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Surrogate modeling of gravitational waves microlensed by spherically symmetric potentials

Physical Review D 2025年第10期111卷 104042-104042页

作者： Uddeepta Deka Gopalkrishna Prabhu Md Arif Shaikh Shasvath J. Kapadia Vijay Varma Scott E. Field International Centre for Theoretical Sciences Tata Institute of Fundamental Research Bangalore 560089 India Inter-University Centre for Astronomy and Astrophysics Post Bag 4 Ganeshkhind Pune 411007 India Department of Physics Vivekananda Satavarshiki Mahavidyalaya (affiliated to Vidyasagar University) Manikpara 721513 West Bengal India Department of Physics and Astronomy Seoul National University Seoul 08826 South Korea Department of Mathematics Center for Scientific Computing and Visualization Research University of Massachusetts Dartmouth Dartmouth Massachusetts 02747 USA

The anticipated observation of the gravitational microlensing of gravitational waves (GWs) promises to shed light on a host of astrophysical and cosmological questions. However, extracting the parameters of the lens from the modulated GWs requires accurate modeling of the lensing amplification factor, accounting for wave-optics effects. Analytic solutions to the lens equation have not been found to date, except for a handful of simplistic lens models. While numerical solutions to this equation have been developed, the time and computational resources required to evaluate the amplification factor numerically make large-scale parameter estimation of the lens (and source) parameters prohibitive. On the other hand, surrogate modeling of GWs has proven to be a powerful tool to accurately, and rapidly, produce GW templates at arbitrary points in parameter space, interpolating from a finite set of available waveforms at discrete parameter values. In this work, we demonstrate that surrogate modeling can also effectively be applied to the evaluation of the time-domain microlensing amplification factor F˜(t). We show this by constructing F˜(t) for two lens models, viz. point-mass lens, and singular isothermal sphere, which notably includes logarithmic divergence behavior. We find both surrogates reproduce the original lens models accurately, with mismatches ≲5×10−4 across a range of plausible microlensed binary black hole sources observed by the Einstein Telescope. This surrogate is between 5 and 103 times faster than the underlying lensing models, and can be evaluated in about 100 ms. The accuracy and efficiency attained by our surrogate models will enable practical parameter estimation analyses of microlensed GWs.

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Comparing numerical relativity and perturbation theory waveforms for a non-spinning equal-mass binary

arXiv

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arXiv 2023年

作者： Islam, Tousif Field, Scott E. Khanna, Gaurav Department of Mathematics University of Massachusetts DartmouthMA02747 United States Department of Physics University of Massachusetts DartmouthMA02747 United States Center for Scientific Computing and Data Science Research University of Massachusetts DartmouthMA02747 United States Department of Physics Center for Computational Research University of Rhode Island KingstonRI02881 United States

Past studies have empirically demonstrated a surprising agreement between gravitational waveforms computed using adiabatic-driven-inspiral point-particle black hole perturbation theory (ppBHPT) and numerical relativity (NR) following a straightforward calibration step, sometimes referred to as α-β scaling. Specifically focusing on the quadrupole mode, this calibration technique necessitates only two time-independent parameters to scale the overall amplitude and time coordinate. In this article, part of a special issue, we investigate this scaling for non-spinning binaries at the equal mass limit. Even without calibration, NR and ppBHPT waveforms exhibit an unexpected degree of similarity after accounting for different mass scale definitions. Post-calibration, good agreement between ppBHPT and NR waveforms extends nearly up to the point of the merger. We also assess the breakdown of the time-independent assumption of the scaling parameters, shedding light on current limitations and suggesting potential generalizations for the α-β scaling technique. Copyright © 2023, The Authors. All rights reserved.

关键词： Black holes

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On the approximate relation between black-hole perturbation theory and numerical relativity

arXiv

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arXiv 2023年

作者： Islam, Tousif Khanna, Gaurav Department of Physics University of Massachusetts DartmouthMA02747 United States Department of Mathematics University of Massachusetts DartmouthMA02747 United States Center for Scientific Computing and Data Science Research University of Massachusetts DartmouthMA02747 United States Department of Physics Center for Computational Research University of Rhode Island KingstonRI02881 United States

We investigate the interplay between numerical relativity (NR) and adiabatic point-particle black hole perturbation theory (ppBHPT) in the comparable mass regime for quasi-circular non-spinning binary black holes. Specifically, we reassess the α-β scaling technique, previously introduced by Islam et al. [1], 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 [2]) 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. Copyright © 2023, The Authors. All rights reserved.

