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IMPROVED LAGUERRE SPECTRAL METHODS WITH LESS ROUND-OFF ERRORS AND BETTER STABILITY

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arXiv 2022年

作者： Huang, Shenghe Yu, Haijun School of Mathematical Sciences University of Chinese Academy of Sciences Beijing100049 China NCMIS & LSEC Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Beijing100190 China

Laguerre polynomials are orthogonal polynomials defined on positive half line with respect to weight e−x. They have wide applications in scientific and engineering computations. However, the exponential growth of Laguerre polynomials of high degree makes it hard to apply them to complicated systems that need to use large numbers of Laguerre bases. In this paper, we introduce modified three-term recurrence formula to reduce the round-off error and to avoid overflow and underflow issues in generating generalized Laguerre polynomials and Laguerre functions. We apply the improved Laguerre methods to solve an elliptic equation defined on the half line. More than one thousand Laguerre bases are used in this application and meanwhile accuracy close to machine precision is achieved. The optimal scaling factor of Laguerre methods are studied and found to be independent of number of quadrature points in two cases that Laguerre methods have better convergence speeds than mapped Jacobi *** Codes 65N35, 65D32, 65G50, 33F05 © 2022, CC BY-NC-ND.

关键词： Polynomials

Fixed-Wing UAV Path Planning and Collision Avoidance using Nonlinear Model Predictive Control and Sensor-based Cloud Detection

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Fixed-Wing UAV Path Planning and Collision Avoidance using N...

Conference on Digital Avionics Systems (DASC)

作者： Jeremy Bertoncini Adrian Dudek Martin Russ Matthias Gerdts Peter Stütz Department of Aerospace Engineering Institute of Applied Mathematics and Scientific Computing University of the Bundeswehr Munich Neubiberg Germany Department of Aerospace Engineering Institute of Flight Systems University of the Bundeswehr Munich Neubiberg Germany

This article proposes a Nonlinear Model Predictive Control (NMPC) method for path planning and obstacle avoidance of a fixed-wing Unmanned Aerial Vehicle (UAV) coupled to an online monocular electro-optical cloud detection. A Nonlinear Programming (NLP) problem is solved at each discrete-time iteration of the NMPC using an inhouse Sequential Quadratic Programming (SQP) method. The proposed NMPC method enables real-time path planning while avoiding clouds, whose distance and extent are determined using electro-optical sensors and computer vision methods. Cloud detection and avoidance is intended to allow UAVs to operate under visual flight rules (VFR) to reduce the risk of collision with other air traffic. The mission task here consists of airborne reconnaissance of targets that can be defined by the user and updated online. The user interacts with the simulation by setting reconnaissance targets for the UAV at anytime during the flight.

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Uncertainty Quantification of Fiber Orientation and Epicardial Activation 50

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Uncertainty Quantification of Fiber Orientation and Epicardi...

50th computing in Cardiology, CinC 2023

作者： Rupp, Lindsay C Busatto, Anna Bergquist, Jake A Gillette, Karli Narayan, Akil Plank, Gernot MacLeod, Rob S Scientific Computing and Imaging Institute University of Utah SLCUT United States Nora Eccles Cardiovascular Research and Training Institute University of Utah SLCUT United States University of Utah Department of Biomedical Engineering SLCUT United States Institute of Biophysics Medical University of Graz Graz Austria University of Utah Department of Mathematics SLCUT United States

ISBN: (纸本)9798350382525

Predictive models and simulations of cardiac function require accurate representations of anatomy, often to the scale of local myocardial fiber structure. However, acquiring this information in a patient-specific manner is challenging. Moreover, the impact of physiological variability in fiber orientation on simulations of cardiac activation is poorly understood. To explore these effects, we implemented bi-ventricular activation simulations using rule-based fiber algorithms and robust uncertainty quantification techniques to generate detailed maps of model variability. Specifically, we utilized polynomial chaos expansion, enabling efficient exploration with reduced computational demand through an emulator function approximating the underlying forward model. Our study focused on examining the epicardial activation sequences of the heart in response to six stimuli locations and five metrics of activation. Our findings revealed that physiological variability in fiber orientation does not significantly affect the location of activation features, but it does impact the overall spread of activation. We observed low variability near the earliest activation sites, but high variability across the rest of the epicardial surface. We conclude that the level of accuracy of myocardial fiber orientation required for simulation depends on the specific goals of the model and the related research or clinical goals. © 2023 CinC.

