369 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

    Development of Quantitative Bone SPECT Analysis Methods for Metastatic Bone Disease

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    Prostate cancer is one of the most prevalent types of cancer in males in the United States. Bone is a common site of metastases for metastatic prostate cancer. However, bone metastases are often considered “unmeasurable” using standard anatomic imaging and the RECIST 1.1 criteria. As a result, response to therapy is often suboptimally evaluated by visual interpretation of planar bone scintigraphy with response criteria related to the presence or absence of new lesions. With the commercial availability of quantitative single-photon emission computed tomography (SPECT) methods, it is now feasible to establish quantitative metrics of therapy response by skeletal metastases. Quantitative bone SPECT (QBSPECT) may provide the ability to estimate bone lesion uptake, volume, and the number of lesions more accurately than planar imaging. However, the accuracy of activity quantification in QBSPECT relies heavily on the precision with which bone metastases and bone structures are delineated. In this research, we aim at developing automated image segmentation methods for fast and accurate delineation of bone and bone metastases in QBSPECT. To begin, we developed registration methods to generate a dataset of realistic and anatomically-varying computerized phantoms for use in QBSPECT simulations. Using these simulations, we develop supervised computer-automated segmentation methods to minimize intra- and inter-observer variations in delineating bone metastases. This project provides accurate segmentation techniques for QBSPECT and paves the way for the development of QBSPECT methods for assessing bone metastases’ therapy response

    Neural function approximation on graphs: shape modelling, graph discrimination & compression

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    Graphs serve as a versatile mathematical abstraction of real-world phenomena in numerous scientific disciplines. This thesis is part of the Geometric Deep Learning subject area, a family of learning paradigms, that capitalise on the increasing volume of non-Euclidean data so as to solve real-world tasks in a data-driven manner. In particular, we focus on the topic of graph function approximation using neural networks, which lies at the heart of many relevant methods. In the first part of the thesis, we contribute to the understanding and design of Graph Neural Networks (GNNs). Initially, we investigate the problem of learning on signals supported on a fixed graph. We show that treating graph signals as general graph spaces is restrictive and conventional GNNs have limited expressivity. Instead, we expose a more enlightening perspective by drawing parallels between graph signals and signals on Euclidean grids, such as images and audio. Accordingly, we propose a permutation-sensitive GNN based on an operator analogous to shifts in grids and instantiate it on 3D meshes for shape modelling (Spiral Convolutions). Following, we focus on learning on general graph spaces and in particular on functions that are invariant to graph isomorphism. We identify a fundamental trade-off between invariance, expressivity and computational complexity, which we address with a symmetry-breaking mechanism based on substructure encodings (Graph Substructure Networks). Substructures are shown to be a powerful tool that provably improves expressivity while controlling computational complexity, and a useful inductive bias in network science and chemistry. In the second part of the thesis, we discuss the problem of graph compression, where we analyse the information-theoretic principles and the connections with graph generative models. We show that another inevitable trade-off surfaces, now between computational complexity and compression quality, due to graph isomorphism. We propose a substructure-based dictionary coder - Partition and Code (PnC) - with theoretical guarantees that can be adapted to different graph distributions by estimating its parameters from observations. Additionally, contrary to the majority of neural compressors, PnC is parameter and sample efficient and is therefore of wide practical relevance. Finally, within this framework, substructures are further illustrated as a decisive archetype for learning problems on graph spaces.Open Acces

    Machine Learning and Its Application to Reacting Flows

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    This open access book introduces and explains machine learning (ML) algorithms and techniques developed for statistical inferences on a complex process or system and their applications to simulations of chemically reacting turbulent flows. These two fields, ML and turbulent combustion, have large body of work and knowledge on their own, and this book brings them together and explain the complexities and challenges involved in applying ML techniques to simulate and study reacting flows. This is important as to the world’s total primary energy supply (TPES), since more than 90% of this supply is through combustion technologies and the non-negligible effects of combustion on environment. Although alternative technologies based on renewable energies are coming up, their shares for the TPES is are less than 5% currently and one needs a complete paradigm shift to replace combustion sources. Whether this is practical or not is entirely a different question, and an answer to this question depends on the respondent. However, a pragmatic analysis suggests that the combustion share to TPES is likely to be more than 70% even by 2070. Hence, it will be prudent to take advantage of ML techniques to improve combustion sciences and technologies so that efficient and “greener” combustion systems that are friendlier to the environment can be designed. The book covers the current state of the art in these two topics and outlines the challenges involved, merits and drawbacks of using ML for turbulent combustion simulations including avenues which can be explored to overcome the challenges. The required mathematical equations and backgrounds are discussed with ample references for readers to find further detail if they wish. This book is unique since there is not any book with similar coverage of topics, ranging from big data analysis and machine learning algorithm to their applications for combustion science and system design for energy generation

