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A Sensitivity Analysis of Cellular Automata and Heterogeneous Topology Networks: Partially-Local Cellular Automata and Homogeneous Homogeneous Random Boolean Networks

arXiv

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arXiv 2024年

作者： Glover, Tom Eivind Jahren, Ruben Martinuzzi, Francesco Lind, Pedro Gonçalves Nichele, Stefano Department of Computer Science OsloMet - Oslo Metropolitan University Oslo Norway Department of Computer Science and Communication Østfold University College Halden Norway Simula Research Laboratory Numerical Analysis and Scientific Computing Oslo0164 Norway Center for Scalable Data Analytics and Artificial Intelligence Leipzig University Leipzig Germany Institute for Earth System Science & Remote Sensing Leipzig University Leipzig Germany Remote Sensing Centre for Earth System Research Leipzig University Leipzig Germany

Elementary Cellular Automata (ECA) are a well-studied computational universe that is, despite its simple configurations, capable of impressive computational variety. Harvesting this computation in a useful way has historically shown itself to be difficult, but if combined with reservoir computing (RC), this becomes much more feasible. Furthermore, RC and ECA enable energy-efficient AI, making the combination a promising concept for Edge AI. In this work, we contrast ECA to substrates of Partially-Local CA (PLCA) and Homogeneous Homogeneous Random Boolean Networks (HHRBN). They are, in comparison, the topological heterogeneous counterparts of ECA. This represents a step from ECA towards more biological-plausible substrates. We analyse these substrates by testing on an RC benchmark (5-bit memory), using Temporal Derrida plots to estimate the sensitivity and assess the defect collapse rate. We find that, counterintuitively, disordered topology does not necessarily mean disordered computation. There are countering computational"forces" of topology imperfections leading to a higher collapse rate (order) and yet, if accounted for, an increased sensitivity to the initial condition. These observations together suggest a shrinking critical range. © 2024, CC BY.

关键词： Sensitivity analysis

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NON-SPLITTING EULERIAN-LAGRANGIAN WENO SCHEMES FOR TWO-DIMENSIONAL NONLINEAR CONVECTION-DIFFUSION EQUATIONS

arXiv

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arXiv 2024年

作者： Zheng, Nanyi Cai, Xiaofeng Qiu, Jing-Mei Qiu, Jianxian Department of Mathematical Sciences University of Delaware NewarkDE19716 United States Research Center for Mathematics Advanced Institute of Natural Sciences Beijing Normal University Zhuhai519087 China Guangdong Provincial Key Laboratory of Interdisciplinary Research and Application for Data Science BNU-HKBU United International College Zhuhai519087 China School of Mathematical Sciences Fujian Provincial Key Laboratory of Mathematical Modeling and High-Performance Scientific Computing Xiamen University Fujian Xiamen361005 China

In this paper, we develop high-order, conservative, non-splitting Eulerian-Lagrangian (EL) Runge-Kutta (RK) finite volume (FV) weighted essentially non-oscillatory (WENO) schemes for convection-diffusion equations. The proposed EL-RK-FV-WENO scheme defines modified characteristic lines and evolves the solution along them, significantly relaxing the time-step constraint for the convection term. The main algorithm design challenge arises from the complexity of constructing accurate and robust reconstructions on dynamically varying Lagrangian meshes. This reconstruction process is needed for flux evaluations on time-dependent upstream quadrilaterals and time integrations along moving characteristics. To address this, we propose a strategy that utilizes a WENO reconstruction on a fixed Eulerian mesh for spatial reconstruction, and updates intermediate solutions on the Eulerian background mesh for implicit-explicit RK temporal integration. This strategy leverages efficient reconstruction and remapping algorithms to manage the complexities of polynomial reconstructions on time-dependent quadrilaterals, while ensuring local mass conservation. The proposed scheme ensures mass conservation due to the flux-form semi-discretization and the mass-conservative reconstruction on both background and upstream cells. Extensive numerical tests have been performed to verify the effectiveness of the proposed scheme. © 2024, CC BY.

