136 research outputs found

    Data-driven deep-learning methods for the accelerated simulation of Eulerian fluid dynamics

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    Deep-learning (DL) methods for the fast inference of the temporal evolution of fluid-dynamics systems, based on the previous recognition of features underlying large sets of fluid-dynamics data, have been studied. Specifically, models based on convolution neural networks (CNNs) and graph neural networks (GNNs) were proposed and discussed. A U-Net, a popular fully-convolutional architecture, was trained to infer wave dynamics on liquid surfaces surrounded by walls, given as input the system state at previous time-points. A term for penalising the error of the spatial derivatives was added to the loss function, which resulted in a suppression of spurious oscillations and a more accurate location and length of the predicted wavefronts. This model proved to accurately generalise to complex wall geometries not seen during training. As opposed to the image data-structures processed by CNNs, graphs offer higher freedom on how data is organised and processed. This motivated the use of graphs to represent the state of fluid-dynamic systems discretised by unstructured sets of nodes, and GNNs to process such graphs. Graphs have enabled more accurate representations of curvilinear geometries and higher resolution placement exclusively in areas where physics is more challenging to resolve. Two novel GNN architectures were designed for fluid-dynamics inference: the MuS-GNN, a multi-scale GNN, and the REMuS-GNN, a rotation-equivariant multi-scale GNN. Both architectures work by repeatedly passing messages from each node to its nearest nodes in the graph. Additionally, lower-resolutions graphs, with a reduced number of nodes, are defined from the original graph, and messages are also passed from finer to coarser graphs and vice-versa. The low-resolution graphs allowed for efficiently capturing physics encompassing a range of lengthscales. Advection and fluid flow, modelled by the incompressible Navier-Stokes equations, were the two types of problems used to assess the proposed GNNs. Whereas a single-scale GNN was sufficient to achieve high generalisation accuracy in advection simulations, flow simulation highly benefited from an increasing number of low-resolution graphs. The generalisation and long-term accuracy of these simulations were further improved by the REMuS-GNN architecture, which processes the system state independently of the orientation of the coordinate system thanks to a rotation-invariant representation and carefully designed components. To the best of the author’s knowledge, the REMuS-GNN architecture was the first rotation-equivariant and multi-scale GNN. The simulations were accelerated between one (in a CPU) and three (in a GPU) orders of magnitude with respect to a CPU-based numerical solver. Additionally, the parallelisation of multi-scale GNNs resulted in a close-to-linear speedup with the number of CPU cores or GPUs.Open Acces

    Oriented trees and paths in digraphs

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    Which conditions ensure that a digraph contains all oriented paths of some given length, or even a all oriented trees of some given size, as a subgraph? One possible condition could be that the host digraph is a tournament of a certain order. In arbitrary digraphs and oriented graphs, conditions on the chromatic number, on the edge density, on the minimum outdegree and on the minimum semidegree have been proposed. In this survey, we review the known results, and highlight some open questions in the area

    Applications

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    Volume 3 describes how resource-aware machine learning methods and techniques are used to successfully solve real-world problems. The book provides numerous specific application examples: in health and medicine for risk modelling, diagnosis, and treatment selection for diseases in electronics, steel production and milling for quality control during manufacturing processes in traffic, logistics for smart cities and for mobile communications

    LIPIcs, Volume 274, ESA 2023, Complete Volume

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    LIPIcs, Volume 274, ESA 2023, Complete Volum

    LIPIcs, Volume 258, SoCG 2023, Complete Volume

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    LIPIcs, Volume 258, SoCG 2023, Complete Volum

    ATHENA Research Book, Volume 2

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    ATHENA European University is an association of nine higher education institutions with the mission of promoting excellence in research and innovation by enabling international cooperation. The acronym ATHENA stands for Association of Advanced Technologies in Higher Education. Partner institutions are from France, Germany, Greece, Italy, Lithuania, Portugal and Slovenia: University of Orléans, University of Siegen, Hellenic Mediterranean University, Niccolò Cusano University, Vilnius Gediminas Technical University, Polytechnic Institute of Porto and University of Maribor. In 2022, two institutions joined the alliance: the Maria Curie-Skłodowska University from Poland and the University of Vigo from Spain. Also in 2022, an institution from Austria joined the alliance as an associate member: Carinthia University of Applied Sciences. This research book presents a selection of the research activities of ATHENA University's partners. It contains an overview of the research activities of individual members, a selection of the most important bibliographic works of members, peer-reviewed student theses, a descriptive list of ATHENA lectures and reports from individual working sections of the ATHENA project. The ATHENA Research Book provides a platform that encourages collaborative and interdisciplinary research projects by advanced and early career researchers

