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A prediction-correction based iterative convolution-thresholding method for topology optimization of heat transfer problems

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arXiv 2024年

作者： Chen, Huangxin Dong, Piaopiao Wang, Dong Wang, Xiao-Ping School of Mathematical Sciences Fujian Provincial Key Laboratory on Mathematical Modeling and High Performance Scientific Computing Xiamen University Fujian361005 China School of Science and Engineering The Chinese University of Hong Kong Guangdong Shenzhen518172 China Shenzhen International Center for Industrial and Applied Mathematics Shenzhen Research Institute of Big Data Guangdong518172 China

In this paper, we propose an iterative convolution-thresholding method (ICTM) based on prediction-correction for solving the topology optimization problem in steady-state heat transfer equations. The problem is formulated as a constrained minimization problem of the complementary energy, incorporating a perimeter/surface-area regularization term, while satisfying a steady-state heat transfer equation. The decision variables of the optimization problem represent the domains of different materials and are represented by indicator functions. The perimeter/surface-area term of the domain is approximated using Gaussian kernel convolution with indicator functions. In each iteration, the indicator function is updated using a prediction-correction approach. The prediction step is based on the variation of the objective functional by imposing the constraints, while the correction step ensures the monotonically decreasing behavior of the objective functional. Numerical results demonstrate the efficiency and robustness of our proposed method, particularly when compared to classical approaches based on the ICTM. Copyright © 2024, The Authors. All rights reserved.

关键词： Convolution

Inverse Design of All-dielectric Metasurfaces with Bound States in the Continuum

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arXiv 2023年

作者： Gladyshev, Sergei Karamanos, Theodosios D. Kuhn, Lina Beutel, Dominik Weiss, Thomas Rockstuhl, Carsten Bogdanov, Andrey Institute of Physics University of Graz Universitätsplatz 5 Graz8010 Austria Institut Langevin ESPCI Paris Université PSL CNRS Paris75005 France Institute of Theoretical Solid State Physics Karlsruhe Institute of Technology Karlsruhe76131 Germany Steinbuch Centre for Computing - Scientific Computing & Mathematics Karlsruhe Institute of Technology Germany Institute of Nanotechnology Karlsruhe Institute of Technology Eggenstein-Leopoldshafen76344 Germany Qingdao Innovation and Development Base of Harbin Engineering University Shandong Qingdao266000 China

Metasurfaces with bound states in the continuum (BICs) have proven to be a powerful platform for drastically enhancing light-matter interactions, improving biosensing, and precisely manipulating near- and far-fields. However, engineering metasurfaces to provide an on-demand spectral and angular position for a BIC remains a prime challenge. A conventional solution involves a fine adjustment of geometrical parameters, requiring multiple time-consuming calculations. In this work, to circumvent such tedious processes, we develop a physics-inspired, inverse design method on all-dielectric metasurfaces for an on-demand spectral and angular position of a BIC. Our suggested method predicts the core-shell particles that constitute the unit cell of the metasurface, while considering practical limitations on geometry and available materials. Our method is based on a smart combination of a semi-analytical solution, for predicting the required dipolar Mie coefficients of the meta-atom, and a machine learning algorithm, for finding a practical design of the meta-atom that provides these Mie coefficients. Although our approach is exemplified in designing a metasurface sustaining a BIC, it can, also, be applied to many more objective functions. With that, we pave the way toward a general framework for the inverse design of metasurfaces in specific and nanophotonic structures in general. Copyright © 2023, The Authors. All rights reserved.

关键词： Geometry

Information Fusion in Smart Agriculture: Machine Learning Applications and Future Research Directions

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arXiv 2024年

作者： Katharria, Aashu Rajwar, Kanchan Pant, Millie Velásquez, Juan D. Snášel, Václav Deep, Kusum Mehta Family School of Data Science and Artificial Intelligence Indian Institute of Technology Roorkee Roorkee India Statistical Quality Control and Operations Research Unit Indian Statistical Institute Hyderabad India Department of Applied Mathematics and Scientific Computing Indian Institute of Technology Roorkee Roorkee India Department of Industrial Engineering University of Chile Santiago Chile Instituto Sistemas Complejos de Ingeniería Santiago Chile Department of Computer Science VSB-Technical University of Ostrava Ostrava Czech Republic Department of Mathematics Indian Institute of Technology Roorkee Roorkee India

