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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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Simulation of Electromagnetic Wave Propagation in Graphene-Coated 1D Photonic Crystals Using the Finite Volume Method

Simulation of Electromagnetic Wave Propagation in Graphene-C...

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2024 International Conference on Interdisciplinary Physics, ICIPs 2024

作者： Negara, Teguh Puja Hardhienata, Hendradi Alatas, Husin Study Program of Computer Science Faculty of Mathematics and Natural Science Universitas Pakuan Bogor Indonesia Theoretical Physics Division Department of Physics Faculty of Mathematics and Natural Science IPB University Bogor Indonesia

A numerical study on the interaction of electromagnetic waves with photonic crystals with one-dimensional periodicity has been carried out using the Finite Volume method. The photonic crystals with one-dimensional periodicity consists of 7 alternating layers of and with thicknesses of and, respectively. Electromagnetic field components have been simulated to propagate through the photonic crystal structure, experiencing reflection and transmission at each layer of the structure. The simulation results show the occurrence of absorption precisely at the Bragg frequency by the photonic crystal, which is referred to as the photonic band gap (PBG). A comparison of the simulation results has been conducted using different fluxes, such as the Lax-Friedrichs and upwind schemes, under PBG conditions. The results show smoother absorption using the Lax-Friedrichs scheme. Additionally, the use of a single-layer graphene on the front side of the photonic crystal has shown more perfect absorption compared to without the single-layer graphene. Therefore, the integrated graphene-photonic crystal system can be used as a perfect reflector. The simulation runs well using effective absorbing boundary conditions (ABCs) to reduce wave reflections at the edges of the computational window. Based on the simulation results, the Finite Volume method has been proven to be a powerful tool in describing electromagnetic wave propagation through photonic crystal systems with or without graphene. These findings provide a foundational model for fabrication approaches and holds potential for future advancements in sensor technologies, moreover two-dimensional and three-dimensional structures. © 2025 Institute of Physics Publishing. All rights reserved.

关键词： Photonic band gap

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Long-term stability from adaptive auto-calibration in mid-infrared sensing instruments 25

Long-term stability from adaptive auto-calibration in mid-in...

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Optical Fibers and Sensors for Medical Diagnostics, Treatment, and Environmental Applications XXV 2025

作者： Alexis, Al Anderson, London Khan, Mohammad A. Division of Physics Engineering Mathematics and Computer Science Optical Science Center for Applied Research Delaware State University 1200 N. Dupont Hwy DoverDE19901 United States

ISBN: (纸本)9781510683686

Mid-infrared laser-based sensing is widely used for the detection and quantification of trace gases for environmental monitoring, industrial process control, defense, and security applications. However, such laser spectroscopy-based field instruments require frequent calibration to correct for long-term drifts and precision. In many situations, such calibrations may be redundant and may not be effective in monitoring instrument errors or discriminating "real"environmental effects with instrument drifts. This paper shows that physics and diffusion-based models can be developed to predict gradual or rapid changes in density at given temperatures and appropriate source characterizations. We used a 3.3μm, laser-based instrument to demonstrate an adaptive and auto-calibration methodology to account for drifts during field deployments and an adaptive method to validate environmental changes, e.g., plume detection, diurnal variations, and flux emissions. We field operation and implementation of adaptive auto-calibration. The instruments are used for the detection of methane and water vapor, but an adaptive auto-calibration technique can be employed for any laser sensing instrument. © 2025 SPIE.

