Готові списки джерел за темами / Certified Numerical Algorithms

Добірка наукової літератури з теми "Certified Numerical Algorithms"

Автор: Grafiati

Опубліковано: 8 червня 2024

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Статті в журналах з теми "Certified Numerical Algorithms":

Bouazizi, Faïçal. "Algebraic certification of numerical algorithms computing Lagrange resolvents." Journal of Algebra and Its Applications 17, no. 01 (January 2018): 1850007. http://dx.doi.org/10.1142/s021949881850007x.

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Segonne, Charlotte, and Pierre Duthon. "Qualification of the PAVIN Fog and Rain Platform and Its Digital Twin for the Evaluation of a Pedestrian Detector in Fog." Journal of Imaging 9, no. 10 (October 3, 2023): 211. http://dx.doi.org/10.3390/jimaging9100211.

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Vehicles featuring partially automated driving can now be certified within a guaranteed operational design domain. The verification in all kinds of scenarios, including fog, cannot be carried out in real conditions (risks or low occurrence). Simulation tools for adverse weather conditions (e.g., physical, numerical) must be implemented and validated. The aim of this study is, therefore, to verify what criteria need to be met to obtain sufficient data to test AI-based pedestrian detection algorithms. It presents both analyses on real and numerically simulated data. A novel method for the test environment evaluation, based on a reference detection algorithm, was set up. The following parameters are taken into account in this study: weather conditions, pedestrian variety, the distance of pedestrians to the camera, fog uncertainty, the number of frames, and artificial fog vs. numerically simulated fog. Across all examined elements, the disparity between results derived from real and simulated data is less than 10%. The results obtained provide a basis for validating and improving standards dedicated to the testing and approval of autonomous vehicles.

Mykhailov, O. V. "Results of Comparative Evaluation of Algorithms for Calculating Scaling Factors of Difficult-To-Measure Nuclides in CHNPP Wastes at 241Am Example." Nuclear Power and the Environment 21, no. 2 (2021): 61–70. http://dx.doi.org/10.31717/2311-8253.21.2.6.

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The criteria for radwaste acceptance valid in the Exclusion Zone of SSE “Chornobyl NPP” require that each batch (package) of solid radioactive waste (SRW) sent for burial be certified. For the radionuclides that are difficult to measure (DTM) with using standard control systems directly in a package, the IAEA recommends using the Scaling Factors (SF). In the course of special studies to determine their quantitative values, some difficulties were encountered when analyzing laboratory data on the DTM nuclide in SRW, which largely consisted of so-called nondetectable (ND) results declared in the reports as <MDA (less than the minimum detectable activity). The work was aimed to evaluate the known algorithms for SF determination used in the world practice of radwaste management, in terms of acceptability of their application to laboratory data sampling with different proportions of ND results (<MDA) on the example of 241Am content in ChNPP historical waste. Three data sampling were formed with the share of ND results equaling to 18, 42 and 55 percent. This work addresses several methods for SF calculation, which are used in radwaste management systems of the countries with developed nuclear fuel cycle. Among the selected algorithms for data process testing, the most powerful one of methods for ND results censoring is included — the method of maximum likelihood estimation (MLE), which allows by restoring the normal law of distribution of random data to most accurately adjust the value of mean contaminant content according to the probability of appearance of each of measurement results, with taking into account the added ND results after their censoring by a numerical value multiple of MDA. The possibilities of selected algorithms, from the viewpoint of accuracy of statistical indicators’ reproduction in the initial arrays of experimental data sampling with SF application, were investigated on “problematic” data sampling related to 241Am content in ChNPP historical waste. The studied algorithms are ranked according to the quantitative scale of acceptability (reliability) assessment for each of them for the use in radwaste management system of ChNPP for certification of DTM activity contained in the SRW packages. The data obtained allowed drawing conclusions on the most acceptable algorithms that can be recommended for SF calculation, depending on the content of experimental data collected after laboratory control. The influence of data censoring on the accuracy of reproduction of the original spectrum of experimental data for different algorithms is estimated. The validity of use of Mean Activity Method recommended by the IAEA for data sampling, which contains a significant proportion of ND results, was confirmed.

Giacomini, Matteo, Olivier Pantz, and Karim Trabelsi. "Certified Descent Algorithm for shape optimization driven by fully-computable a posteriori error estimators." ESAIM: Control, Optimisation and Calculus of Variations 23, no. 3 (April 28, 2017): 977–1001. http://dx.doi.org/10.1051/cocv/2016021.

