1,426 research outputs found

    A Fast Geometric Multigrid Method for Curved Surfaces

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    We introduce a geometric multigrid method for solving linear systems arising from variational problems on surfaces in geometry processing, Gravo MG. Our scheme uses point clouds as a reduced representation of the levels of the multigrid hierarchy to achieve a fast hierarchy construction and to extend the applicability of the method from triangle meshes to other surface representations like point clouds, nonmanifold meshes, and polygonal meshes. To build the prolongation operators, we associate each point of the hierarchy to a triangle constructed from points in the next coarser level. We obtain well-shaped candidate triangles by computing graph Voronoi diagrams centered around the coarse points and determining neighboring Voronoi cells. Our selection of triangles ensures that the connections of each point to points at adjacent coarser and finer levels are balanced in the tangential directions. As a result, we obtain sparse prolongation matrices with three entries per row and fast convergence of the solver.Comment: Ruben Wiersma and Ahmad Nasikun contributed equally. To be published in SIGGRAPH 2023. 16 pages total (8 main, 5 supplement), 14 figure

    Machine learning in solar physics

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    The application of machine learning in solar physics has the potential to greatly enhance our understanding of the complex processes that take place in the atmosphere of the Sun. By using techniques such as deep learning, we are now in the position to analyze large amounts of data from solar observations and identify patterns and trends that may not have been apparent using traditional methods. This can help us improve our understanding of explosive events like solar flares, which can have a strong effect on the Earth environment. Predicting hazardous events on Earth becomes crucial for our technological society. Machine learning can also improve our understanding of the inner workings of the sun itself by allowing us to go deeper into the data and to propose more complex models to explain them. Additionally, the use of machine learning can help to automate the analysis of solar data, reducing the need for manual labor and increasing the efficiency of research in this field.Comment: 100 pages, 13 figures, 286 references, accepted for publication as a Living Review in Solar Physics (LRSP

    Aerial Drone-based System for Wildfire Monitoring and Suppression

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    Wildfire, also known as forest fire or bushfire, being an uncontrolled fire crossing an area of combustible vegetation, has become an inherent natural feature of the landscape in many regions of the world. From local to global scales, wildfire has caused substantial social, economic and environmental consequences. Given the hazardous nature of wildfire, developing automated and safe means to monitor and fight the wildfire is of special interest. Unmanned aerial vehicles (UAVs), equipped with appropriate sensors and fire retardants, are available to remotely monitor and fight the area undergoing wildfires, thus helping fire brigades in mitigating the influence of wildfires. This thesis is dedicated to utilizing UAVs to provide automated surveillance, tracking and fire suppression services on an active wildfire event. Considering the requirement of collecting the latest information of a region prone to wildfires, we presented a strategy to deploy the estimated minimum number of UAVs over the target space with nonuniform importance, such that they can persistently monitor the target space to provide a complete area coverage whilst keeping a desired frequency of visits to areas of interest within a predefined time period. Considering the existence of occlusions on partial segments of the sensed wildfire boundary, we processed both contour and flame surface features of wildfires with a proposed numerical algorithm to quickly estimate the occluded wildfire boundary. To provide real-time situational awareness of the propagated wildfire boundary, according to the prior knowledge of the whole wildfire boundary is available or not, we used the principle of vector field to design a model-based guidance law and a model-free guidance law. The former is derived from the radial basis function approximated wildfire boundary while the later is based on the distance between the UAV and the sensed wildfire boundary. Both vector field based guidance laws can drive the UAV to converge to and patrol along the dynamic wildfire boundary. To effectively mitigate the impacts of wildfires, we analyzed the advancement based activeness of the wildfire boundary with a signal prominence based algorithm, and designed a preferential firefighting strategy to guide the UAV to suppress fires along the highly active segments of the wildfire boundary