关键词： Laser spectroscopy

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Unbiased Parameter Estimation for Bayesian Inverse Problems

arXiv

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arXiv 2025年

作者： Chada, Neil K. Jasra, Ajay Maama, Mohamed Tempone, Raul Department of Mathematics City University of Hong Kong China School of Data Science The Chinese University of Hong Kong Shenzhen CN Shenzhen China Applied Mathematics and Computational Science Program Computer Electrical and Mathematical Sciences and Engineering Division King Abdullah University of Science and Technology Thuwal23955-6900 Saudi Arabia

In this paper we consider the estimation of unknown parameters in Bayesian inverse problems. In most cases of practical interest, there are several barriers to performing such estimation, This includes a numerical approximation of a solution of a differential equation and, even if exact solutions are available, an analytical intractability of the marginal likelihood and its associated gradient, which is used for parameter estimation. The focus of this article is to deliver unbiased estimates of the unknown parameters, that is, stochastic estimators that, in expectation, are equal to the maximizer of the marginal likelihood, and possess no numerical approximation error. Based upon the ideas of [4] we develop a new approach for unbiased parameter estimation for Bayesian inverse problems. We prove unbiasedness and establish numerically that the associated estimation procedure is faster than the current state-of-the-art methodology for this problem. We demonstrate the performance of our methodology on a range of problems which include a PDE and ODE. Copyright © 2025, The Authors. All rights reserved.

关键词： Markov processes

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Applying Layer-Wise Relevance Propagation on U-Net Architectures 27th

Applying Layer-Wise Relevance Propagation on U-Net Architect...

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27th International Conference on Pattern Recognition, ICPR 2024

作者： Weinberger, Patrick Fröhler, Bernhard Heim, Anja Gall, Alexander Bodenhofer, Ulrich Senck, Sascha Research Group Computed Tomography University of Applied Sciences Upper Austria Wels Austria School of Informatics Communication and Media University of Applied Sciences Upper Austria Wels Austria Johannes Kepler University Linz Linz Austria Faculty of Computer Science and Mathematics University of Passau Passau Germany Division Development Center X-ray Technology Fraunhofer Institute for Integrated Circuits IIS Erlangen Germany

ISBN: (纸本)9783031781971

For safety critical applications, it is still a challenge to use AI and fulfill all regulatory requirements. Medicine/healthcare and transportation are two fields where regulatory requirements are of fundamental importance. A wrong decision can lead to serious hazards or even deaths. In these fields, semantic segmentation is often utilized to extract features. Especially U-Net architectures are used. This paper shows how to apply layer-wise relevance propagation (LRP) to a trained U-Net architecture. We achieve an efficient explanation of a segmentation by back-propagating the whole resulting image. To tackle the non-linear results of the LRP, we introduce a threshold mechanism in combination with a logarithmic transfer function to preprocess the data for visualization. We demonstrate our method on three use cases: the segmentation of a fiber-reinforced polymer in the field of non-destructive testing, the segmentation of pedestrians in an automotive application, and a lung segmentation example from the medical domain. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2025.

关键词： Semantic Segmentation

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Lung Cancer Diagnosis Based on Object Detection Technology 14th

Lung Cancer Diagnosis Based on Object Detection Technology

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14th International Conference on Frontier Computing, FC 2024

作者： Xu, Jia-Lang Wang, Pei-Yun Huang, Tzu-Hsuan Hsu, Ying-Lin Huang, Kuo-Yang Chen, Mu-Yen Artificial Intelligence Development Center Changhua Christian Hospital Changhua Taiwan Doctoral Program in Data Science and Industrial Analytics National Chung Hsing University Taichung Taiwan Department of Applied Mathematics and Institute of Statistics National Chung Hsing University Taichung Taiwan Division of Chest Medicine Department of Internal Medicine Changhua Christian Hospital Changhua Taiwan Department of Engineering Science National Cheng Kung University Tainan Taiwan

ISBN: (纸本)9789819623945

With the rise of artificial intelligence, many people nowadays use artificial intelligence to help solve some problems in life, and the medical field is also with the rise of artificial intelligence, many people are slowly applying artificial intelligence to medical images to assist in decision-making, this study proposes a Yolov8 algorithm for object tracking of CT images of lung cancer, which can quickly tell the doctor where the cancer is and what the type of cancer is. The results of this study show that the Box_Loss, Cls_Loss, and Dfl_loss of the Yolov8 algorithm in detecting the location of lung cancer are 1.3689, 0.4552, and 1.5569 in the validation data, respectively, and thus this study suggests that this method can help physicians know the location of the tumor and what kind of tumor it belongs to. Therefore, this study suggests that this method can help physicians know the location of the tumor and the type of tumor. © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2025.

