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On Error-Based Step Size Control for Discontinuous Galerkin Methods for Compressible Fluid Dynamics

应用数学与计算数学学报 2025年第1期7卷 3-39页

作者： Hendrik Ranocha Andrew R.Winters Hugo Guillermo Castro Lisandro Dalcin Michael Schlottke-Lakemper Gregor J.Gassner Matteo Parsani Applied Mathematics University of HamburgBundesstr.5520146 HamburgGermany Department of Mathematics Applied Mathematics Linköping UniversityLinköpingSweden Extreme Computing Research Center(ECRC) Computer Electrical and Mathematical Science and Engineering Division(CEMSE)King Abdullah University of Science and Technology(KAUST)Thuwal 23955-6900Saudi Arabia Applied and Computational Mathematics RWTH Aachen UniversityAachenGermany High-Performance Computing Center Stuttgart University of StuttgartStuttgartGermany Department of Mathematics and Computer Science University of CologneCologneGermany Center for Data and Simulation Science University of CologneCologneGermany Extreme Computing Research Center(ECRC) Computer Electrical and Mathematical Science and Engineering Division(CEMSE)King Abdullah University of Science and Technology(KAUST)Thuwal 23955-6900Saudi Arabia Physical Science and Engineering Division(PSE) King Abdullah University of Science and Technology(KAUST)Thuwal 23955-6900Saudi Arabia

We study a temporal step size control of explicit Runge-Kutta(RK)methods for com-pressible computational fluid dynamics(CFD),including the Navier-Stokes equations and hyperbolic systems of conservation laws such as the Euler *** demonstrate that error-based approaches are convenient in a wide range of applications and compare them to more classical step size control based on a Courant-Friedrichs-Lewy(CFL)*** numerical examples show that the error-based step size control is easy to use,robust,and efficient,e.g.,for(initial)transient periods,complex geometries,nonlinear shock captur-ing approaches,and schemes that use nonlinear entropy *** demonstrate these properties for problems ranging from well-understood academic test cases to industrially relevant large-scale computations with two disjoint code bases,the open source Julia pack-ages *** with *** and the C/Fortran code SSDC based on PETSc.

关键词： Explicit Runge-Kutta(RK)methods Step size control Compressible fluid dynamics Adaptivity in space and time Shock capturing

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Reduced Order Modeling for First Order Hyperbolic Systems with Application to Multiparameter Acoustic Waveform Inversion

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SIAM Journal on Imaging Sciences 2025年第2期18卷 851-880页

作者： Borcea, Liliana Garnier, Josselin Mamonov, Alexander V. Zimmerling, Jorn Applied Physics and Applied Mathematics Columbia University New YorkNY10027 United States CMAP CNRS Ecole Polytechnique Institut Polytechnique de Paris Palaiseau91120 France Department of Mathematics University of Houston HoustonTX77204-3008 United States Department of Information Technology Division of Scientific Computing Uppsala Universitet Uppsala75105 Sweden

Waveform inversion seeks to estimate an inaccessible heterogeneous medium from data gathered by sensors that emit probing signals and measure the generated waves. It is an inverse problem for a second order wave equation or a first order hyperbolic system, with the sensor excitation modeled as a forcing term and the heterogeneous medium described by unknown, spatially variable coefficients. The traditional ``full waveform inversion"" (FWI) formulation estimates the unknown coefficients via minimization of the nonlinear, least squares data fitting objective function. For typical band-limited and high frequency data, this objective function has spurious local minima near and far from the true coefficients. Thus, FWI implemented with gradient based optimization algorithms may fail, even for good initial guesses. Recently, it was shown that it is possible to obtain a better behaved objective function for wave speed estimation, using data driven reduced order models (ROMs) that capture the propagation of pressure waves, governed by the classic second order wave equation. Here we introduce ROMs for vectorial waves, satisfying a general first order hyperbolic system. They are defined via Galerkin projection on the space spanned by the wave snapshots, evaluated on a uniform time grid with appropriately chosen time step. Our ROMs are data driven: They are computed in an efficient and noniterative manner, from the sensor measurements, without knowledge of the medium and the snapshots. The ROM computation applies to any linear waves in lossless and nondispersive media. For the inverse problem we focus attention on acoustic waves in a medium with unknown variable wave speed and density. We show that these can be determined via minimization of an objective function that uses a ROM based approximation of the vectorial wave field inside the inaccessible medium. We assess the performance of our inversion approach with numerical simulations and compare the results to those given by

