are introduced, with each following different training regimes to study the impact of precession on the classifiers. Although all classifiers show highly accurate performance, the classifier found to perform best was trained following the principle of curriculum learning, where new examples are introduced only after the mastery of easier preceding examples. This classifier obtains an accuracy of approximately 95% on a synthetic test set consisting of signals and glitches injected into coloured noise from the O3 LIGO Hanford power spectral density. The model is compared to matched filtering, the state-of-the-art in modelled gravitational-wave searches, and analysed in search of particular sensitivities to black hole binary parameters. It was found that while the classifier is affected by the total mass of a system, the prediction of a misclassification is most strongly determined by visibility through the signal-to-noise ratio. The analysis of the three classifiers demonstrates that precession is handled differently depending on the training regime, meaning the architecture is not fully robust to precession and advancements can still be made through the development of training routines. Copyright © 2024, The Authors. All rights reserved.

关键词： Signal to noise ratio

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

arXiv

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arXiv 2024年

作者： Rink, Katie Bachhar, Ritesh Islam, Tousif Rifat, Nur E.M. González-Quesada, Kevin Field, Scott E. Khanna, Gaurav Hughes, Scott A. Varma, Vijay Department of Physics Center for Scientific Computing & Visualization Research University of Massachusetts DartmouthMA02747 United States Department of Physics Center for Gravitational Physics University of Texas AustinTX78712 United States Department of Physics Center for Computational Research University of Rhode Island East Hall KingstonRI02881 United States Kavli Institute for Theoretical Physics University of California Santa Barbara Kohn Hall Lagoon Rd Santa BarbaraCA93106 United States Kavli Institute for Theoretical Physics University of California Santa BarbaraCA93106 United States Department of Physics University of Virginia 1827 University Avenue CharlottesvilleVA22903 United States Case Western Reserve University ClevelandOH44106 United States Department of Mathematics Center for Scientific Computing & Visualization Research University of Massachusetts DartmouthMA02747 United States Department of Physics Massachusetts Institute of Technology CambridgeMA02139 United States

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 ≤ 4 spin-weighted spherical harmonic modes except the (4, 1) and m = 0 modes. We find that for binaries with χ1 −0.5, retrograde quasi-normal 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. © 2024, CC BY.

关键词： Perturbation techniques

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THE RQR ALGORITHM

arXiv

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arXiv 2024年

作者： Camps, Daan Mach, Thomas Vandebril, Raf Watkins, David S. National Energy Research Scientific Computing Center Lawrence Berkeley National Laboratory United States University of Potsdam Institute of Mathematics Karl-Liebknecht-Str. 24–25 Potsdam14476 Germany Department of Computer Science KU Leuven Belgium Department of Mathematics Washington State University United States

Pole-swapping algorithms, generalizations of bulge-chasing algorithms, have been shown to be a viable alternative to the bulge-chasing QZ algorithm for solving the generalized eigenvalue problem for a matrix pencil A − λB. It is natural to try to devise a pole-swapping algorithm that solves the standard eigenvalue problem for a single matrix A. This paper introduces such an algorithm and shows that it is competitive with Francis’s bulge-chasing QR *** Codes 65F15, 15A18 © 2024, CC BY.

关键词： Consensus algorithm

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Relativistic Digital Twin: Bringing the IoT to the Future

arXiv

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arXiv 2023年

作者： Sciullo, Luca De Marchi, Alberto Trotta, Angelo Montori, Federico Bononi, Luciano Felice, Marco Di Department of Computer Science and Engineering University of Bologna Italy Advanced Research Center on Electronic Systems University of Bologna Italy Institute of Applied Mathematics and Scientific Computing Department of Aerospace Engineering University of the Bundeswehr Munich Germany

Complex IoT ecosystems often require the usage of Digital Twins (DTs) of their physical assets in order to perform predictive analytics and simulate what-if scenarios. DTs are able to replicate IoT devices and adapt over time to their behavioral changes. However, DTs in IoT are typically tailored to a specific use case, without the possibility to seamlessly adapt to different scenarios. Further, the fragmentation of IoT poses additional challenges on how to deploy DTs in heterogeneous scenarios characterized by the usage of multiple data formats and IoT network protocols. In this paper, we propose the Relativistic Digital Twin (RDT) framework, through which we automatically generate general-purpose DTs of IoT entities and tune their behavioral models over time by constantly observing their real counterparts. The framework relies on the object representation via the Web of Things (WoT), to offer a standardized interface to each of the IoT devices as well as to their DTs. To this purpose, we extended the W3C WoT standard in order to encompass the concept of behavioral model and define it in the Thing Description (TD) through a new vocabulary. Finally, we evaluated the RDT framework over two disjoint use cases to assess its correctness and learning performance, i.e., the DT of a simulated smart home scenario with the capability of forecasting the indoor temperature, and the DT of a real-world drone with the capability of forecasting its trajectory in an outdoor scenario. Experiments show that the generated DT can estimate the behavior of its real counterpart after an observation stage, regardless of the considered scenario. © 2023, CC BY.