关键词： Black holes

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The Advanced Encryption Standard with a Dynamic S-Box Using the RC4 Key Schedule 4

The Advanced Encryption Standard with a Dynamic S-Box Using ...

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4th IEEE International Conference on Electrical, Computer, and Energy Technologies, ICECET 2024

作者： Altigani, Abdelrahman Ghalib, Muhammad Rukunuddin Elshoush, Huwaida T. Elsadig, Muawia A. Alrefai, Nashat Naserelden, Shiraz Higher Colleges of Technology Computer Information Science Al Ain United Arab Emirates School of Engineering & Computing De Monfort University Dubai United Arab Emirates University of Khartoum Faculty of Mathematical Sciences and Informatics Computer Science Department Khartoum Sudan College of Computer Science and Information Technology Imam Abdulrahman bin Faisal University Dammam Saudi Arabia College of Science Imam Abdulrahman Bin Faisal University Basic and Applied Scientific Research Center Imam Abdulrahman Bin Faisal University Department of Mathematics Dammam Saudi Arabia Faculty of Science Universiti Teknologi Malaysia Department of Mathematical Sciences Johor Malaysia

ISBN: (纸本)9798350395914

Since the inception of secure communication, safeguarding data confidentiality has been paramount. With the increased reliance on technology, the need for robust security mechanisms is more critical than ever. This paper explores confidentiality in cybersecurity, focusing on symmetric encryption algorithms. While symmetric encryption, particularly the Advanced Encryption Standard (AES), is in wide use, concerns arise regarding its static nature. Therefore, the paper introduces a dynamic cipher, augmenting AES security by introducing a key-dependent S-Box. By leveraging the RC4 key schedule, the proposed cipher generates unique S-Boxes for each encryption key, significantly increasing security against non-generic attacks. Theoretical analysis demonstrates the proposed cipher is capable of resisting brute force, linear cryptanalysis, and differential cryptanalysis. Furthermore, its adaptability to existing AES implementations ensures practicality and ease of adoption. © 2024 IEEE.

关键词： Ciphertext

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Divergence-Free Flux Globalization Based Well-Balanced Path-Conservative Central-Upwind Schemes for Rotating Shallow Water Magnetohydrodynamics

arXiv

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arXiv 2023年

作者： Chertock, Alina Kurganov, Alexander Redle, Michael Zeitlin, Vladimir Department of Mathematics Center for Research in Scientific Computing North Carolina State University RaleighNC27695 United States Department of Mathematics Shenzhen International Center for Mathematics Guangdong Provincial Key Laboratory of Computational Science and Material Design Southern University of Science and Technology Shenzhen518055 China Applied and Computational Mathematics RWTH Aachen University Aachen52062 Germany Department of Mathematics North Carolina State University RaleighNC27695 United States CNRS Paris75231 France Shenzhen International Center for Mathematics Southern University of Science and Technology Shenzhen518055 China

We develop a new second-order flux globalization based path-conservative central-upwind (PCCU) scheme for rotating shallow water magnetohydrodynamic equations. The new scheme is designed not only to maintain the divergence-free constraint of the magnetic field at the discrete level but also to satisfy the well-balanced (WB) property by exactly preserving some physically relevant steady states of the underlying system. The locally divergence-free constraint of the magnetic field is enforced by following the method recently introduced in [A. Chertock, A. Kurganov, M. Redle, and K. Wu, ArXiv preprint (2022), arXiv:2212.02682]: we consider a Godunov-Powell modified version of the studied system, introduce additional equations by spatially differentiating the magnetic field equations, and modify the reconstruction procedures for magnetic field variables. The WB property is ensured by implementing a flux globalization approach within the PCCU scheme, leading to a method capable of preserving both still- and moving-water equilibria exactly. In addition to provably achieving both the WB and divergence-free properties, the new method is implemented on an unstaggered grid and does not require any (approximate) Riemann problem solvers. The performance of the proposed method is demonstrated in several numerical experiments that confirm the lack of spurious oscillations, robustness, and high resolution of the obtained results. © 2023, CC BY.