关键词： Mesh generation

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Fully precessing higher-mode surrogate model of effective-one-body waveforms

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Physical Review D 2024年第12期110卷 124038-124038页

作者： Bhooshan Gadre Michael Pürrer Scott E. Field Serguei Ossokine Vijay Varma Max Planck Institute for Gravitational Physics (Albert Einstein Institute) Am Mühlenberg 1 Potsdam 14476 Germany Institute for Gravitational and Subatomic Physics (GRASP) Utrecht University Princetonplein 1 3584 CC Utrecht The Netherlands Department of Physics East Hall University of Rhode Island Kingston Rhode Island 02881 USA URI Center for Computational Research Tyler Hall University of Rhode Island Kingston Rhode Island 02881 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

We present a surrogate model of SEOBNRv4PHM, a fully precessing time-domain effective-one-body waveform model including subdominant modes. We follow an approach similar to that used to build recent numerical relativity surrogate models. Our surrogate is 5000 M in duration, covers mass ratios up to 1∶20 and dimensionless spin magnitudes up to 0.8. Validating the surrogate against an independent test set, we find that the median mismatch error is less than 10−3, which is typically smaller than the modeling error of SEOBNRv4PHM itself. At high total mass, a few percent of configurations can exceed mismatches of 10−2 if they are highly precessing and exceed a mass ratio of 1∶4. This surrogate is nearly 2 orders of magnitude faster than the underlying time-domain SEOBNRv4PHM model and can be evaluated in ∼50 ms. Bayesian inference analyses with SEOBNRv4PHM are typically very computationally demanding and can take from weeks to months to complete. The 2 order of magnitude speedup attained by our surrogate model enables practical parameter estimation analyses with this waveform family. This is crucial because Bayesian inference allows us to recover the masses and spins of binary black hole mergers given a model of the emitted gravitational waveform along with a description of the noise.

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Defining eccentricity for gravitational wave astronomy

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Physical Review D 2023年第10期108卷 104007-104007页

作者： Md Arif Shaikh Vijay Varma Harald P. Pfeiffer Antoni Ramos-Buades Maarten van de Meent Department of Physics and Astronomy Seoul National University Seoul 08826 Korea International Centre for Theoretical Sciences Tata Institute of Fundamental Research Bangalore 560089 India Max Planck Institute for Gravitational Physics (Albert Einstein Institute) D-14476 Potsdam Germany Department of Mathematics Center for Scientific Computing and Data Science Research University of Massachusetts Dartmouth Massachusetts 02747 USA Niels Bohr International Academy Niels Bohr Institute Blegdamsvej 17 2100 Copenhagen Denmark

Eccentric compact binary mergers are significant scientific targets for current and future gravitational wave observatories. To detect and analyze eccentric signals, there is an increasing effort to develop waveform models, numerical relativity simulations, and parameter estimation frameworks for eccentric binaries. Unfortunately, current models and simulations use different internal parametrizations of eccentricity in the absence of a unique natural definition of eccentricity in general relativity, which can result in incompatible eccentricity measurements. In this paper, we adopt a standardized definition of eccentricity and mean anomaly based solely on waveform quantities and make our implementation publicly available through an easy-to-use python package, gw_eccentricity. This definition is free of gauge ambiguities, has the correct Newtonian limit, and can be applied as a postprocessing step when comparing eccentricity measurements from different models. This standardization puts all models and simulations on the same footing and enables direct comparisons between eccentricity estimates from gravitational wave observations and astrophysical predictions. We demonstrate the applicability of this definition and the robustness of our implementation for waveforms of different origins, including post-Newtonian theory, effective-one-body, extreme mass ratio inspirals, and numerical relativity simulations. We focus on binaries without spin precession in this work, but possible generalizations to spin-precessing binaries are discussed.

关键词： Gravitational waves Classical black holes Gravitational wave detection Numerical relativity

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Quantum-parallel vectorized data encodings and computations on trapped-ions and transmons QPUs

arXiv

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arXiv 2023年

作者： Balewski, Jan Amankwah, Mercy G. Van Beeumen, Roel Bethel, E. Wes Perciano, Talita Camps, Daan National Energy Research Scientific Computing Center Lawrence Berkeley National Laboratory BerkeleyCA United States Department of Mathematics Case Western Reserve University ClevelandOH United States Applied Mathematics and Computational Research Division Lawrence Berkeley National Laboratory BerkeleyCA United States Computer Science Department San Francisco State University San FranciscoCA United States Scientific Data Division Lawrence Berkeley National Laboratory BerkeleyCA United States

Compact quantum data representations are essential to the emerging field of quantum algorithms for data analysis. We introduce two new data encoding schemes, QCrank and QBArt, which have a high degree of quantum parallelism through uniformly controlled rotation gates. QCrank encodes a sequence of real-valued data as rotations of the data qubits, allowing for high storage density. QBArt directly embeds a binary representation of the data in the computational basis, requiring fewer quantum measurements and lending itself to well-understood arithmetic operations on binary data. We present several applications of the proposed encodings for different types of data. We demonstrate quantum algorithms for DNA pattern matching, Hamming weight calculation, complex value conjugation, and retrieving an O(400) bits image, all executed on the Quantinuum QPU. Finally, we use various cloud-accessible QPUs, including IBMQ and IonQ, to perform additional benchmarking experiments. Copyright © 2023, The Authors. All rights reserved.