关键词： Chemical activation

Frequency-domain criterion on the stabilizability for infinite-dimensional linear control systems

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arXiv 2023年

作者： Kunisch, Karl Wang, Gengsheng Yu, Huaiqiang Johann Radon Institute for Computational and Applied Mathematics ÖAW Altenbergerstrasse 69 Linz4040 Austria Institute of Mathematics and Scientific Computing University of Graz Heinrichstrasse 36 Graz8010 Austria Center for Applied Mathematics Tianjin University Tianjin300072 China School of Mathematics Tianjin University Tianjin300354 China

A quantitative frequency-domain condition related to the exponential stabilizability for infinite-dimensional linear control systems is presented. It is proven that this condition is necessary and sufficient for the stabilizability of special systems, while it is a necessary condition for the stabilizability in general. Applications are *** Codes 93D15, 93C25, 93C80, 93D20 © 2023, CC BY-NC-SA.

关键词： Linear control systems

New semidefinite relaxations for a class of complex quadratic programming problems

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arXiv 2023年

作者： Xu, Yingzhe Lu, Cheng Deng, Zhibin Liu, Ya-Feng School of Economics and Management North China Electric Power University Beijing102206 China School of Economics and Management University of Chinese Academy of Sciences MOE Social Science Laboratory of Digital Economic Forecasts and Policy Simulation at UCAS Beijing100190 China State Key Laboratory of Scientific and Engineering Computing Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China

In this paper, we propose some new semidefinite relaxations for a class of nonconvex complex quadratic programming problems, which widely appear in the areas of signal processing and power system. By deriving new valid constraints to the matrix variables in the lifted space, we derive some enhanced semidefinite relaxations of the complex quadratic programming problems. Then, we compare the proposed semidefinite relaxations with existing ones, and show that the newly proposed semidefinite relaxations could be strictly tighter than the previous ones. Moreover, the proposed semidefinite relaxations can be applied to more general cases of complex quadratic programming problems, whereas the previous ones are only designed for special cases. Numerical results indicate that the proposed semidefinite relaxations © 2023, CC BY.

关键词： Approximation algorithms

Helmholtz Decomposition Based Windowed Green Function Methods for Elastic Scattering Problems on a Half-Space

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SSRN

SSRN 2023年

作者： Yin, Tao Zhang, Lu Zheng, Weiying Zhu, Xiaopeng LSEC Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China School of Mathematical Sciences Zhejiang University Hangzhou310027 China School of Mathematical Science University of Chinese Academy of Sciences Beijing100049 China

This paper proposes a new Helmholtz decomposition based windowed Green function (HD-WGF) method for solving the time-harmonic elastic scattering problems on a half-space with Dirichlet boundary conditions in both 2D and 3D. The Helmholtz decomposition is applied to separate the pressure and shear waves, which satisfy the Helmholtz and Helmholtz/Maxwell equations, respectively, and the corresponding boundary integral equations of type $(\mathbb{I}+\mathbb{T})\bs\phi=\bs f$, that couple these two waves on the unbounded surface, are derived based on the free-space fundamental solution of Helmholtz equation. This approach avoids the treatment of the complex elastic displacement tensor and traction operator that involved in the classical integral equation method for elastic problems. Then a smooth ``slow-rise'' windowing function is introduced to truncate the boundary integral equations and a ``correction'' strategy is proposed to ensure the uniformly fast convergence for all incident angles of plane incidence. Numerical experiments for both two and three dimensional problems are presented to demonstrate the accuracy and efficiency of the proposed method. © 2023, The Authors. All rights reserved.

关键词： Boundary integral equations

A Novel Family of Q1−Finite Volume Element Schemes on Quadrilateral Meshes

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SSRN

SSRN 2024年

作者： Zhou, Yanhui Su, Shuai School of Mathematics and Systems Science Guangdong Polytechnic Normal University Guangzhou510665 China Beijing Institute for Scientific and Engineering Computing Faculty of Science Beijing University of Technology Beijing100124 China

A novel family of isoparametric bilinear finite volume element schemes are constructed and analyzed to solve the anisotropic diffusion problems on general convex quadrilateral meshes. These new schemes are obtained by employing a special quadrature rule to approximate the line integrals in classical Q1−finite volume element method. The new quadrature rule is a linear combination of trapezoidal and midpoint rules, and the weights depend on a parameter ωK. The novelty of this work is that, for any fully anisotropic diffusion tensor, we provide some specific ωK to ensure the coercivity result of the proposed schemes on arbitrary parallelogram, quasi-parallelogram, trapezoidal and some general convex quadrilateral meshes. More interesting is that, the parameter ωK can only involves the anisotropic diffusion tensor and the geometry of quadrilateral cell. An optimal H1 error estimate is also proved on quasi-parallelogram meshes. Finally, the theoretical findings are validated by several numerical examples. © 2024, The Authors. All rights reserved.

