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Developing and analyzing a DG method for modeling of metasurfaces

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Journal of computational Physics 2025年 534卷

作者： Li, Chanjie Huang, Yunqing Li, Jichun School of Mathematics and Computational Science Xiangtan University Hunan Xiangtan411105 China National Center for Applied Mathematics in Hunan Xiangtan University Hunan Xiangtan411105 China Department of Mathematical Sciences University of Nevada Las Vegas Las VegasNV89154-4020 United States

Metasurfaces, with their unique ability to manipulate electromagnetic waves at subwavelength scales, have garnered significant attention for their applications in various areas such as wavefront shaping, beam steering, and cloaking. Accurately modeling these structures presents a complex challenge due to the intricate interactions between electromagnetic waves and the metasurface's subwavelength geometry. In this work, we present a discontinuous Galerkin time-domain (DGTD) method for the efficient and accurate modeling of metasurfaces by coupling with the generalized sheet transition conditions (GSTCs). Numerical stability is proved for two types of metasurfaces. Through a series of benchmark numerical simulations, we demonstrate the accuracy and computational efficiency of the DGTD method in modeling metasurfaces, especially those with irregular geometries. This work opens new avenues for the accurate simulation and design of metasurfaces in a wide range of electromagnetic applications. © 2025 Elsevier Inc.

关键词： Maxwell equations

Unbiased Parameter Estimation for Bayesian Inverse Problems

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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

Accuracy versus Predominance: Reassessing the validity of the quasi-steady-state approximation

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arXiv 2025年

作者： Srivastava, Kashvi Eilertsen, Justin Booth, Victoria Schnell, Santiago Department of Mathematics University of Michigan Ann ArborMI48109 United States Mathematical Reviews American Mathematical Society 416 4th Street Ann ArborMI48103 United States Department of Biological Sciences Department of Applied & Computational Mathematics & Statistics University of Notre Dame Notre DameIN46556 United States

The application of the standard quasi-steady-state approximation to the Michaelis–Menten reaction mechanism is a textbook example of biochemical model reduction, derived using singular perturbation theory. However, determining the specific biochemical conditions that dictate the validity of the standard quasi-steady-state approximation remains a challenging endeavor. Emerging research suggests that the accuracy of the standard quasi-steady-state approximation improves as the ratio of the initial enzyme concentration, e0, to the Michaelis constant, KM, decreases. In this work, we examine this ratio and its implications for the accuracy and validity of the standard quasi-steady-state approximation. Using standard tools from the analysis of ordinary differential equations, we show that while e0/KM provides an indication of the standard quasi-steady-state approximation’s asymptotic accuracy, the sQSSA’s predominance relies on a small ratio of e0 to the Van Slyke-Cullen constant, K. We conclude that the magnitude of e0/K offers the most accurate measure of the validity of the standard quasi-steady-state *** Codes 34E15, 34A34, 34A34, 37N25, 93A30, 65L20 © 2025, CC BY.

关键词： Perturbation techniques

Integral equations for flexural-gravity waves: analysis and numerical methods

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arXiv 2025年

作者： Askham, Travis Hoskins, Jeremy G. Nekrasov, Peter Rachh, Manas Department of Mathematical Sciences New Jersey Institute of Technology NewarkNJ07102 United States Department of Statistics and CCAM University of Chicago ChicagoIL60637 United States Committee on Computational and Applied Mathematics University of Chicago ChicagoIL60637 United States Center for Computational Mathematics Flatiron Institute New YorkNY10010 United States

In this work, we develop a fast and accurate method for the scattering of flexural-gravity waves by a thin plate of varying thickness overlying a fluid of infinite depth. This problem commonly arises in the study of sea ice and ice shelves, which can have complicated heterogeneities that include ridges and rolls. With certain natural assumptions on the thickness, we present an integral equation formulation for solving this class of problems and analyze its mathematical properties. The integral equation is then discretized and solved using a high-order-accurate, FFT-accelerated algorithm. The speed, accuracy, and scalability of this approach are demonstrated through a variety of illustrative examples. © 2025, CC BY.

关键词： Gravity waves

SymScore: Machine learning accuracy meets transparency in a symbolic regression-based clinical score generator

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Computers in Biology and Medicine 2025年 185卷 109589-109589页

作者： Cawiding, Olive R. Lee, Sieun Jo, Hyeontae Kim, Sungmoon Suh, Sooyeon Joo, Eun Yeon Chung, Seockhoon Kim, Jae Kyoung Department of Mathematical Sciences KAIST Daejeon34141 Korea Republic of Biomedical Mathematics Group Pioneer Research Center for Mathematical and Computational Sciences Institute for Basic Science Daejeon34126 Korea Republic of Department of Medicine College of Medicine Korea University Seoul02841 Korea Republic of Department of Mathematics Kyungpook National University Daegu41566 Korea Republic of Division of Applied Mathematical Sciences Korea University Sejong30019 Korea Republic of Department of Psychology Sungshin Women's University Seoul02844 Korea Republic of Department of Neurology Neuroscience Center Samsung Medical Center Sungkyunkwan University School of Medicine Seoul06351 Korea Republic of Department of Psychiatry Asan Medical Center University of Ulsan College of Medicine Seoul05505 Korea Republic of