Machine learning (ML) is a rapidly evolving technology with expanding applications across various fields. This paper presents a comprehensive survey of recent ML applications in agriculture for sustainability and efficiency. Existing reviews mainly focus on narrow subdomains or lack a fusion-driven perspectives. This study provides a combined analysis of ML applications in agriculture, structured around five key objectives: (i) Analyzing ML techniques across pre-harvesting, harvesting, and post-harvesting phases. (ii) Demonstrating how ML can be used with agricultural data and data fusion. (iii) Conducting a bibliometric and statistical analysis to reveal research trends and activity. (iv) Investigating real-world case studies of leading artificial intelligence (AI)-driven agricultural companies that use different types of multisensors and multisource data. (v) Compiling publicly available datasets to support ML model training. Going beyond existing previous reviews, this review focuses on how machine learning (ML) techniques, combined with multi-source data fusion (integrating remote sensing, IoT, and climate analytics), enhance precision agriculture by improving predictive accuracy and decision-making. Case studies and statistical insights illustrate the evolving landscape of AI driven smart farming, while future research directions also discusses challenges associated with data fusion for heterogeneous datasets. This review bridges the gap between AI research and agricultural applications, offering a roadmap for researchers, industry professionals, and policymakers to harness information fusion and ML for advancing precision agriculture. Copyright © 2024, The Authors. All rights reserved.

关键词： Adversarial machine learning

Stability implies robust convergence of a class of preconditioned parallel-in-time iterative algorithms

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arXiv 2021年

作者： Wu, Shu-Lin Zhou, Tao Zhou, Zhi School of Mathematics and Statistics Northeast Normal University Changchun130024 China LSEC Institute of Computational Mathematics and Scientific/Engineering Computing AMSS Chinese Academy of Sciences Beijing100190 China Department of Applied Mathematics Hong Kong Polytechnic University Kowloon Hong Kong

Solving evolutionary equations in a parallel-in-time manner is an attractive topic and many algorithms are proposed in recent two decades. The algorithm based on the block α-circulant preconditioning technique has shown promising advantages, especially for wave propagation problems. By fast Fourier transform for factorizing the involved circulant matrices, the preconditioned iteration can be computed efficiently via the so-called diagonalization technique, which yields a direct parallel implementation across all time levels. In recent years, considerable efforts have been devoted to exploring the convergence of the preconditioned iteration by studying the spectral radius of the iteration matrix, and this leads to many case-by-case studies depending on the used time-integrator. In this paper, we propose a unified convergence analysis for the algorithm applied to u0 + Au = f, where σ(A) ⊂ C+ with σ(A) being the spectrum of A ∈ Cm×m. For any one-step method (such as the Runge-Kutta methods) with stability function R(z), we prove that the decay rate of the global error is bounded by α/(1 - α), provided the method is stable, i.e., maxλ∈σ(A) |R(∆tλ)| ≤ 1. For any linear multistep method, such a bound becomes cα/(1 - cα), where c ≥ 1 is a constant specified by the multistep method itself. Our proof only relies on the stability of the time-integrator and the estimate is independent of the step size ∆t and the spectrum σ(A). © 2021, CC0.

关键词： Stability

Efficacy of reduced order source terms for a coupled wave-circulation model in the Gulf of Mexico

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arXiv 2023年

作者： Loveland, Mark Meixner, Jessica Valseth, Eirik Dawson, Clint Oden Institute for Computational Engineering and Sciences University of Texas at Austin Oden Institute for Computational Engineering and Sciences The University of Texas at Austin 201 E. 24th St. AustinTX78712 United States College ParkMD United States The Department of Data Science The Norwegian University of Life Science Drøbakveien 31 Ås1433 Norway Department of Scientific Computing and Numerical Analysis Simula Research Laboratory Kristian Augusts gate 23 Oslo0164 Norway

During hurricanes, coupled wave-circulation models are critical tools for public safety. The standard approach is to use a high fidelity circulation model coupled with a wave model that uses the most advanced source terms. As a result, the models can be computationally expensive and so this study investigates the potential consequences of using simplified (reduced order) source terms within the wave model component of the coupled wave-circulation model. The trade-off between run time and accuracy with respect to observations is quantified for a set of two storms that impacted the Gulf of Mexico, Hurricane Ike and Hurricane Ida. Water surface elevations as well as wave statistics (significant wave height, peak period, and mean wave direction) are compared to observations. The usage of the reduced order source terms yielded significant savings in computational cost. Additionally, relatively low amounts of additional error with respect to observations during the simulations with reduced order source terms are observed in our computational experiments. However, large changes in global model outputs of the wave statistics were observed based on the choice of source terms particularly near the track of each hurricane. © 2023, CC BY.