关键词： Internet of things

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Optimizing post-Newtonian parameters and fixing the BMS frame for numerical-relativity waveform hybridizations

arXiv

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arXiv 2024年

作者： Sun, Dongze Boyle, Michael Mitman, Keefe Scheel, Mark A. Stein, Leo C. Teukolsky, Saul A. Varma, Vijay Theoretical Astrophysics 350-17 California Institute of Technology 1200 E California Boulevard PasadenaCA91125 United States Cornell Center for Astrophysics and Planetary Science Cornell University IthacaNY14853 United States Department of Physics and Astronomy University of Mississippi UniversityMS38677 United States Department of Mathematics Center for Scientific Computing and Visualization Research University of Massachusetts DartmouthMA02747 United States PotsdamD-14476 Germany

Numerical relativity (NR) simulations of binary black holes provide precise waveforms, but are typically too computationally expensive to produce waveforms with enough orbits to cover the whole frequency band of gravitational-wave observatories. Accordingly, it is important to be able to hybridize NR waveforms with analytic, post-Newtonian (PN) waveforms, which are accurate during the early inspiral phase. We show that to build such hybrids, it is crucial to both fix the Bondi-Metzner-Sachs (BMS) frame of the NR waveforms to match that of PN theory, and optimize over the PN parameters to mitigate the error caused by the discrepancy between NR and PN parameters. We test such a hybridization procedure including all spin-weighted spherical harmonic modes with |m| ≤ for ≤ 8, using 29 NR waveforms with mass ratios q ≤ 10 and spin magnitudes |χ1|, |χ2| ≤ 0.8. We find that for spin-aligned systems, the PN and NR waveforms agree very well. The difference is limited by the small nonzero orbital eccentricity of the NR waveforms, or equivalently by the lack of eccentric terms in the PN waveforms. To maintain full accuracy of the simulations, the matching window for spin-aligned systems should be at least 5 orbits long and end at least 15 orbits before merger. For precessing systems, the errors are larger than for spin-aligned cases. The errors are likely limited by the absence of precession-related spin-spin PN terms. Using 105 M long NR waveforms, we find that there is no optimal choice of the matching window within this time span, because the hybridization result for precessing cases is always better if using earlier or longer matching windows. We provide the mean orbital frequency of the smallest acceptable matching window as a function of the target error between the PN and NR waveforms and the black hole spins. Copyright © 2024, The Authors. All rights reserved.

关键词： Relativity

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A fast and accurate domain decomposition nonlinear manifold reduced order model

arXiv

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arXiv 2023年

作者： Diaz, Alejandro N. Choi, Youngsoo Heinkenschloss, Matthias Department of Compuational Applied Mathematics and Operations Research Rice University HoustonTX77005 United States Center for Applied Scientific Computing Lawrence Livermore National Laboratory LivermoreCA94550 United States

This paper integrates nonlinear-manifold reduced order models (NM-ROMs) with domain decomposition (DD). NM-ROMs approximate the full order model (FOM) state in a nonlinear-manifold by training a shallow, sparse autoencoder using FOM snapshot data. These NM-ROMs can be advantageous over linear-subspace ROMs (LS-ROMs) for problems with slowly decaying Kolmogorov n-width. However, the number of NM-ROM parameters that need to be trained scales with the size of the FOM. Moreover, for "extreme-scale" problems, the storage of high-dimensional FOM snapshots alone can make ROM training expensive. To alleviate the training cost, this paper applies DD to the FOM, computes NM-ROMs on each subdomain, and couples them to obtain a global NM-ROM. This approach has several advantages: Subdomain NM-ROMs can be trained in parallel, involve fewer parameters to be trained than global NM-ROMs, require smaller subdomain FOM dimensional training data, and can be tailored to subdomain-specific features of the FOM. The shallow, sparse architecture of the autoencoder used in each subdomain NM-ROM allows application of hyper-reduction (HR), reducing the complexity caused by nonlinearity and yielding computational speedup of the NM-ROM. This paper provides the first application of NM-ROM (with HR) to a DD problem. In particular, this paper details an algebraic DD reformulation of the FOM, training a NM-ROM with HR for each subdomain, and a sequential quadratic programming (SQP) solver to evaluate the coupled global NM-ROM. Theoretical convergence results for the SQP method and a priori and a posteriori error estimates for the DD NM-ROM with HR are provided. The proposed DD NM-ROM with HR approach is numerically compared to a DD LS-ROM with HR on the 2D steady-state Burgers’ equation, showing an order of magnitude improvement in accuracy of the proposed DD NM-ROM over the DD LS-ROM. Copyright © 2023, The Authors. All rights reserved.

关键词： Quadratic programming

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