Self-report questionnaires play a crucial role in healthcare for assessing disease risks, yet their extensive length can be burdensome for respondents, potentially compromising data quality. To address this, machine learning-based shortened questionnaires have been developed. While these questionnaires possess high levels of accuracy, their practical use in clinical settings is hindered by a lack of transparency and the need for specialized machine learning expertise. This makes their integration into clinical workflows challenging and also decreases trust among healthcare professionals who prefer interpretable tools for decision-making. To preserve both predictive accuracy and interpretability, this study introduces the Symbolic Regression-Based Clinical Score Generator (SymScore). SymScore produces score tables for shortened questionnaires, which enable clinicians to estimate the results that reflect those of the original questionnaires. SymScore generates the score tables by optimally grouping responses, assigning weights based on predictive importance, imposing necessary constraints, and fitting models via symbolic regression. We compared SymScore's performance with the machine learning-based shortened questionnaires MCQI-6 (n=310) and SLEEPS (n=4257), both renowned for their high accuracy in assessing sleep disorders. SymScore's questionnaire demonstrated comparable performance (MAE = 10.73, R2 = 0.77) to that of the MCQI-6 (MAE = 9.94, R2 = 0.82) and achieved AUROC values of 0.85-0.91 for various sleep disorders, closely matching those of SLEEPS (0.88-0.94). By generating accurate and interpretable score tables, SymScore ensures that healthcare professionals can easily explain and trust its results without specialized machine learning knowledge. Thus, SymScore advances explainable AI for healthcare by offering a user-friendly and resource-efficient alternative to machine learning-based questionnaires, supporting improved patient outcomes and workflow efficienc

关键词： Risk assessment

Asymptotic Analysis of Quantum Dynamics in Crystals: the Bloch-Wigner Transform, Bloch Dynamics and Berry Phase

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Acta Mathematicae Applicatae Sinica 2013年第3期29卷 465-476页

作者： Weinan E Jian-feng LU Xu YANG Department of Mathematics Princeton University Program in Applied and Computational Mathematics Princeton University School of Mathematical Sciences Peking University

We study the semi-classical limit of the Schro¨dinger equation in a crystal in the presence of an external potential and magnetic field. We first introduce the Bloch-Wigner transform and derive the asymptotic equations governing this transform in the semi-classical setting. For the second part, we focus on the appearance of the Berry curvature terms in the asymptotic equations. These terms play a crucial role in many important physical phenomena such as the quantum Hall effect. We give a simple derivation of these terms in different settings using asymptotic analysis.

关键词： semiclassical limit Bloch-Wigner transform Bloch dynamics Berry phase asymptotic analysis

SEMICLASSICAL LIMIT FOR BIPOLAR QUANTUM DRIFT-DIFFUSION MODEL

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Acta Mathematica Scientia 2009年第2期29卷 285-293页

作者：琚强昌陈丽 Institute of Applied Physics and Computational Mathematics Department of Mathematical Sciences Tsinghua University

Semiclassical limit to the solution of transient bipolar quantum drift-diffusion model in semiconductor simulation is discussed. It is proved that the semiclassical limit of this solution satisfies the classical bipol... 详细信息

关键词： Quantum drift-diffusion weak solution semiclassical limit bipolar

ON THE 3D VISCOUS PRIMITIVE EQUATIONS OF THE LARGE-SCALE ATMOSPHERE

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Acta Mathematica Scientia 2009年第4期29卷 846-866页

作者：郭柏灵黄代文 Institute of Applied Physics and Computational Mathematics Department of Mathematical Sciences Tsinghua University

This paper is devoted to considering the three-dimensional viscous primitive equations of the large-scale atmosphere. First, we prove the global well-posedness for the primitive equations with weaker initial data than that in [11]. Second, we obtain the existence of smooth solutions to the equations. Moreover, we obtain the compact global attractor in V for the dynamical system generated by the primitive equations of large-scale atmosphere, which improves the result of [11].

关键词： primitive equations Navier-Stokes equations global well-posedness smooth solutions

NEURAL NETWORK-ENHANCED hr-ADAPTIVE FINITE ELEMENT ALGORITHM FOR PARABOLIC EQUATIONS

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arXiv 2025年

作者： Hao, Jiaxiong Huang, Yunqing Yi, Nianyu Yin, Peimeng Hunan Key Laboratory for Computation and Simulation in Science and Engineering School of Mathematics and Computational Science Xiangtan University Hunan Xiangtan411105 China National Center for Applied Mathematics in Hunan Key Laboratory of Intelligent Computing & Information Processing of Ministry of Education Xiangtan University Hunan Xiangtan411105 China Department of Mathematical Sciences University of Texas at El Paso El PasoTX79968 United States

In this paper, we present a novel enhancement to the conventional hr-adaptive finite element methods for parabolic equations, integrating traditional h-adaptive and r-adaptive methods via neural networks. A major challenge in hr-adaptive finite element methods lies in projecting the previous step’s finite element solution onto the updated mesh. This projection depends on the new mesh and must be recomputed for each adaptive iteration. To address this, we introduce a neural network to construct a mesh-free surrogate of the previous step finite element solution. Since the neural network is mesh-free, it only requires training once per time step, with its parameters initialized using the optimizer from the previous time step. This approach effectively overcomes the interpolation challenges associated with non-nested meshes in computation, making node insertion and movement more convenient and efficient. The new algorithm also emphasizes SIZING and GENERATE, allowing each refinement to roughly double the number of mesh nodes of the previous iteration and then redistribute them to form a new mesh that effectively captures the singularities. It significantly reduces the time required for repeated refinement and achieves the desired accuracy in no more than seven space-adaptive iterations per time step. Numerical experiments confirm the efficiency of the proposed algorithm in capturing dynamic changes of *** Codes 92B20, 65M60, 35K57 © 2025, CC BY.

关键词： Interpolation