    Embedded SLAM algorithm based on ORB-SLAM2

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    The goal of this dissertation was to present a comprehensive analysis of the ORB-SLAM2 algorithm. By introducing the basis of points triangulation and ORB features, the whole structure of the algorithm has been analyzed, with a centralized focus on the graph-based optimization involved, as well as the place recognition mechanism. Additionally, the original code has been analyzed and optimized, resulting in a substantial increase in time performance while keeping a similar accuracy to the original one, proved by several simulations performed. The final goal of this thesis has been the testing of the obtained algorithm on a real quadcopter and the analysis of its outcomes: the results were affected by the limited computational resources available in the vehicle, obtaining a lower accuracy with respect to the simulation, but still proving the efficiency of the improvements applied on the original code

    Conditional Invertible Generative Models for Supervised Problems

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    Invertible neural networks (INNs), in the setting of normalizing flows, are a type of unconditional generative likelihood model. Despite various attractive properties compared to other common generative model types, they are rarely useful for supervised tasks or real applications due to their unguided outputs. In this work, we therefore present three new methods that extend the standard INN setting, falling under a broader category we term generative invertible models. These new methods allow leveraging the theoretical and practical benefits of INNs to solve supervised problems in new ways, including real-world applications from different branches of science. The key finding is that our approaches enhance many aspects of trustworthiness in comparison to conventional feed-forward networks, such as uncertainty estimation and quantification, explainability, and proper handling of outlier data

    Recent advances in describing and driving crystal nucleation using machine learning and artificial intelligence

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    With the advent of faster computer processors and especially graphics processing units (GPUs) over the last few decades, the use of data-intensive machine learning (ML) and artificial intelligence (AI) has increased greatly, and the study of crystal nucleation has been one of the beneficiaries. In this review, we outline how ML and AI have been applied to address four outstanding difficulties of crystal nucleation: how to discover better reaction coordinates (RCs) for describing accurately non-classical nucleation situations; the development of more accurate force fields for describing the nucleation of multiple polymorphs or phases for a single system; more robust identification methods for determining crystal phases and structures; and as a method to yield improved course-grained models for studying nucleation.Comment: 15 pages; 1 figur

    LIPIcs, Volume 261, ICALP 2023, Complete Volume

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    LIPIcs, Volume 261, ICALP 2023, Complete Volum

    Spherical and Hyperbolic Toric Topology-Based Codes On Graph Embedding for Ising MRF Models: Classical and Quantum Topology Machine Learning

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    The paper introduces the application of information geometry to describe the ground states of Ising models by utilizing parity-check matrices of cyclic and quasi-cyclic codes on toric and spherical topologies. The approach establishes a connection between machine learning and error-correcting coding. This proposed approach has implications for the development of new embedding methods based on trapping sets. Statistical physics and number geometry applied for optimize error-correcting codes, leading to these embedding and sparse factorization methods. The paper establishes a direct connection between DNN architecture and error-correcting coding by demonstrating how state-of-the-art architectures (ChordMixer, Mega, Mega-chunk, CDIL, ...) from the long-range arena can be equivalent to of block and convolutional LDPC codes (Cage-graph, Repeat Accumulate). QC codes correspond to certain types of chemical elements, with the carbon element being represented by the mixed automorphism Shu-Lin-Fossorier QC-LDPC code. The connections between Belief Propagation and the Permanent, Bethe-Permanent, Nishimori Temperature, and Bethe-Hessian Matrix are elaborated upon in detail. The Quantum Approximate Optimization Algorithm (QAOA) used in the Sherrington-Kirkpatrick Ising model can be seen as analogous to the back-propagation loss function landscape in training DNNs. This similarity creates a comparable problem with TS pseudo-codeword, resembling the belief propagation method. Additionally, the layer depth in QAOA correlates to the number of decoding belief propagation iterations in the Wiberg decoding tree. Overall, this work has the potential to advance multiple fields, from Information Theory, DNN architecture design (sparse and structured prior graph topology), efficient hardware design for Quantum and Classical DPU/TPU (graph, quantize and shift register architect.) to Materials Science and beyond.Comment: 71 pages, 42 Figures, 1 Table, 1 Appendix. arXiv admin note: text overlap with arXiv:2109.08184 by other author

