495 research outputs found
Advances and Applications of DSmT for Information Fusion. Collected Works, Volume 5
This ļ¬fth volume on Advances and Applications of DSmT for Information Fusion collects theoretical and applied contributions of researchers working in different ļ¬elds of applications and in mathematics, and is available in open-access. The collected contributions of this volume have either been published or presented after disseminating the fourth volume in 2015 in international conferences, seminars, workshops and journals, or they are new. The contributions of each part of this volume are chronologically ordered.
First Part of this book presents some theoretical advances on DSmT, dealing mainly with modiļ¬ed Proportional Conļ¬ict Redistribution Rules (PCR) of combination with degree of intersection, coarsening techniques, interval calculus for PCR thanks to set inversion via interval analysis (SIVIA), rough set classiļ¬ers, canonical decomposition of dichotomous belief functions, fast PCR fusion, fast inter-criteria analysis with PCR, and improved PCR5 and PCR6 rules preserving the (quasi-)neutrality of (quasi-)vacuous belief assignment in the fusion of sources of evidence with their Matlab codes.
Because more applications of DSmT have emerged in the past years since the apparition of the fourth book of DSmT in 2015, the second part of this volume is about selected applications of DSmT mainly in building change detection, object recognition, quality of data association in tracking, perception in robotics, risk assessment for torrent protection and multi-criteria decision-making, multi-modal image fusion, coarsening techniques, recommender system, levee characterization and assessment, human heading perception, trust assessment, robotics, biometrics, failure detection, GPS systems, inter-criteria analysis, group decision, human activity recognition, storm prediction, data association for autonomous vehicles, identiļ¬cation of maritime vessels, fusion of support vector machines (SVM), Silx-Furtif RUST code library for information fusion including PCR rules, and network for ship classiļ¬cation.
Finally, the third part presents interesting contributions related to belief functions in general published or presented along the years since 2015. These contributions are related with decision-making under uncertainty, belief approximations, probability transformations, new distances between belief functions, non-classical multi-criteria decision-making problems with belief functions, generalization of Bayes theorem, image processing, data association, entropy and cross-entropy measures, fuzzy evidence numbers, negator of belief mass, human activity recognition, information fusion for breast cancer therapy, imbalanced data classiļ¬cation, and hybrid techniques mixing deep learning with belief functions as well
Beam scanning by liquid-crystal biasing in a modified SIW structure
A fixed-frequency beam-scanning 1D antenna based on Liquid Crystals (LCs) is designed for application in 2D scanning with lateral alignment. The 2D array environment imposes full decoupling of adjacent 1D antennas, which often conflicts with the LC requirement of DC biasing: the proposed design accommodates both. The LC medium is placed inside a Substrate Integrated Waveguide (SIW) modified to work as a Groove Gap Waveguide, with radiating slots etched on the upper broad wall, that radiates as a Leaky-Wave Antenna (LWA). This allows effective application of the DC bias voltage needed for tuning the LCs. At the same time, the RF field remains laterally confined, enabling the possibility to lay several antennas in parallel and achieve 2D beam scanning. The design is validated by simulation employing the actual properties of a commercial LC medium
Data-driven deep-learning methods for the accelerated simulation of Eulerian fluid dynamics
Deep-learning (DL) methods for the fast inference of the temporal evolution of ļ¬uid-dynamics systems, based on the previous recognition of features underlying large sets of ļ¬uid-dynamics data, have been studied. Speciļ¬cally, 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 oļ¬er higher freedom on how data is organised and processed. This motivated the use of graphs to represent the state of ļ¬uid-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 ļ¬uid-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 deļ¬ned from the original graph,
and messages are also passed from ļ¬ner to coarser graphs and vice-versa. The low-resolution graphs allowed for eļ¬ciently capturing physics encompassing a range of lengthscales.
Advection and ļ¬uid ļ¬ow, 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 suļ¬cient to achieve high generalisation accuracy in advection simulations, ļ¬ow simulation highly beneļ¬ted 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 authorās knowledge, the REMuS-GNN architecture was the ļ¬rst 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
Easy-to-implement hp-adaptivity for non-elliptic goal-oriented problems
The FEM has become a foundational numerical technique in computational mechanics and civil engineering since its inception by Courant in 1943 Courant1943. Originating from the Ritz method and variational calculus, the FEM was primarily employed to derive solutions for vibrational systems. A distinctive strength of the FEM is its capability to represent mathematical models through the weak variational formulation of PDE, facilitating computational feasibility even in intricate geometries. However, the search for accuracy often imposes a significant computational task.