关键词： Inverse problems

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Machine learning algorithm partially reconfigured on FPGA for an image edge detection system

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Journal of Electronic Science and technology 2024年第2期22卷 48-68页

作者： Gracieth Cavalcanti Batista Johnny Oberg Osamu Saotome Haroldo F.de Campos Velho Elcio Hideiti Shiguemori Ingemar Soderquist Division of Electronic and Embedded Systems KTH Royal Institute of TechnologyStockholm 16440Sweden Electronic Engineering Division Aeronautics Institute of TechnologySao Josédos Campos SP 12228-900Brazil Laboratory of Applied Computing and Mathematics National Institute for Space ResearchSao Josédos Campos SP 12227-900Brazil Department of C4ISR Institute of Advanced StudiesSao Josédos Campos SP 12228-001Brazil Saab AB Linkoping 58188Sweden

Unmanned aerial vehicles(UAVs)have been widely used in military,medical,wireless communications,aerial surveillance,*** key topic involving UAVs is pose estimation in autonomous navigation.A standard procedure for this process is to combine inertial navigation system sensor information with the global navigation satellite system(GNSS)***,some factors can interfere with the GNSS signal,such as ionospheric scintillation,jamming,or *** alternative method to avoid using the GNSS signal is to apply an image processing approach by matching UAV images with georeferenced *** a high effort is required for image edge *** a support vector regression(SVR)model is proposed to reduce this computational load and processing *** dynamic partial reconfiguration(DPR)of part of the SVR datapath is implemented to accelerate the process,reduce the area,and analyze its granularity by increasing the grain size of the reconfigurable *** show that the implementation in hardware is 68 times faster than that in *** architecture with DPR also facilitates the low power consumption of 4 mW,leading to a reduction of 57%than that without *** is also the lowest power consumption in current machine learning hardware ***,the circuitry area is 41 times *** with Gaussian kernel shows a success rate of 99.18%and minimum square error of 0.0146 for testing with the planning *** system is useful for adaptive applications where the user/designer can modify/reconfigure the hardware layout during its application,thus contributing to lower power consumption,smaller hardware area,and shorter execution time.

关键词： Dynamic partial reconfiguration(DPR) Field programmable gate array(FPGA)implementation Image edge detection Support vector regression(SVR) Unmanned aerial vehicle(UAV) pose estimation

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XAI Based Cattle Identification with YOLO and SIFT Technique

XAI Based Cattle Identification with YOLO and SIFT Technique

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2024 IEEE International Conference on Future Machine Learning and Data Science, FMLDS 2024

作者： Katharria, Aashu Pant, Millie Deep, Kusum Devi, Indu Mehta Family School of Data Science and Artificial Intelligence Indian Institute of Technology Roorkee Uttarakhand Roorkee India Applied Mathematics and Scientific Computing Indian Institute of Technology Roorkee Uttarakhand Roorkee India Indian Institute of Technology Roorkee Department of Mathematics Uttarakhand Roorkee India ICAR-National Dairy Research Institute Livestock Production Management Division Haryana Karnal132001 India

ISBN: (纸本)9798350391213

In precision livestock farming, accurate cattle identification is essential for enhancing animal welfare, health monitoring, and productivity, while also supporting traceability and minimizing false insurance claims. This paper presents a novel approach for cattle identification using muzzle prints, with a focus on both efficiency and explainability. Taxicab metric, employed for efficient annotation of muzzle patterns significantly reduces the labeling time for training of YOLOv8 model. YOLOv8 is utilized for detecting muzzle prints in images, followed by SIFT (Scale-Invariant Feature Transform) for feature extraction and matching. The incorporation of Explainable AI (XAI) methods, particularly Grad-CAM, further enhances the transparency and interpretability of the SIFT model. © 2024 IEEE.

关键词： Precision agriculture

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A Fast Exponential Analysis and Variable Projection Based Method for Linear Array Synthesis

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IEEE Antennas and Wireless Propagation Letters 2025年第6期24卷 1527-1531页

作者： Sengupta, Ramonika Knaepkens, Ferre Cuyt, Annie Prinsloo, David S. Schäfer, Thomas Smolders, A. Bart Department of Electrical Engineering Eindhoven University of Technology Eindhoven5600 MB Netherlands Faculty of Applied Engineering University of Antwerp Groenenborgerlaan 171 Antwerp2020 Belgium Computing Science and Mathematics Division University of Stirling Scotland StirlingFK9 4LA United Kingdom ASTRON Dwindloo Oude Hoogeveensedjik 4 7991 PD Netherlands SATCUBE Nellickevägen 22 Gothenburg41263 Sweden