    Micromechanics of passive and active inclusions in granular media

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    Passive and active inclusions in granular materials play an increasingly important role in the development of sustainable infrastructure. Passive inclusions, such as geogrids, have been shown to augment the service life of roadways and reduce aggregate consumption in pavement base layers. This is possible due to the aggregate-geogrid composite action, that results in the redistribution of traffic loads. The present study presents three-dimensional models that simulate the cyclic-loading behavior of geogrid-reinforced base layers using the discrete element method. It introduces a new framework by which upper and lower performance bounds are established by simulating unreinforced and perfectly reinforced aggregate bases. The model works as a tool for systematic prototyping of new geogrid geometries and mechanical properties. Furthermore, important insights into how aggregate morphology works in combination with different geogrids were obtained via a parametric study. The sustainability of linear infrastructure can also be improved with the use of active inclusions for thorough soil exploration and characterization. Self-motile probes are an emergent technology that will enable multidirectional testing of soils in situ. The locomotion systems of several of these technologies have been inspired by annelid peristalsis. Annelids such as the earthworm Lumbricus terrestris use synchronized muscle expansion and contraction to anchor portions of their segmented bodies while other portions push into the medium. In this doctoral work, the peristaltic locomotion and the design of burrowing robots are investigated on multiple fronts. First, the anchorage mechanism developed by expanded segments is studied by conducting pullout experiments in sand and numerical modeling using the discrete element method. The results revealed the expansion ratio to be critical in the development of anchorage resistance by promoting different soil responses. Subsequently, the effect of tip shape in reducing penetration resistance to enable greater advancement into granular beds is investigated using experiments and numerical modeling with the discrete element method. Results reveal that under low interface friction, penetration resistance can be decreased threefold by utilizing sharper tips. Later, the soil response to the anchor–push mechanism employed is investigated utilizing robotic analogs and X-ray micro-tomography. Results revealed a significant contrast between the soil response in loose and dense materials. Finally, a transparent synthetic soil testbed is developed. It enables the prototyping and testing of burrowing devices with real-time imaging. Results demonstrate the ability of the setup to provide important insight into geometrical aspects of robot designs that improve their advancement and overall performance.Ph.D

    Nonconforming Virtual Element basis functions for space-time Discontinuous Galerkin schemes on unstructured Voronoi meshes

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    We introduce a new class of Discontinuous Galerkin (DG) methods for solving nonlinear conservation laws on unstructured Voronoi meshes that use a nonconforming Virtual Element basis defined within each polygonal control volume. The basis functions are evaluated as an L2 projection of the virtual basis which remains unknown, along the lines of the Virtual Element Method (VEM). Contrarily to the VEM approach, the new basis functions lead to a nonconforming representation of the solution with discontinuous data across the element boundaries, as typically employed in DG discretizations. To improve the condition number of the resulting mass matrix, an orthogonalization of the full basis is proposed. The discretization in time is carried out following the ADER (Arbitrary order DERivative Riemann problem) methodology, which yields one-step fully discrete schemes that make use of a coupled space-time representation of the numerical solution. The space-time basis functions are constructed as a tensor product of the virtual basis in space and a one-dimensional Lagrange nodal basis in time. The resulting space-time stiffness matrix is stabilized by an extension of the dof-dof stabilization technique adopted in the VEM framework, hence allowing an element-local space-time Galerkin finite element predictor to be evaluated. The novel methods are referred to as VEM-DG schemes, and they are arbitrarily high order accurate in space and time. The new VEM-DG algorithms are rigorously validated against a series of benchmarks in the context of compressible Euler and Navier-Stokes equations. Numerical results are verified with respect to literature reference solutions and compared in terms of accuracy and computational efficiency to those obtained using a standard modal DG scheme with Taylor basis functions. An analysis of the condition number of the mass and space-time stiffness matrix is also forwarded
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