关键词： Lung cancer

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Integrated LIBS and Mid-infrared Spectroscopy of Lunar Regolith Simulants 25

Integrated LIBS and Mid-infrared Spectroscopy of Lunar Regol...

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Optical Fibers and Sensors for Medical Diagnostics, Treatment, and Environmental Applications XXV 2025

作者： Alexis, Al Anderson, London Markushin, Yuriy Wilson, Emily Khan, Mohammad A. Division of Physics Engineering Mathematics and Computer Science Delaware State University 1200 N. Dupont Hwy DoverDE19901 United States Optical Center for Applied Research Delaware State University 1200 N. Dupont Hwy DoverDE19901 United States GreenbeltMD20771 United States

ISBN: (纸本)9781510683686

Mid-infrared (MIR) spectroscopy and laser-induced breakdown spectroscopy (LIBS) have evolved to be suitable for developing and deploying science instruments for planetary missions. For instance, the NASA Mars rover missions included a suite of instruments (SUPERCAM) with laser spectrometers and LIBS instruments. Both combined can provide a critical chemical composition and quantitative detection of trace gases, solids, and liquids from excited electronics state and rotational, vibrational transitions. LIBS enables rapid in situ detection, spectral information of multi-elemental targets, and profile of lighter elements. In the LIBS technique, a laser is used to ablate a small amount of the sample of interest and turn it into a luminous microplasma, which is then analyzed spectroscopically. In this paper, we show the LIBS study of Lunar regolith, e.g., Lunar Mare and Lunar Highlands simulants. The paper will explore the electrical and physical properties of lunar regolith to enable electrically modified coatings of the lander for dust discharge. In addition, we also investigate the retention of water molecules in these regolith simulants using MIR laser spectroscopy. © 2025 SPIE.

关键词： Laser induced breakdown spectroscopy

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EAIRA: Establishing a Methodology for Evaluating AI Models as Scientific Research Assistants

arXiv

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arXiv 2025年

作者： Cappello, Franck Madireddy, Sandeep Underwood, Robert Getty, Neil Chia, Nicholas Lee-Ping Ramachandra, Nesar Nguyen, Josh Keçeli, Murat Mallick, Tanwi Li, Zilinghan Ngom, Marieme Zhang, Chenhui Yanguas-Gil, Angel Antoniuk, Evan Kailkhura, Bhavya Tian, Minyang Du, Yufeng Ting, Yuan-Sen Wells, Azton Nicolae, Bogdan Maurya, Avinash Mustafa Rafique, M. Huerta, Eliu Li, Bo Foster, Ian Stevens, Rick Mathematics and Computer Science Division Argonne National Laboratory United States Data Science and Learning Division Argonne National Laboratory United States Computational Science Division Argonne National Laboratory United States Applied Materials Division Argonne National Laboratory United States Department of Computer Science The University of Chicago United States University of Pennsylvania United States Lawrence Livermore National Laboratory United States The Ohio State University United States Rochester Institute of Technology United States Massachusetts Institute of Technology United States