In the FEM, adaptive methods have emerged to balance the accuracy of solutions with computational costs. The -adaptive FEM designs more efficient meshes by reducing the mesh size locally while keeping the polynomial order of approximation fixed (usually ). An alternative approach to the -adaptive FEM is the -adaptive FEM, which locally enriches the polynomial space while keeping the mesh size constant. By dynamically adapting and , the -adaptive FEM achieves exponential convergence rates.
Adaptivity is crucial for obtaining accurate solutions. However, the traditional focus on global norms, such as or , might only sometimes serve the requirements of specific applications. In engineering, controlling errors in specific domains related to a particular QoI is often more critical than focusing on the overall solution. That motivated the development of GOA strategies.
In this dissertation, we develop automatic GO -adaptive algorithms tailored for non-elliptic problems. These algorithms shine in terms of robustness and simplicity in their implementation, attributes that make them especially suitable for industrial applications. A key advantage of our methodologies is that they do not require computing reference solutions on globally refined grids. Nevertheless, our approach is limited to anisotropic and isotropic refinements.
We conduct multiple tests to validate our algorithms. We probe the convergence behavior of our GO - and -adaptive algorithms using Helmholtz and convection-diffusion equations in one-dimensional scenarios. We test our GO -adaptive algorithms on Poisson, Helmholtz, and convection-diffusion equations in two dimensions. We use a Helmholtz-like scenario for three-dimensional cases to highlight the adaptability of our GO algorithms.
We also create efficient ways to build large databases ideal for training DNN using MAGO FEM. As a result, we efficiently generate large databases, possibly containing hundreds of thousands of synthetic datasets or measurements
Multiscale Modeling and Gaussian Process Regression for Applications in Composite Materials
An ongoing challenge in advanced materials design is the development of accurate multiscale models that consider uncertainty while establishing a link between knowledge or information about constituent materials to overall composite properties. Successful models can accurately predict composite properties, reducing the high financial and labor costs associated with experimental determination and accelerating material innovation. Whereas early pioneers in micromechanics developed simplistic theoretical models to map these relationships, modern advances in computer technology have enabled detailed simulators capable of accurately predicting complex and multiscale phenomena.
This work advances domain knowledge via two means: firstly, through the development of high-fidelity, physics-based finite element (FE) models of composite microstructures that incorporate uncertainty in predictions, and secondly, through the development of a novel inverse analysis framework that enables the discovery of unknown or obscure constituent properties using literature data and Gaussian process (GP) surrogate models trained on FE model predictions. This work presents a generalizable approach to modeling a diverse array of composite subtypes, from a simple particulate system to a complex commercial composite.
The inverse analysis framework was demonstrated for a thermoplastic composite reinforced by spherical fillers with unknown interphase properties. The framework leverages computer model simulations with easily obtainable macroscale elastic property measurements to infer interphase properties that are otherwise challenging to measure. The interphase modulus and thickness were determined for six different thermoplastic composites; four were reinforced by micron-scale particles and two with nano-scale particles.
An alginate fiber embedded with a helically symmetric arrangement of cellulose nanocrystals (CNCs) was investigated using multiscale FE analysis to quantify microstructural uncertainty and the subsequent effect on macroscopic behavior. The macroscale uniaxial tensile simulation revealed that the microstructure induces internal stresses sufficient to rotate or twist the fiber about its axis. The reduction in axial elastic modulus for increases in CNC spiral angle was quantified in a sensitivity analysis using a GP surrogate modeling approach.