关键词： Hurricanes

AN EXTENSION OPERATOR FOR MANIFOLD-VALUED SOBOLEV MAPS ON PERFORATED DOMAINS

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arXiv 2024年

作者： Gavioli, Chiara Happ, Leon Pagliari, Valerio Department of Mathematics Faculty of Civil Engineering Czech Technical University Thákurova 7 Prague 616629 Czech Republic Institute of Analysis and Scientific Computing TU Wien Wiedner Hauptstraße 8-10 Vienna1040 Austria MedUni Wien Währinger Gürtel 18-20 Vienna1090 Austria

Motivated by manifold-constrained homogenization problems, we construct an extension operator for Sobolev functions defined on a perforated domain and taking values in a compact, connected C2-manifold without boundary. The proof combines a by now classical extension result for the unconstrained case with a retraction argument that heavily relies on the topological properties of the manifold. With the ultimate goal of providing necessary conditions for the existence of suitable extension operators for Sobolev maps between manifolds, we additionally investigate the relationship between this problem and the surjectivity of the trace operator for such *** Codes 54C20, 46T10, 46E35, 55S35 Copyright © 2024, The Authors. All rights reserved.

关键词： Topology

A Prediction-Correction Based Iterative Convolution-Thresholding Method for Topology Optimization of Heat Transfer Problems

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SSRN

SSRN 2024年

关键词： Convolution

Link Prediction Accuracy on Real-World Networks Under Non-Uniform Missing Edge Patterns

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arXiv 2024年

作者： He, Xie Ghasemian, Amir Lee, Eun Schwarze, Alice C. Clauset, Aaron Mucha, Peter J. The Department of Mathematics Dartmouth College HanoverNH03755 United States The Human Nature Lab Yale University CT06520 United States The Computational Social Science Lab The University of Pennsylvania PA19104 United States The Department of Scientific Computing Pukyong National University Busan Korea Republic of The Department of Computer Science The BioFrontiers Institute The University of Colorado BoulderCO80309 United States The Santa Fe Institute Santa FeNM87501 United States

Real-world network datasets are typically obtained in ways that fail to capture all edges. The patterns of missing data are often non-uniform as they reflect biases and other shortcomings of different data collection methods. Nevertheless, uniform missing data is a common assumption made when no additional information is available about the underlying missing-edge pattern, and link prediction methods are frequently tested against uniformly missing edges. To investigate the impact of different missing-edge patterns on link prediction accuracy, we employ 9 link prediction algorithms from 4 different families to analyze 20 different missing-edge patterns that we categorize into 5 groups. Our comparative simulation study, spanning 250 real-world network datasets from 6 different domains, provides a detailed picture of the significant variations in the performance of different link prediction algorithms in these different settings. With this study, we aim to provide a guide for future researchers to help them select a link prediction algorithm that is well suited to their sampled network data, considering the data collection process and application domain. © 2024, CC BY.

关键词： Data acquisition

Freezing dynamics of wetting droplet under a uniform electric field

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arXiv 2024年

作者： Huang, Jiangxu Li, Hanqing Che, Jiaqi Chai, Zhenhua Wang, Lei Shi, Baochang School of Mathematics and Statistics Huazhong University of Science and Technology Wuhan430074 China Institute of Interdisciplinary Research for Mathematics and Applied Science Huazhong University of Science and Technology Wuhan430074 China Hubei Key Laboratory of Engineering Modeling and Scientific Computing Huazhong University of Science and Technology Wuhan430074 China Marine Design & Research Institute of China China The State Key Laboratory of Digital Manufacturing Equipment and Technology Huazhong University of Science and Technology Wuhan430074 China School of Mathematics and Physics China University of Geosciences Wuhan430074 China

Electrofreezing is a powerful technique that employs the electric field to control and enhance the freezing process. In this work, a phase-field-based lattice Boltzmann (LB) method is developed to study the electrofreezing process of sessile droplet on a cooled substrate. The accuracy of the present LB method is first validated through performing some simulations of the three-phase Stefan problem, the droplet freezing on a cold wall, and the droplet deformation under a uniform electric field. Then it is used to investigate the effect of an electric field on the freezing of a wetting droplet on a cold substrate, and the numerical results show that the electric field has a significant influence on the freezing time of the droplet mainly through changing the morphology of the droplet. In particular, under the effect of the electric field, the freezing time is increased for the droplet with a prolate pattern, while the freezing time of the droplet with an oblate pattern is decreased. These numerical results bring some new insights on the electrofreezing and provide a valuable guidance for the precise regulation of droplet freezing. Copyright © 2024, The Authors. All rights reserved.

关键词： Wetting