    Collected Papers (Neutrosophics and other topics), Volume XIV

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    This fourteenth volume of Collected Papers is an eclectic tome of 87 papers in Neutrosophics and other fields, such as mathematics, fuzzy sets, intuitionistic fuzzy sets, picture fuzzy sets, information fusion, robotics, statistics, or extenics, comprising 936 pages, published between 2008-2022 in different scientific journals or currently in press, by the author alone or in collaboration with the following 99 co-authors (alphabetically ordered) from 26 countries: Ahmed B. Al-Nafee, Adesina Abdul Akeem Agboola, Akbar Rezaei, Shariful Alam, Marina Alonso, Fran Andujar, Toshinori Asai, Assia Bakali, Azmat Hussain, Daniela Baran, Bijan Davvaz, Bilal Hadjadji, Carlos Díaz Bohorquez, Robert N. Boyd, M. Caldas, Cenap Özel, Pankaj Chauhan, Victor Christianto, Salvador Coll, Shyamal Dalapati, Irfan Deli, Balasubramanian Elavarasan, Fahad Alsharari, Yonfei Feng, Daniela Gîfu, Rafael Rojas Gualdrón, Haipeng Wang, Hemant Kumar Gianey, Noel Batista Hernández, Abdel-Nasser Hussein, Ibrahim M. Hezam, Ilanthenral Kandasamy, W.B. Vasantha Kandasamy, Muthusamy Karthika, Nour Eldeen M. Khalifa, Madad Khan, Kifayat Ullah, Valeri Kroumov, Tapan Kumar Roy, Deepesh Kunwar, Le Thi Nhung, Pedro López, Mai Mohamed, Manh Van Vu, Miguel A. Quiroz-Martínez, Marcel Migdalovici, Kritika Mishra, Mohamed Abdel-Basset, Mohamed Talea, Mohammad Hamidi, Mohammed Alshumrani, Mohamed Loey, Muhammad Akram, Muhammad Shabir, Mumtaz Ali, Nassim Abbas, Munazza Naz, Ngan Thi Roan, Nguyen Xuan Thao, Rishwanth Mani Parimala, Ion Pătrașcu, Surapati Pramanik, Quek Shio Gai, Qiang Guo, Rajab Ali Borzooei, Nimitha Rajesh, Jesús Estupiñan Ricardo, Juan Miguel Martínez Rubio, Saeed Mirvakili, Arsham Borumand Saeid, Saeid Jafari, Said Broumi, Ahmed A. Salama, Nirmala Sawan, Gheorghe Săvoiu, Ganeshsree Selvachandran, Seok-Zun Song, Shahzaib Ashraf, Jayant Singh, Rajesh Singh, Son Hoang Le, Tahir Mahmood, Kenta Takaya, Mirela Teodorescu, Ramalingam Udhayakumar, Maikel Y. Leyva Vázquez, V. Venkateswara Rao, Luige Vlădăreanu, Victor Vlădăreanu, Gabriela Vlădeanu, Michael Voskoglou, Yaser Saber, Yong Deng, You He, Youcef Chibani, Young Bae Jun, Wadei F. Al-Omeri, Hongbo Wang, Zayen Azzouz Omar

    LIPIcs, Volume 244, ESA 2022, Complete Volume

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    LIPIcs, Volume 244, ESA 2022, Complete Volum

    Approximate Distance Oracles for Planar Graphs with Subpolynomial Error Dependency

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    Thorup [FOCS'01, JACM'04] and Klein [SODA'01] independently showed that there exists a (1+ϵ)(1+\epsilon)-approximate distance oracle for planar graphs with O(n(logn)ϵ1)O(n (\log n)\epsilon^{-1}) space and O(ϵ1)O(\epsilon^{-1}) query time. While the dependency on nn is nearly linear, the space-query product of their oracles depend quadratically on 1/ϵ1/\epsilon. Many follow-up results either improved the space \emph{or} the query time of the oracles while having the same, sometimes worst, dependency on 1/ϵ1/\epsilon. Kawarabayashi, Sommer, and Thorup [SODA'13] were the first to improve the dependency on 1/ϵ1/\epsilon from quadratic to nearly linear (at the cost of log(n)\log^*(n) factors). It is plausible to conjecture that the linear dependency on 1/ϵ1/\epsilon is optimal: for many known distance-related problems in planar graphs, it was proved that the dependency on 1/ϵ1/\epsilon is at least linear. In this work, we disprove this conjecture by reducing the dependency of the space-query product on 1/ϵ1/\epsilon from linear all the way down to \emph{subpolynomial} (1/ϵ)o(1)(1/\epsilon)^{o(1)}. More precisely, we construct an oracle with O(nlog(n)(ϵo(1)+logn))O(n\log(n)(\epsilon^{-o(1)} + \log^*n)) space and log2+o(1)(1/ϵ)\log^{2+o(1)}(1/\epsilon) query time. Our construction is the culmination of several different ideas developed over the past two decades.Comment: 34 pages, 10 figure
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