A predictive model using GP regression was employed to investigate the link between input features and the mechanical properties of fiberglass-reinforced magnesium oxychloride (MOC) cement boards produced from a commercial process. The model evaluated the effect of formulation, crystalline phase compositions, and process control parameters on various mechanical performance metrics
Drift-diffusion models for innovative semiconductor devices and their numerical solution
We present charge transport models for novel semiconductor devices which may include ionic species as well as their thermodynamically consistent finite volume discretization
Virtual Structures Based Autonomous Formation Flying Control for Small Satellites
Many space organizations have a growing need to fly several small satellites close together in order to collect and correlate data from different satellite sensors. To do this requires teams of engineers monitoring the satellites orbits and planning maneuvers for the satellites every time the satellite leaves its desired trajectory or formation. This task of maintaining the satellites orbits quickly becomes an arduous and expensive feat for satellite operations centers. This research develops and analyzes algorithms that allow satellites to autonomously control their orbit and formation without human intervention. This goal is accomplished by developing and evaluating a decentralized, optimization-based control that can be used for autonomous formation flight of small satellites. To do this, virtual structures, model predictive control, and switching surfaces are used. An optimized guidance trajectory is also develop to reduce fuel usage of the system. The Hill-Clohessy-Wiltshire equations and the D\u27Amico relative orbital elements are used to describe the relative motion of the satellites. And a performance comparison of the L1, L2, and Lā norms is completed as part of this work. The virtual structure, MPC based framework combined with the switching surfaces enables a scalable method that allows satellites to maneuver safely within their formation, while also minimizing fuel usage
LIPIcs, Volume 261, ICALP 2023, Complete Volume
LIPIcs, Volume 261, ICALP 2023, Complete Volum
Lattice Boltzmann Methods for Partial Differential Equations
Lattice Boltzmann methods provide a robust and highly scalable numerical technique in modern computational fluid dynamics. Besides the discretization procedure, the relaxation principles form the basis of any lattice Boltzmann scheme and render the method a bottom-up approach, which obstructs its development for approximating broad classes of partial differential equations. This work introduces a novel coherent mathematical path to jointly approach the topics of constructability, stability, and limit consistency for lattice Boltzmann methods. A new constructive ansatz for lattice Boltzmann equations is introduced, which highlights the concept of relaxation in a top-down procedure starting at the targeted partial differential equation. Modular convergence proofs are used at each step to identify the key ingredients of relaxation frequencies, equilibria, and moment bases in the ansatz, which determine linear and nonlinear stability as well as consistency orders of relaxation and space-time discretization. For the latter, conventional techniques are employed and extended to determine the impact of the kinetic limit at the very foundation of lattice Boltzmann methods. To computationally analyze nonlinear stability, extensive numerical tests are enabled by combining the intrinsic parallelizability of lattice Boltzmann methods with the platform-agnostic and scalable open-source framework OpenLB. Through upscaling the number and quality of computations, large variations in the parameter spaces of classical benchmark problems are considered for the exploratory indication of methodological insights. Finally, the introduced mathematical and computational techniques are applied for the proposal and analysis of new lattice Boltzmann methods. Based on stabilized relaxation, limit consistent discretizations, and consistent temporal filters, novel numerical schemes are developed for approximating initial value problems and initial boundary value problems as well as coupled systems thereof. In particular, lattice Boltzmann methods are proposed and analyzed for temporal large eddy simulation, for simulating homogenized nonstationary fluid flow through porous media, for binary fluid flow simulations with higher order free energy models, and for the combination with Monte Carlo sampling to approximate statistical solutions of the incompressible Euler equations in three dimensions
Deep Learning Methods for Partial Differential Equations and Related Parameter Identification Problems
Recent years have witnessed a growth in mathematics for deep learning--which
seeks a deeper understanding of the concepts of deep learning with mathematics
and explores how to make it more robust--and deep learning for mathematics,
where deep learning algorithms are used to solve problems in mathematics. The
latter has popularised the field of scientific machine learning where deep
learning is applied to problems in scientific computing. Specifically, more and
more neural network architectures have been developed to solve specific classes
of partial differential equations (PDEs). Such methods exploit properties that
are inherent to PDEs and thus solve the PDEs better than standard feed-forward
neural networks, recurrent neural networks, or convolutional neural networks.
This has had a great impact in the area of mathematical modeling where
parametric PDEs are widely used to model most natural and physical processes
arising in science and engineering. In this work, we review such methods as
well as their extensions for parametric studies and for solving the related
inverse problems. We equally proceed to show their relevance in some industrial
applications
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