This paper presents a fast exponential analysis and variable projection method to reduce the number of elements in linear phased arrays. The numerical examples given in this work demonstrate a reduction of approximately 20% or 10% in the number of elements, with only a slight decrease in directivity of 0.63 dBi observed for a scan range of [−45◦, 45◦]. Compared to the combined matrix pencil and Tabu search algorithm, the proposed technique converges in fewer iterations and exhibits ≈ 5 dB reduction in maximum side lobe level. © 2002-2011 IEEE All rights reserved.

关键词： Antenna phased arrays

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Optimized Runge-Kutta Methods with Automatic Step Size Control for Compressible Computational Fluid Dynamics

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Communications on applied mathematics and Computation 2022年第4期4卷 1191-1228页

作者： Hendrik Ranocha Lisandro Dalcin Matteo Parsani David I.Ketcheson Applied Mathematics Münster University of MünsterMunsterGermany Computer Electrical and Mathematical Science and Engineering Division(CEMSE) Extreme Computing Research Center(ECRC)King Abdullah University of Science and Technology(KAUST)Thuwal 23955-6900Saudi Arabia Computer Electrical and Mathematical Science and Engineering Division(CEMSE) King Abdullah University of Science and Technology(KAUST)Thuwal 23955-6900Saudi Arabia

We develop error-control based time integration algorithms for compressible fluid dynam-ics(CFD)applications and show that they are efficient and robust in both the accuracy-limited and stability-limited *** on discontinuous spectral element semidis-cretizations,we design new controllers for existing methods and for some new embedded Runge-Kutta *** demonstrate the importance of choosing adequate controller parameters and provide a means to obtain these in *** compare a wide range of error-control-based methods,along with the common approach in which step size con-trol is based on the Courant-Friedrichs-Lewy(CFL)*** optimized methods give improved performance and naturally adopt a step size close to the maximum stable CFL number at loose tolerances,while additionally providing control of the temporal error at tighter *** numerical examples include challenging industrial CFD applications.

关键词： Explicit Runge-Kutta methods Step size control Compressible Euler equations Compressible Navier-Stokes equations hp-adaptive spatial discretizations

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SUPERFAST DIRECT INVERSION OF THE NONUNIFORM DISCRETE FOURIER TRANSFORM VIA HIERARCHICALLY SEMI-SEPARABLE LEAST SQUARES

arXiv

引用

arXiv 2024年

作者： Wilber, Heather Epperly, Ethan N. Barnett, Alex H. Department of Applied Mathematics University of Washington SeattleWA98105 United States Division of Computing and Mathematical Sciences California Institute of Technology PasadenaCA91125 United States Center for Computational Mathematics Flatiron Institute New YorkNY10010 United States

A direct solver is introduced for solving overdetermined linear systems involving nonuniform discrete Fourier transform matrices. Such matrices can be transformed into a Cauchy-like form that has hierarchical low rank structure. The rank structure of this matrix is explained, and it is shown that the ranks of the relevant submatrices grow only logarithmically with the number of columns of the matrix. A fast rank-structured hierarchical approximation method based on this analysis is developed, along with a hierarchical least-squares solver for these and related systems. This result is a direct method for inverting nonuniform discrete transforms with a complexity that is usually nearly linear with respect to the degrees of freedom in the problem. This solver is benchmarked against various iterative and direct solvers in the setting of inverting the one-dimensional type-II (or forward) transform, for a range of condition numbers and problem sizes (up to 4 × 106 by 2 × 106). These experiments demonstrate that this method is especially useful for large problems with multiple right-hand *** Codes 65T50, 65F55, 65F20 Copyright © 2024, The Authors. All rights reserved.