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In this paper we introduce a novel certified shape optimization strategy – named Certified Descent Algorithm (CDA) – to account for the numerical error introduced by the Finite Element approximation of the shape gradient. We present a goal-oriented procedure to derive a certified upper bound of the error in the shape gradient and we construct a fully-computable, constant-free a posteriori error estimator inspired by the complementary energy principle. The resulting CDA is able to identify a genuine descent direction at each iteration and features a reliable stopping criterion. After validating the error estimator, some numerical simulations of the resulting certified shape optimization strategy are presented for the well-known inverse identification problem of Electrical Impedance Tomography.

Imbach, Rémi, Guillaume Moroz, and Marc Pouget. "A certified numerical algorithm for the topology of resultant and discriminant curves." Journal of Symbolic Computation 80 (May 2017): 285–306. http://dx.doi.org/10.1016/j.jsc.2016.03.011.

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Horai, Mio, Hideo Kobayashi, and Takashi G. Nitta. "A Linearized Relaxing Algorithm for the Specific Nonlinear Optimization Problem." Abstract and Applied Analysis 2016 (2016): 1–8. http://dx.doi.org/10.1155/2016/1304954.

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We propose a new method for the specific nonlinear and nonconvex global optimization problem by using a linear relaxation technique. To simplify the specific nonlinear and nonconvex optimization problem, we transform the problem to the lower linear relaxation form, and we solve the linear relaxation optimization problem by the Branch and Bound Algorithm. Under some reasonable assumptions, the global convergence of the algorithm is certified for the problem. Numerical results show that this method is more efficient than the previous methods.

Krait, George, Sylvain Lazard, Guillaume Moroz, and Marc Pouget. "Certified numerical algorithm for isolating the singularities of the plane projection of generic smooth space curves." Journal of Computational and Applied Mathematics 394 (October 2021): 113553. http://dx.doi.org/10.1016/j.cam.2021.113553.

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Arkhipova, O. V., N. N. Dolgikh, S. Yu Dolinger, V. Z. Kovalev, and D. S. Osipov. "Wavelet transform algorithm of daily load graphs for choosing parameters of hybrid energy storage." Omsk Scientific Bulletin, no. 174 (2020): 57–62. http://dx.doi.org/10.25206/1813-8225-2020-174-57-62.

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The paper presents an algorithm for frequency decomposition of daily load graphs based on a discrete wavelet transform. This algorithm makes it possible to choose the optimal type of wavelet function, optimal level and wavelet decomposition tree. The inverse wavelet transform (recovery) along a single branch of the approximating coefficient allows obtaining the lowfrequency component of the power graph for selecting the optimal mode of the hybrid energy storage battery. The detailing branch of the wavelet coefficients determines the operating mode of the supercapacitor. A numerical experiment is built on the basis of data obtained using certified equipment

Tran, Gia, Ricardo Santos, Hiroaki Ogawa, Makoto Nakamura, Kei Sakaguchi, and Andreas Kassler. "Context-Based Dynamic Meshed Backhaul Construction for 5G Heterogeneous Networks." Journal of Sensor and Actuator Networks 7, no. 4 (October 2, 2018): 43. http://dx.doi.org/10.3390/jsan7040043.

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Five-G heterogeneous network overlaid by millimeter-wave (mmWave) access employs mmWave meshed backhauling as a promising cost-efficient backhaul architecture. Due to the nature of mobile traffic distribution in practice which is both time-variant and spatially non-uniform, dynamic construction of mmWave meshed backhaul is a prerequisite to support the varying traffic distribution. Focusing on such scenario of outdoor dynamic crowd (ODC), this paper proposes a novel method to control mmWave meshed backhaul for efficient operation of mmWave overlay 5G HetNet through Software-Defined Network (SDN) technology. Our algorithm is featured by two functionalities, i.e., backhauling route multiplexing for overloaded mmWave small cell base stations (SC-BSs) and mmWave SC-BSs’ ON/OFF status switching for underloaded spot. In this paper, the effectiveness of the proposed meshed network is confirmed by both numerical analyses and experimental results. Simulations are conducted over a practical user distribution modeled from measured data in realistic environments. Numerical results show that the proposed algorithm can cope with the locally intensive traffic and reduce energy consumption. Furthermore, a WiGig (Wireless Gigabit Alliance certified) device based testbed is developed for Proof-of-Concept (PoC) and preliminary measurement results confirm the proposed dynamic formation of the meshed network’s efficiency.