Recent advancements have positioned AI, and particularly Large Language Models (LLMs) as transformative tools for scientific research, capable of addressing complex tasks that require reasoning, problem-solving, and decision-making. Their exceptional capabilities suggest their potential as scientific research assistants, but also highlight the need for holistic, rigorous, and domain-specific evaluation to assess effectiveness in real-world scientific applications. This paper describes a multifaceted methodology for Evaluating AI models as scientific Research Assistants (EAIRA) developed at Argonne National Laboratory. This methodology incorporates four primary classes of evaluations. 1) Multiple Choice Questions to assess factual recall;2) Open Response to evaluate advanced reasoning and problem-solving skills;3) Lab-Style Experiments involving detailed analysis of capabilities as research assistants in controlled environments;and 4) Field-Style Experiments to capture researcher-LLM interactions at scale in a wide range of scientific domains and applications. These complementary methods enable a comprehensive analysis of LLM strengths and weaknesses with respect to their scientific knowledge, reasoning abilities, and adaptability. Recognizing the rapid pace of LLM advancements, we designed the methodology to evolve and adapt so as to ensure its continued relevance and applicability. This paper describes the methodology’s state at the end of February 2025. Although developed within a subset of scientific domains, the methodology is designed to be generalizable to a wide range of scientific domains. Copyright © 2025, The Authors. All rights reserved.

关键词： Decision making

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Bayesian Inference for Non-Synchronously Observed Diffusions

arXiv

引用

arXiv 2025年

作者： Jasra, Ajay Kamatani, Kengo Wu, Amin School of Data Science The Chinese University of Hong Kong Shenzhen Shenzhen China Institute of Statistical Mathematics Tokyo190-0014 Japan Statistics Program Computer Electrical and Mathematical Sciences and Engineering Division King Abdullah University of Science and Technology Thuwal23955-6900 Saudi Arabia

We consider the problem of Bayesian inference for bi-variate data observed in time but with observation times which occur non-synchronously. In particular, this occurs in a wide variety of applications in finance, such as high-frequency trading or crude oil futures trading. We adopt a diffusion model for the data and formulate a Bayesian model with priors on unknown parameters along with a latent representation for the the so-called missing data. We then consider computational methodology to fit the model using Markov chain Monte Carlo (MCMC). We have to resort to time-discretization methods as the complete data likelihood is intractable and this can cause considerable issues for MCMC when the data are observed in low frequencies. In a high frequency observation frequencies we present a simple particle MCMC method based on an Euler–Maruyama time discretization, which can be enhanced using multilevel Monte Carlo (MLMC). In the low frequency observation regime we introduce a novel bridging representation of the posterior in continuous time to deal with the issues of MCMC in this case. This representation is discretized and fitted using MCMC and MLMC. We apply our methodology to real and simulated data to establish the efficacy of our methodology. © 2025, CC BY.

关键词： Crude oil

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A SPECTRAL LEVENBERG-MARQUARDT-DEFLATION METHOD FOR MULTIPLE SOLUTIONS OF SEMILINEAR ELLIPTIC SYSTEMS

arXiv

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arXiv 2025年

作者： Li, Lin Zhou, Yuheng Xie, Pengcheng Li, Huiyuan School of Mathematics and Physics University of South China Hengyang China Applied Mathematics and Computational Research Division Lawrence Berkeley National Laboratory 1 Cyclotron Road BerkeleyCA94720 United States State Key Laboratory of Computer Science Laboratory of Parallel Computing Institute of Software Chinese Academy of Sciences Beijing100190 China

Many nonlinear differential equations arising from practical problems may permit nontrivial multiple solutions relevant to applications, and these multiple solutions are helpful to deeply understand these practical problems and to improve some applications. Developing an efficient numerical method for finding multiple solutions is very necessary due to the nonlinearity and multiple solutions of these equations. Moreover, providing an efficient iteration plays an important role in successfully obtaining multiple solutions with fast and stable convergence. In the current paper, an efficient algorithm for finding multiple solutions of semilinear elliptic systems is proposed, where the trust region Levenberg-Marquardt method is firstly used to iterate the resulted nonlinear algebraic system. When the nonlinear term in these equations has only the first derivative, our algorithm can efficiently find multiple solutions as well. Several numerical experiments are tested to show the efficiency of our algorithm, and some solutions which have not been shown in the literature are also found and *** Codes 65N35, 65N22, 65F05, 65L10 Copyright © 2025, The Authors. All rights reserved.

关键词： Nonlinear equations

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