关键词： Coercive force

Optimization of Crop Yields in Sustainable Agriculture: Application of Big Data Analytics and Artificial Intelligence

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Remote Sensing in Earth Systems Sciences 2025年第2期8卷 375-386页

作者： Nimma, Divya Dhanke, Jyoti A. Murthy, G.S.N. Khandekar, Sachin Dadu Hymavathi, J. Jangir, Pradeep Singh, Mahesh Department of Computational Science University of Southern Mississippi Hattiesburg 39406 MS United States Department of Engineering Science (Mathematics) Bharati Vidyapeeth’s College of Engineering Lavale Maharashtra Pune India Department of CSE Aditya University Surampalem India Department of Civil Engineering Sinhgad College of Engineering Maharashtra Pune India Department of CSE Koneru Lakshmaiah Education Foundation Andhra Pradesh Vaddeswaram India Department of Biosciences Saveetha School of Engineering Saveetha Institute of Medical and Technical Sciences Chennai India Hourani Center for Applied Scientific Research Al-Ahliyya Amman University Amman 19328 Jordan Department of Robotics and Automation Symbiosis Institute of Technology Pune Campus Symbiosis International (Deemed University) Pune India

Making informed economic decisions based on agricultural data is challenging without proper crop management. Data has become the single most important part of modern farming, and its rapid evolution is a major contributor to the rise of “smart farming.” Using sensors to gather objective data with the end aim of increasing productivity and sustainability has several advantages. Information that might boost productivity while decreasing resource waste and pollution levels is essential for managed farms. The cornerstone of future sustainable farming will be data-driven agriculture using robotic solutions based on AI-based techniques. This paper examines the current state of advanced farm management systems, discussing topics like data acquisition in crop fields and variable rate applications, to assist farmers in saving money, protecting the environment, and transforming food production so that it can sustainably keep up with the expected increase in population. The advent of machine learning, big data technologies, and high-performance computers has opened up new avenues for data-intensive research in the interdisciplinary subject of agro technology. These avenues of exploration have been aided by the development of more capable computers. A comprehensive literature review on the issue of the applications of machine learning in agricultural manufacturing is provided in this research. Machine learning has shown its utility in agriculture via two applications: filtering and categorizing products. The use of machine learning on sensor data is transforming conventional farm management systems into AI-enabled programs. These services provide farmers instantaneous, complete access to ideas and insights that may guide their decisions. © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2025.

关键词： Artificial intelligence Big data analytics Optimize crop yields Sustainable agriculture

IB-UQ: Information bottleneck based uncertainty quantification for neural function regression and neural operator learning

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arXiv 2023年

作者： Guo, Ling Wu, Hao Zhou, Wenwen Wang, Yan Zhou, Tao Department of Mathematics Shanghai Normal University Shanghai China School of Mathematical Sciences Institute of Natural Sciences MOE-LSC Shanghai Jiaotong University Shanghai China School of Mathematical Sciences Tongji University Shanghai China LSEC Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing China

We propose a novel framework for uncertainty quantification via information bottleneck (IB-UQ) for scientific machine learning tasks, including deep neural network (DNN) regression and neural operator learning (DeepONet). Specifically, we incorporate the bottleneck by a confidence-aware encoder, which encodes inputs into latent representations according to the confidence of the input data belonging to the region where training data is located, and utilize a Gaussian decoder to predict means and variances of outputs conditional on representation variables. Furthermore, we propose a data augmentation based information bottleneck objective which can enhance the quantification quality of the extrapolation uncertainty, and the encoder and decoder can be both trained by minimizing a tractable variational bound of the objective. In comparison to uncertainty quantification (UQ) methods for scientific learning tasks that rely on Bayesian neural networks with Hamiltonian Monte Carlo posterior estimators, the model we propose is computationally efficient, particularly when dealing with large-scale data sets. The effectiveness of the IB-UQ model has been demonstrated through several representative examples, such as regression for discontinuous functions, real-world data set regression, learning nonlinear operators for partial differential equations, and a large-scale climate model. The experimental results indicate that the IB-UQ model can handle noisy data, generate robust predictions, and provide confident uncertainty evaluation for out-of-distribution data. © 2023, CC BY-NC-ND.

关键词： Monte Carlo methods