关键词： Digital storage

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Scalable Multiscale-Spectral Gfem with an Application to Composite Aero-Structures

SSRN

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SSRN 2023年

作者： Bénézech, Jean Seelinger, Linus Bastian, Peter Butler, Richard Dodwell, Timothy Ma, Chupeng Scheichl, Robert Centre for Integrated Materials Processes and Structures University of Bath BathBA2 7AY United Kingdom Institute for Applied Mathematics Interdisciplinary Center for Scientific Computing Heidelberg University Heidelberg Germany Institute of Data Science and AI University of Exeter UK & digiLab Exeter Exeter United Kingdom Department of Mathematical Sciences University of Bath Bath United Kingdom Institute of Scientific Research Great Bay University Dongguan China

In this paper, the first large-scale application of multiscale-spectral generalized finite element methods (MS-GFEM) to composite aero-structures is presented. The crucial novelty lies in the introduction of A-harmonicity in the local approximation spaces, which in contrast to [Babuska, Lipton,Multiscale Model. Simul.9,[Babuska, Lipton, Multiscale Model. Simul. 9, 2011] is enforced more efficiently via a constraint in the local eigenproblems. This significant modification leads to excellent approximation properties, which turn out to be essential to capture accurately material strains and stresses with a low dimensional approximation space, hence maximising model order reduction. The implementation of the framework in the DUNE software package, as well as a detailed description of all components of the method are presented and exemplified on a composite laminated beam under compressive loading. The excellent parallel scalability of the method, as well as its superior performance compared to the related, previously introduced GenEO method are demonstrated on two realistic application cases, including a C-shaped wing spar with complex geometry. Further, by allowing low-cost approximate solves for closely related models or geometries this efficient, novel technology provides the basis for future applications in optimisation or uncertainty quantification on challenging problems in composite aero-structures. © 2023, The Authors. All rights reserved.

关键词： Finite element method

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TotalSegmentator MRI: Robust Sequence-independent Segmentation of Multiple Anatomic Structures in MRI

arXiv

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arXiv 2024年

作者： D'Antonoli, Tugba Akinci Berger, Lucas K. Indrakanti, Ashraya K. Vishwanathan, Nathan Weiss, Jakob Jung, Matthias Berkarda, Zeynep Rau, Alexander Reisert, Marco Küstner, Thomas Walter, Alexandra Merkle, Elmar M. Boll, Daniel Breit, Hanns-Christian Nicoli, Andrew Phillip Segeroth, Martin Cyriac, Joshy Yang, Shan Wasserthal, Jakob Clinic of Radiology and Nuclear Medicine University Hospital Basel Petersgraben 4 BaselCH-4031 Switzerland Department of Diagnostic and Interventional Radiology Faculty of Medicine Medical Center University of Freiburg University of Freiburg Germany Department of Stereotactic and Functional Neurosurgery Faculty of Medicine Medical Center University of Freiburg University of Freiburg Freiburg Germany Medical Image and Data Analysis University Hospital of Tuebingen Tuebingen Germany Department of Biomedical Physics in Radiation Oncology German Cancer Research Center Heidelberg Germany Scientific Computing Center Karlsruhe Institute of Technology Karlsruhe Germany

Background Since the introduction of TotalSegmentator CT, there is demand for a similar robust automated MRI segmentation tool that can be applied across all MRI sequences and anatomic structures. Purpose To develop and evaluate an automated MRI segmentation model for robust segmentation of major anatomic structures independently of MRI sequence. Materials and Methods In this retrospective study, a nnU-Net model (TotalSegmentator) was trained on MRI and CT examinations to segment 80 anatomic structures relevant for use cases such as organ volumetry, disease characterization, surgical planning and opportunistic screening. Examinations were randomly sampled from routine clinical studies to represent real-world examples. Dice scores were calculated between the predicted segmentations and expert radiologist reference standard segmentations to evaluate model performance on an internal test set, two external test sets and against two publicly available models, and TotalSegmentator CT. The model was applied to an internal dataset containing abdominal MRIs to investigate age-dependent volume changes. Wilcoxon signed-rank test was used. Results A total of 1143 examinations (616 MRIs, 527 CTs) (median age 61 years, IQR 50-72) were split into training (n=1088, CT and MRI) and an internal test set (n=55;only MRI), two external test sets (AMOS, n=20;CHAOS, n=20;only MRI), and an internal aging-study dataset of 8672 abdominal MRIs (median age 59 years, IQR 45-70) were included. The model showed a Dice Score of 0.839 on the internal test set and outperformed two other models (Dice Score, 0.862 versus 0.759;and 0.838 versus 0.560;p Copyright © 2024, The Authors. All rights reserved.