关键词： Magnetohydrodynamics

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Divergence-Free Flux Globalization Based Well-Balanced Path-Conservative Central-Upwind Schemes for Rotating Shallow Water Magnetohydrodynamics

SSRN

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SSRN 2023年

作者： Chertock, Alina Kurganov, Alexander Redle, Michael Zeitlin, Vladimir Department of Mathematics Center for Research in Scientific Computing North Carolina State University RaleighNC27695 United States Department of Mathematics Shenzhen International Center for Mathematics Guangdong Provincial Key Laboratory of Computational Science and Material Design Southern University of Science and Technology Shenzhen518055 China Applied and Computational Mathematics RWTH Aachen University Aachen52062 Germany Department of Mathematics North Carolina State University RaleighNC27695 United States CNRS Paris 75231 France Shenzhen International Center for Mathematics Southern University of Science and Technology Shenzhen518055 China

关键词： Magnetohydrodynamics

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Fast And Automatic Floating Point Error Analysis With CHEF-FP

Fast And Automatic Floating Point Error Analysis With CHEF-F...

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International Symposium on Parallel and Distributed Processing (IPDPS)

作者： Garima Singh Baidyanath Kundu Harshitha Menon Alexander Penev David J. Lange Vassil Vassilev European Council for Nuclear Research Meyrin Switzerland Department of Physics Princeton University Princeton New Jersey USA Lawrence Livermore National Laboratory Center for Applied Scientific Computing Livermore California USA Faculty of Mathematics and Informatics University of Plovdiv Plovdiv Bulgaria

As we reach the limit of Moore’s Law, researchers are exploring different paradigms to achieve unprecedented performance. Approximate computing (AC), which relies on the ability of applications to tolerate some error in the results to trade-off accuracy for performance, has shown significant promise. Despite the success of AC in domains such as Machine Learning, its acceptance in High-Performance computing (HPC) is limited due to its stringent requirement of accuracy. We need tools and techniques to identify regions of the code that are amenable to approximations and their impact on the application output quality so as to guide developers to employ selective approximation. To this end, we propose CHEF-FP, a flexible, scalable, and easy-to-use source-code transformation tool based on Automatic Differentiation (AD) for analysing approximation errors in HPC ***-FP uses Clad, an efficient AD tool built as a plugin to the Clang compiler and based on the LLVM compiler infrastructure, as a backend and utilizes its AD abilities to evaluate approximation errors in C++ code. CHEF-FP works at the source level by injecting error estimation code into the generated adjoints. This enables the error-estimation code to undergo compiler optimizations resulting in improved analysis time and reduced memory usage. We also provide theoretical and architectural augmentations to source code transformation-based AD tools to perform FP error analysis. In this paper, we primarily focus on analyzing errors introduced by mixed-precision AC techniques, the most popular approximate technique in HPC. We also show the applicability of our tool in estimating other kinds of errors by evaluating our tool on codes that use approximate functions. Moreover, we demonstrate the speedups achieved by CHEF-FP during analysis time as compared to the existing state-of-the-art tool as a result of its ability to generate and insert approximation error estimate code directly into the derivative sourc

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Combined influences of Soret effect and horizontal magnetic field on dynamics of vertical convection in binary fluids

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Physical Review Fluids 2025年第5期10卷 053503-053503页

作者： Chao-Nan Zhang Lai-yun Zheng Xu-Long Li Juan-Juan Qin Bing-Xin Zhao Don Liu School of Mathematics and Statistics Ningxia University Yinchuan 750021 China School of Mechanical Engineering Ningxia University Yinchuan 750021 China Ningxia Key Laboratory of Interdisciplinary Mechanics and Scientific Computing Yinchuan 750021 China Ningxia Basic Science Research Center of Mathematics Yinchuan 750021 China Department of Mathematics and Mechanical Engineering Louisiana Tech University Ruston Louisiana 71270 USA