    Innovative Techniques for the Retrieval of Earth’s Surface and Atmosphere Geophysical Parameters: Spaceborne Infrared/Microwave Combined Analyses

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    With the advent of the first satellites for Earth Observation: Landsat-1 in July 1972 and ERS-1 in May 1991, the discipline of environmental remote sensing has become, over time, increasingly fundamental for the study of phenomena characterizing the planet Earth. The goal of environmental remote sensing is to perform detailed analyses and to monitor the temporal evolution of different physical phenomena, exploiting the mechanisms of interaction between the objects that are present in an observed scene and the electromagnetic radiation detected by sensors, placed at a distance from the scene, operating at different frequencies. The analyzed physical phenomena are those related to climate change, weather forecasts, global ocean circulation, greenhouse gas profiling, earthquakes, volcanic eruptions, soil subsidence, and the effects of rapid urbanization processes. Generally, remote sensing sensors are of two primary types: active and passive. Active sensors use their own source of electromagnetic radiation to illuminate and analyze an area of interest. An active sensor emits radiation in the direction of the area to be investigated and then detects and measures the radiation that is backscattered from the objects contained in that area. Passive sensors, on the other hand, detect natural electromagnetic radiation (e.g., from the Sun in the visible band and the Earth in the infrared and microwave bands) emitted or reflected by the object contained in the observed scene. The scientific community has dedicated many resources to developing techniques to estimate, study and analyze Earth’s geophysical parameters. These techniques differ for active and passive sensors because they depend strictly on the type of the measured physical quantity. In my P.h.D. work, inversion techniques for estimating Earth’s surface and atmosphere geophysical parameters will be addressed, emphasizing methods based on machine learning (ML). In particular, the study of cloud microphysics and the characterization of Earth’s surface changes phenomenon are the critical points of this work

    Large Scale Kernel Methods for Fun and Profit

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    Kernel methods are among the most flexible classes of machine learning models with strong theoretical guarantees. Wide classes of functions can be approximated arbitrarily well with kernels, while fast convergence and learning rates have been formally shown to hold. Exact kernel methods are known to scale poorly with increasing dataset size, and we believe that one of the factors limiting their usage in modern machine learning is the lack of scalable and easy to use algorithms and software. The main goal of this thesis is to study kernel methods from the point of view of efficient learning, with particular emphasis on large-scale data, but also on low-latency training, and user efficiency. We improve the state-of-the-art for scaling kernel solvers to datasets with billions of points using the Falkon algorithm, which combines random projections with fast optimization. Running it on GPUs, we show how to fully utilize available computing power for training kernel machines. To boost the ease-of-use of approximate kernel solvers, we propose an algorithm for automated hyperparameter tuning. By minimizing a penalized loss function, a model can be learned together with its hyperparameters, reducing the time needed for user-driven experimentation. In the setting of multi-class learning, we show that – under stringent but realistic assumptions on the separation between classes – a wide set of algorithms needs much fewer data points than in the more general setting (without assumptions on class separation) to reach the same accuracy. The first part of the thesis develops a framework for efficient and scalable kernel machines. This raises the question of whether our approaches can be used successfully in real-world applications, especially compared to alternatives based on deep learning which are often deemed hard to beat. The second part aims to investigate this question on two main applications, chosen because of the paramount importance of having an efficient algorithm. First, we consider the problem of instance segmentation of images taken from the iCub robot. Here Falkon is used as part of a larger pipeline, but the efficiency afforded by our solver is essential to ensure smooth human-robot interactions. In the second instance, we consider time-series forecasting of wind speed, analysing the relevance of different physical variables on the predictions themselves. We investigate different schemes to adapt i.i.d. learning to the time-series setting. Overall, this work aims to demonstrate, through novel algorithms and examples, that kernel methods are up to computationally demanding tasks, and that there are concrete applications in which their use is warranted and more efficient than that of other, more complex, and less theoretically grounded models

    Exploring Animal Behavior Through Sound: Volume 1

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    This open-access book empowers its readers to explore the acoustic world of animals. By listening to the sounds of nature, we can study animal behavior, distribution, and demographics; their habitat characteristics and needs; and the effects of noise. Sound recording is an efficient and affordable tool, independent of daylight and weather; and recorders may be left in place for many months at a time, continuously collecting data on animals and their environment. This book builds the skills and knowledge necessary to collect and interpret acoustic data from terrestrial and marine environments. Beginning with a history of sound recording, the chapters provide an overview of off-the-shelf recording equipment and analysis tools (including automated signal detectors and statistical methods); audiometric methods; acoustic terminology, quantities, and units; sound propagation in air and under water; soundscapes of terrestrial and marine habitats; animal acoustic and vibrational communication; echolocation; and the effects of noise. This book will be useful to students and researchers of animal ecology who wish to add acoustics to their toolbox, as well as to environmental managers in industry and government
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