Ma, Ceyi, Yinghong Wen, and Jinbao Zhang. "A Fast, Hybrid, Time-Domain Discontinuous Galerkin-Physical Optics Method for Composite Electromagnetic Scattering Analysis." Applied Sciences 11, no. 6 (March 17, 2021): 2694. http://dx.doi.org/10.3390/app11062694.

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To accelerate the solution of transient electromagnetic scattering from composite scatters, a novel hybrid discontinuous Galerkin time domain (DGTD) and time-domain physical optics (TDPO) method is proposed. The DGTD method is used to solve the accurate scattering field of the multi-scale objects region, and a hybrid explicit-implicit time integration method is also used to improve the efficiency of multi-scale problems in the time domain. Meanwhile, the TDPO method is used to accelerate the speed of surface current integration in an electrically large region. In addition, the DGTDPO method considers the mutual coupling between two regions, and effectively reduces the number of numerical calculations for the other space of the composite target, thereby significantly reducing the computer memory consumption. Numerical results certified the high efficiency and accuracy of the hybrid DGTDPO. According to the results, in comparison with the DGTD algorithm in the entire computational domain, the DGTDPO method can reduce computing time and memory by 90% and 70% respectively. Meanwhile, the normalized root mean square deviation (NRMSD) of the time-domain, high-frequency approximation method is over 0.2, and that of the DGTDPO method is only 0.0971. That is, compared with the approximation methods, the hybrid method improves the accuracy by more than 64%.

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Дисертації з теми "Certified Numerical Algorithms":

Krait, George. "Isolating the Singularities of the Plane Projection of Generic Space Curves and Applications in Robotics." Electronic Thesis or Diss., Université de Lorraine, 2021. http://www.theses.fr/2021LORR0092.

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L’isolation des points singuliers d'une courbe plane est la première étape vers le calcul de sa topologie. Pour cela, les méthodes numériques sont efficaces mais non certifiées en général. Nous sommes intéressés par le développement d'algorithmes numériques certifiés pour isoler les singularités. Pour ce faire, nous limitons notre attention au cas particulier des courbes planes qui sont des projections de courbes lisses en dimensions supérieures. Ce type de courbes apparaît naturellement dans les applications robotiques et la visualisation scientifique. Dans ce cadre, nous montrons que les singularités peuvent être encodées par un système carré et régulier dont les solutions peuvent être isolées avec des méthodes numériques certifiées. Notre analyse est conditionnée par des hypothèses que nous démontrons comme étant génériques en utilisant la théorie de la transversalité ; nous fournissons également un semi-algorithme pour vérifier leur validité. Enfin, nous présentons des expériences de visualisation et de robotique, dont certaines ne sont pas accessibles par d'autres méthodes, et discutons de l'efficacité de notre méthode
Isolating the singularities of a plane curve is the first step towards computing its topology. For this, numerical methods are efficient but not certified in general. We are interested in developing certified numerical algorithms for isolating the singularities. In order to do so, we restrict our attention to the special case of plane curves that are projections of smooth curves in higher dimensions. This type of curves appears naturally in robotics applications and scientific visualization. In this setting, we show that the singularities can be encoded by a regular square system whose solutions can be isolated with certified numerical methods. Our analysis is conditioned by assumptions that we prove to be generic using transversality theory. We also provide a semi-algorithm to check their validity. Finally, we present experiments in visualization and robotics, some of which are not reachable by other methods, and discuss the efficiency of our method

Giacomini, Matteo. "Quantitative a posteriori error estimators in Finite Element-based shape optimization." Thesis, Université Paris-Saclay (ComUE), 2016. http://www.theses.fr/2016SACLX070/document.