关键词： Discrete Fourier transforms

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Leveraging Interpolation Models and Error Bounds for Verifiable Scientific Machine Learning

arXiv

引用

arXiv 2024年

作者： Chang, Tyler Gillette, Andrew Maulik, Romit Mathematics and Computer Science Division Argonne National Laboratory United States Center for Applied Scientific Computing Lawrence Livermore National Laboratory United States Information Sciences and Technology Department The Pennsylvania State University United States

Effective verification and validation techniques for modern scientific machine learning workflows are challenging to devise. Statistical methods are abundant and easily deployed, but often rely on speculative assumptions about the data and methods involved. Error bounds for classical interpolation techniques can provide mathematically rigorous estimates of accuracy, but often are difficult or impractical to determine computationally. In this work, we present a best-of-both-worlds approach to verifiable scientific machine learning by demonstrating that (1) multiple standard interpolation techniques have informative error bounds that can be computed or estimated efficiently;(2) comparative performance among distinct interpolants can aid in validation goals;(3) deploying interpolation methods on latent spaces generated by deep learning techniques enables some interpretability for black-box models. We present a detailed case study of our approach for predicting lift-drag ratios from airfoil images. Code developed for this work is available in a public Github repository. © 2024, CC BY-NC-SA.

关键词： Interpolation

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Rapid quantum ground state preparation via dissipative dynamics

arXiv

引用

arXiv 2025年

作者： Zhan, Yongtao Ding, Zhiyan Huhn, Jakob Gray, Johnnie Preskill, John Chan, Garnet Kin-Lic Lin, Lin Institute for Quantum Information and Matter California Institute of Technology United States Division of Physics Mathematics and Astronomy California Institute of Technology United States Department of Mathematics University of California Berkeley United States Department of Physics Arnold Sommerfeld Center for Theoretical Physics Ludwig-Maximilians-Universität München Germany Division of Chemistry and Chemical Engineering California Institute of Technology United States Department of Physics California Institute of Technology United States AWS Center for Quantum Computing Applied Mathematics and Computational Research Division Lawrence Berkeley National Laboratory United States

Inspired by natural cooling processes, dissipation has become a promising approach for preparing low-energy states of quantum systems. However, the potential of dissipative protocols remains unclear beyond certain commuting Hamiltonians. This work provides significant analytical and numerical insights into the power of dissipation for preparing the ground state of non-commuting Hamiltonians. For quasi-free dissipative dynamics, including certain 1D spin systems with boundary dissipation, our results reveal a new connection between the mixing time in trace distance and the spectral properties of a non-Hermitian Hamiltonian, leading to an explicit and sharp bound on the mixing time that scales polynomially with system size. For more general spin systems, we develop a tensor network-based algorithm for constructing the Lindblad jump operator and for simulating the dynamics. Using this algorithm, we demonstrate numerically that dissipative ground state preparation protocols can achieve rapid mixing for certain 1D local Hamiltonians under bulk dissipation, with a mixing time that scales logarithmically with the system size. We then prove the rapid mixing result for certain weakly interacting spin and fermionic systems in arbitrary dimensions, extending recent results for high-temperature quantum Gibbs samplers to the zero-temperature regime. Our theoretical approaches are applicable to systems with singular stationary states, and are thus expected to have applications beyond the specific systems considered in this study. © 2025, CC BY.

关键词： Dynamics

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The ESPRIT algorithm under high noise: Optimal error scaling and noisy super-resolution

arXiv

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arXiv 2024年

作者： Ding, Zhiyan Epperly, Ethan N. Lin, Lin Zhang, Ruizhe Department of Mathematics University of California Berkeley United States Department of Computing and Mathematical Sciences California Institute of Technology PasadenaCA United States Applied Mathematics and Computational Research Division Lawrence Berkeley National Laboratory United States Challenge Institute for Quantum Computation University of California Berkeley United States Simons Institute for the Theory of Computing United States

Subspace-based signal processing techniques, such as the Estimation of Signal Parameters via Rotational Invariant Techniques (ESPRIT) algorithm, are popular methods for spectral estimation. These algorithms can achieve the so-called super-resolution scaling under low noise conditions, surpassing the well-known Nyquist limit. However, the performance of these algorithms under high-noise conditions is not as well understood. Existing state-of-the-art analysis indicates that ESPRIT and related algorithms can be resilient even for signals where each observation is corrupted by statistically independent, mean-zero noise of size O(1), but these analyses only show that the error ∊ decays at a slow rate ∊ = O͂(n−1/2) with respect to the cutoff frequency n (i.e., the maximum frequency of the measurements). In this work, we prove that under certain assumptions, the ESPRIT algorithm can attain a significantly improved error scaling ∊ = O͂(n−3/2), exhibiting noisy super-resolution scaling beyond the Nyquist limit ∊ = O(n−1) given by the Nyquist-–Shannon sampling theorem. We further establish a theoretical lower bound and show that this scaling is optimal. Our analysis introduces novel matrix perturbation results, which could be of independent interest. © 2024, CC BY.

关键词： Cutoff frequency

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