The influence of the Soret effect and a uniform magnetic field on the dynamic behavior of vertical convection are investigated using a high-accuracy numerical method. The effects of the Soret number (Sr, which quantifies the direction and magnitude of species migration relative to the temperature gradient; positive Sr denotes migration toward hotter regions, negative toward cooler regions) on flow, heat and mass transfer, and flow transition in the presence of a magnetic field are analyzed. The results reveal that, for a given magnetic field strength, positive and negative Soret effects have significantly different influences on heat and mass transfer as well as on flow structure. For a high Rayleigh number (Ra, vigor of the buoyancy) and a small magnetic field, the heat transfer initially decreases and then increases with increasing Soret number, while the mass transfer consistently decreases. In cases where temperature is dominant, heat transfer for Sr=−1 exceeds that for Sr=0 by 24%, while mass transfer with Sr=−1 exceeds that for Sr=0 by 85%. When concentration is dominant, heat transfer reaches a minimum at Sr=0, whereas mass transfer peaks at Sr=−1, corresponding to an approximate 71% increase over heat transfer at Sr=0, and around a 210% increase in mass transfer. Additionally, the flow exhibits greater complexity when the Soret number is negative than when it is positive. When the magnetic field is weak, the temperature-dominated flow changes from chaotic to periodic with increasing Soret number and eventually returns to a chaotic state. When the magnetic field is strong, the flow transitions from chaotic to periodic and finally to a steady state. The transition route involves two types of periodic flow: a simple periodic flow with an integer multiple of the fundamental frequency, and a complex periodic flow with multiple lower-frequency subharmonic waves. Furthermore, as the strength of the magnetic field increases, the flow in the rectangular enclosure is

关键词： Diffusion in solids

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Learning orbital dynamics of binary black hole systems from gravitational wave measurements

arXiv

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arXiv 2021年

作者： Keith, Brendan Khadse, Akshay Field, Scott E. Brown University United States Department of Physics and Astronomy The University of Mississippi UniversityMS38677 United States Department of Mathematics Center for Scientific Computing and Visualization Research University of Massachusetts DartmouthMA02747 United States

We introduce a gravitational waveform inversion strategy that discovers mechanical models of binary black hole (BBH) systems. We show that only a single time series of (possibly noisy) waveform data is necessary to construct the equations of motion for a BBH system. Starting with a class of universal differential equations parameterized by feed-forward neural networks, our strategy involves the construction of a space of plausible mechanical models and a physics-informed constrained optimization within that space to minimize the waveform error. We apply our method to various BBH systems including extreme and comparable mass ratio systems in eccentric and non-eccentric orbits. We show that the resulting differential equations apply to time durations longer than the training interval, and relativistic effects, such as perihelion precession, radiation reaction, and orbital plunge, are automatically accounted for. The methods outlined here provide a new, data-driven approach to studying the dynamics of binary black hole systems. Copyright © 2021, The Authors. All rights reserved.

关键词： Constrained optimization

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Gaussian Process Emulators for Few-Shot Segmentation in Cardiac MRI 15th

Gaussian Process Emulators for Few-Shot Segmentation in Ca...

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15th International Workshop on Statistical Atlases and Computational Models of the Heart, STACOM 2024, Held in Conjunction with MICCAI 2024

作者： Viti, Bruno Thaler, Franz Kapper, Kathrin Lisa Urschler, Martin Holler, Martin Karabelas, Elias Department of Mathematics and Scientific Computing University of Graz Graz Austria Institute for Medical Informatics Statistics and Documentation Medical University of Graz Graz Austria Institute of Computer Graphics and Vision Graz University of Technology Graz Austria Gottfried Schatz Research Center: Medical Physics and Biophysics Medical University of Graz Graz Austria BioTechMed-Graz Graz Austria

ISBN: (纸本)9783031877551

Segmentation of cardiac magnetic resonance images (MRI) is crucial for the analysis and assessment of cardiac function, helping to diagnose and treat various cardiovascular diseases. Most recent techniques rely on deep learning and usually require an extensive amount of labeled data. To overcome this problem, few-shot learning has the capability of reducing data dependency on labeled data. In this work, we introduce a new method that merges few-shot learning with a U-Net architecture and Gaussian Process Emulators (GPEs), enhancing data integration from a support set for improved performance. GPEs are trained to learn the relation between the support images and the corresponding masks in latent space, facilitating the segmentation of unseen query images given only a small labeled support set at inference. We test our model with the M&Ms-2 public dataset to assess its ability to segment the heart in cardiac magnetic resonance imaging from different orientations, and compare it with state-of-the-art unsupervised and few-shot methods. Our architecture shows higher DICE coefficients compared to these methods, especially in the more challenging setups where the size of the support set is considerably small. The code is available on GitLab (https://***/bruno_viti/gpe_4_cardiac_fss). © The Author(s), under exclusive license to Springer Nature Switzerland AG 2025.

关键词： Gaussian distribution

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