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Les méthodes d’optimisation de forme basées sur le gradient reposent sur le calcul de la dérivée de forme. Dans beaucoup d’applications, la fonctionnelle coût dépend de la solution d’une EDP. Il s’en suit qu’elle ne peut être résolue exactement et que seule une approximation de celle-ci peut être calculée, par exemple par la méthode des éléments finis. Il en est de même pour la dérivée de forme. Ainsi, les méthodes de gradient en optimisation de forme - basées sur des approximations du gradient - ne garantissent pas a priori que la direction calculée à chaque itération soit effectivement une direction de descente pour la fonctionnelle coût. Cette thèse est consacrée à la construction d’une procédure de certification de la direction de descente dans des algorithmes de gradient en optimisation de forme grâce à des estimations a posteriori de l’erreur introduite par l’approximation de la dérivée de forme par la méthode des éléments finis. On présente une procédure pour estimer l’erreur dans une Quantité d’Intérêt et on obtient une borne supérieure certifiée et explicitement calculable. L’Algorithme de Descente Certifiée (CDA) pour l’optimisation de forme identifie une véritable direction de descente à chaque itération et permet d’établir un critère d’arrêt fiable basé sur la norme de la dérivée de forme. Deux applications principales sont abordées dans la thèse. Premièrement, on considère le problème scalaire d’identification de forme en tomographie d’impédance électrique et on étudie différentes estimations d’erreur. Une première approche est basée sur le principe de l’énergie complémentaire et nécessite la résolution de problèmes globaux additionnels. Afin de réduire le coût de calcul de la procédure de certification, une estimation qui dépend seulement de quantités locales est dérivée par la reconstruction des flux équilibrés. Après avoir validé les estimations de l’erreur pour un cas bidimensionnel, des résultats numériques sont présentés pour tester les méthodes discutées. Une deuxième application est centrée sur le problème vectoriel de la conception optimale des structures élastiques. Dans ce cadre figure, on calcule l’expression volumique de la dérivée de forme de la compliance à partir de la formulation primale en déplacements et de la formulation duale mixte pour l’équation de l’élasticité linéaire. Quelques résultats numériques préliminaires pour la minimisation de la compliance sous une contrainte de volume en 2D sont obtenus à l’aide de l’Algorithme de Variation de Frontière et une estimation a posteriori de l’erreur de la dérivée de forme basée sur le principe de l’énergie complémentaire est calculée
Gradient-based shape optimization strategies rely on the computation of the so-called shape gradient. In many applications, the objective functional depends both on the shape of the domain and on the solution of a PDE which can only be solved approximately (e.g. via the Finite Element Method). Hence, the direction computed using the discretized shape gradient may not be a genuine descent direction for the objective functional. This Ph.D. thesis is devoted to the construction of a certification procedure to validate the descent direction in gradient-based shape optimization methods using a posteriori estimators of the error due to the Finite Element approximation of the shape gradient.By means of a goal-oriented procedure, we derive a fully computable certified upper bound of the aforementioned error. The resulting Certified Descent Algorithm (CDA) for shape optimization is able to identify a genuine descent direction at each iteration and features a reliable stopping criterion basedon the norm of the shape gradient.Two main applications are tackled in the thesis. First, we consider the scalar inverse identification problem of Electrical Impedance Tomography and we investigate several a posteriori estimators. A first procedure is inspired by the complementary energy principle and involves the solution of additionalglobal problems. In order to reduce the computational cost of the certification step, an estimator which depends solely on local quantities is derived via an equilibrated fluxes approach. The estimators are validated for a two-dimensional case and some numerical simulations are presented to test the discussed methods. A second application focuses on the vectorial problem of optimal design of elastic structures. Within this framework, we derive the volumetric expression of the shape gradient of the compliance using both H 1 -based and dual mixed variational formulations of the linear elasticity equation. Some preliminary numerical tests are performed to minimize the compliance under a volume constraint in 2D using the Boundary Variation Algorithm and an a posteriori estimator of the error in the shape gradient is obtained via the complementary energy principle

Частини книг з теми "Certified Numerical Algorithms":

Peruffo, Andrea, Daniele Ahmed, and Alessandro Abate. "Automated and Formal Synthesis of Neural Barrier Certificates for Dynamical Models." In Tools and Algorithms for the Construction and Analysis of Systems, 370–88. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-72016-2_20.

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AbstractWe introduce an automated, formal, counterexample-based approach to synthesise Barrier Certificates (BC) for the safety verification of continuous and hybrid dynamical models. The approach is underpinned by an inductive framework: this is structured as a sequential loop between a learner, which manipulates a candidate BC structured as a neural network, and a sound verifier, which either certifies the candidate’s validity or generates counter-examples to further guide the learner. We compare the approach against state-of-the-art techniques, over polynomial and non-polynomial dynamical models: the outcomes show that we can synthesise sound BCs up to two orders of magnitude faster, with in particular a stark speedup on the verification engine (up to three orders less), whilst needing a far smaller data set (up to three orders less) for the learning part. Beyond improvements over the state of the art, we further challenge the new approach on a hybrid dynamical model and on larger-dimensional models, and showcase the numerical robustness of our algorithms and codebase.