关键词： Computerized tomography

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The directional isotropy of LIGO-Virgo binaries

arXiv

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arXiv 2023年

作者： Isi, Maximiliano Farr, Will M. Varma, Vijay Center for Computational Astrophysics Flatiron Institute 162 5th Ave New YorkNY10010 United States Department of Physics and Astronomy Stony Brook University Stony BrookNY11794 United States Am Mühlenberg 1 Potsdam14476 Germany Department of Mathematics Center for Scientific Computing and Data Science Research University of Massachusetts DartmouthMA02747 United States

We demonstrate how to constrain the degree of absolute alignment of the total angular momenta of LIGO-Virgo binary black holes, looking for a special direction in space that would break isotropy. We also allow for inhomogeneities in the distribution of black holes over the sky. Making use of dipolar models for the spatial distribution and orientation of the sources, we analyze 57 signals with false-alarm rates ≤ 1/yr from the third LIGO-Virgo observing run. Accounting for selection biases, we find the population of LIGO-Virgo black holes to be fully consistent with both homogeneity and isotropy. We additionally find the data to constrain some directions of alignment more than others, and produce posteriors for the directions of total angular momentum of all binaries in our set. All code and data are made publicly available in https://***/maxisi/gwisotropy/. © 2023, CC BY.

关键词： Black holes

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The Fundamental Limit of Jet Tagging

arXiv

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arXiv 2024年

作者： Geuskens, Joep Gite, Nishank Krämer, Michael Mikuni, Vinicius Mück, Alexander Nachman, Benjamin Reyes-González, Humberto Institute for Theoretical Particle Physics and Cosmology RWTH Aachen University Germany Department of Physics University of California BerkeleyCA94720 United States National Energy Research Scientific Computing Center Berkeley Lab BerkeleyCA94720 United States Physics Division Lawrence Berkeley National Laboratory BerkeleyCA94720 United States Berkeley Institute for Data Science University of California BerkeleyCA94720 United States

Identifying the origin of high-energy hadronic jets (‘jet tagging’) has been a critical benchmark problem for machine learning in particle physics. Jets are ubiquitous at colliders and are complex objects that serve as prototypical examples of collections of particles to be categorized. Over the last decade, machine learning-based classifiers have replaced classical observables as the state of the art in jet tagging. Increasingly complex machine learning models are leading to increasingly more effective tagger performance. Our goal is to address the question of convergence - are we getting close to the fundamental limit on jet tagging or is there still potential for computational, statistical, and physical insights for further improvements? We address this question using state-of-the-art generative models to create a realistic, synthetic dataset with a known jet tagging optimum. Various state-of-the-art taggers are deployed on this dataset, showing that there is a significant gap between their performance and the optimum. Our dataset and software are made public to provide a benchmark task for future developments in jet tagging and other areas of particle physics. © 2024, CC BY.

关键词： Hadrons

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Improving Generative Model-based Unfolding with Schrödinger Bridges

arXiv

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arXiv 2023年

作者： Diefenbacher, Sascha Liu, Guan-Horng Mikuni, Vinicius Nachman, Benjamin Nie, Weili Physics Division Lawrence Berkeley National Laboratory BerkeleyCA94720 United States Autonomous Control and Decision Systems Laboratory Georgia Institute of Technology AtlantaGA30332 United States National Energy Research Scientific Computing Center Berkeley Lab BerkeleyCA94720 United States Berkeley Institute for Data Science University of California BerkeleyCA94720 United States Machine Learning Research Group NVIDIA Research United States

Machine learning-based unfolding has enabled unbinned and high-dimensional differential cross section measurements. Two main approaches have emerged in this research area: one based on discriminative models and one based on generative models. The main advantage of discriminative models is that they learn a small correction to a starting simulation while generative models scale better to regions of phase space with little data. We propose to use Schrödinger Bridges and diffusion models to create SBUnfold, an unfolding approach that combines the strengths of both discriminative and generative models. The key feature of SBUnfold is that its generative model maps one set of events into another without having to go through a known probability density as is the case for normalizing flows and standard diffusion models. We show that SBUnfold achieves excellent performance compared to state of the art methods on a synthetic Z+jets dataset. © 2023, CC BY.

关键词： Phase space methods

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