Тези доповідей конференцій з теми "Certified Numerical Algorithms":

Arusoaie, Andrei, David Nowak, Vlad Rusu, and Dorel Lucanu. "A Certified Procedure for RL Verification." In 2017 19th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing (SYNASC). IEEE, 2017. http://dx.doi.org/10.1109/synasc.2017.00031.

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Martin-Dorel, Erik, Laurence Rideau, Laurent Thery, Micaela Mayero, and Ioana Pasca. "Certified, Efficient and Sharp Univariate Taylor Models in COQ." In 2013 15th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing (SYNASC). IEEE, 2013. http://dx.doi.org/10.1109/synasc.2013.33.

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Mehrabi, Mehdi, Tuhid Pashaee, Mohsen Sharifpur, and Josua P. Meyer. "Application of Genetic Algorithm-Polynomial Neural Network for Modelling Heat Transfer and Fluid Flow Characteristics of a Double-Pipe Heat Exchanger." In ASME 2013 Heat Transfer Summer Conference collocated with the ASME 2013 7th International Conference on Energy Sustainability and the ASME 2013 11th International Conference on Fuel Cell Science, Engineering and Technology. American Society of Mechanical Engineers, 2013. http://dx.doi.org/10.1115/ht2013-17194.

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In this paper a genetic algorithm-polynomial neural network approach is used in order to model the effect of important parameters on heat transfer as well as fluid flow characteristics for a double-pipe helical heat exchanger by using numerical-certified results. In this way, overall heat transfer coefficient (Uo), inner and annular pressure drop (ΔPin, ΔPan) are modeled with respect to the variation of inner and annular dean number, inner and annular Prandtl number, and pitch of coil which are defined as input (design) variables. The numerical-certified data was randomly divided into test and train sections which the former is used for benchmark. The GA-PNN structure was instructed by 75 percent of the numerical-validated data. 25 percent of the primary data which had been considered for testing procedure were entered into GA-PNN proposed models and results were compared by statistical criteria.

Graillat, Stef, and Philippe Trébuchet. "A new algorithm for computing certified numerical approximations of the roots of a zero-dimensional system." In the 2009 international symposium. New York, New York, USA: ACM Press, 2009. http://dx.doi.org/10.1145/1576702.1576727.

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Chen, Jingjing, Yadong Wu, Zhonglin Wang, and Anjenq Wang. "Nacelle: Air Intake Aerodynamic Design and Inlet Compatibility." In ASME 2014 Gas Turbine India Conference. American Society of Mechanical Engineers, 2014. http://dx.doi.org/10.1115/gtindia2014-8182.

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One of the most challenging operating conditions to be certified for FAR33 & FAR25 requirements is ground crosswind condition. When “Engine” is operated using the designed inlet and nacelle, within the flight envelope, could accommodate inlet separation/distortion resulted from crosswind and high angle-of-attack operating conditions. Inlet flow separation and distortion could trigger fan or core stall, as well as induce high fan and/or engine vibrations. The air induction system or inlet of the engine is designed to provide velocity and pressure distributions with minimum distortion and maximum pressure recovery to the propulsion system. Engine-inlet-airframe compatibility is one of the major tasks required to be evaluated in detail during the engine developing phase. This research is a parametric study of using CFD to evaluate operational characteristics of the air induction system. Comparisons of various inlet designs are made and characterized into three categories, i.e., i) Inlet flow recovery, ii) Inlet flow distortion, iii) Inlet Mach distribution. The objective is to assess the impact of air induction design of turbofan upon inlet compatibility. The current research work includes four parts, i.e., i) A geometry modeling process of nacelle, inlet, wing and fuselage, ii) A meshes generator ICEM, iii) The ANSYS CFX CFD software which could achieves numerical simulation and post-processing, iv) The Matlab platform with the function of coupling all considerations listed above for inlet compatibility optimization, based on genetic algorithm and Kriging agent model. The research introduces the Kriging model and weighting coefficient to optimize total pressure loss coefficient and static pressure recovery coefficient, with the external nacelle flow ignored. Bezier equation was used to fit the optimized curves obtained by changing two control points at the inter surface of nacelle. The wing-mounted model coupled with the nacelles, fuselage and wings was then built to make the assessment of inlet compatibility of air intake system relative to the isolate model. Comparison of aerodynamic performance was then made between the original and optimal nacelle, to show correlation between inlet compatibility and air intake profile.