12 research outputs found

    Super-resolving multiresolution images with band-independant geometry of multispectral pixels

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    A new resolution enhancement method is presented for multispectral and multi-resolution images, such as these provided by the Sentinel-2 satellites. Starting from the highest resolution bands, band-dependent information (reflectance) is separated from information that is common to all bands (geometry of scene elements). This model is then applied to unmix low-resolution bands, preserving their reflectance, while propagating band-independent information to preserve the sub-pixel details. A reference implementation is provided, with an application example for super-resolving Sentinel-2 data.Comment: Source code with a ready-to-use script for super-resolving Sentinel-2 data is available at http://nicolas.brodu.net/recherche/superres

    Lessons in uncertainty quantification for turbulent dynamical systems

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    Physics-guided machine learning for turbulence closure and reduced-order modeling

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    A recent advance in scientific machine learning has started to show promising results in fluid mechanics. Despite their early success, the application of data-driven methods to turbulent flow simulation is non-trivial due to underlying highly nonlinear multiscale interactions. Here we present novel physics-guided machine learning (PGML) approaches for turbulence closure model discovery and model order reduction of complex multiscale systems. Our turbulence closure model discovery approach is based on exploiting big data without relying on underlying turbulence physics and learning from physical constraints. Specifically, we propose a frame invariant neural network model that can incorporate physical symmetries as inductive biases and illustrates its stable performance in the coarse-grid simulation without any kind of post-processing of the predicted subgrid-scale closure model. The frame invariant SGS model guarantees desired physical constraints without the need for any regularization terms and ultimately generalizes to different initial conditions and Reynolds numbers. To achieve data-efficient training and improved generalization, we propose a concatenated neural network with an uncertainty quantification mechanism that leverages information from hierarchies of models. The concatenated neural network is based on embedding information from cheap to evaluate low-fidelity approximations into the certain hidden layer of the neural network both during training and deployment. This framework is demonstrated for a range of problems, including turbulent boundary layer reconstruction, and reduced-order modeling of the vortex merging process. Furthermore, we investigate the seamless integration of sparse and noisy observations into non-intrusive reduced-order models, and hybrid models where the dynamical core of the system is modeled using the known governing equations, and the subgrid-scale processes are modeled using a deep learning model. To summarize, this work builds a bridge between extensive physics-based theories and data-driven modeling paradigms and paves the way for using hybrid physics-informed learning algorithms to generate predictive technologies for turbulent fluid flows

    Image Registration Workshop Proceedings

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    Automatic image registration has often been considered as a preliminary step for higher-level processing, such as object recognition or data fusion. But with the unprecedented amounts of data which are being and will continue to be generated by newly developed sensors, the very topic of automatic image registration has become and important research topic. This workshop presents a collection of very high quality work which has been grouped in four main areas: (1) theoretical aspects of image registration; (2) applications to satellite imagery; (3) applications to medical imagery; and (4) image registration for computer vision research

    Ocean Turbulent Dynamics at Superresolution From Optimal Multiresolution Analysis and Multiplicative Cascade

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    International audienceThe synoptic determination of ocean circulation using the data acquired from space, with a coherent depiction of its turbulent characteristics, remains a fundamental challenge in oceanography. This determination has the potential of revealing all aspects of the ocean dynamic variability on a wide range of spatiotemporal scales and will enhance our understanding of ocean–atmosphere exchanges at superresolution, as required in the present context of climate change. Here, we show a four-year time series of spatial superresolution (4 km) turbulent ocean dynamics generated from satellite data using emerging ideas in signal processing coming from nonlinear physics, low-resolution dynamics, and superresolution oceanic sea surface temperature data acquired from optical sensors. The method at its core consists in propagating across the scales the low-resolution dynamics in a multiresolution analysis computed on adimensional critical transition information

    MS FT-2-2 7 Orthogonal polynomials and quadrature: Theory, computation, and applications

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    Quadrature rules find many applications in science and engineering. Their analysis is a classical area of applied mathematics and continues to attract considerable attention. This seminar brings together speakers with expertise in a large variety of quadrature rules. It is the aim of the seminar to provide an overview of recent developments in the analysis of quadrature rules. The computation of error estimates and novel applications also are described

    Generalized averaged Gaussian quadrature and applications

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    A simple numerical method for constructing the optimal generalized averaged Gaussian quadrature formulas will be presented. These formulas exist in many cases in which real positive GaussKronrod formulas do not exist, and can be used as an adequate alternative in order to estimate the error of a Gaussian rule. We also investigate the conditions under which the optimal averaged Gaussian quadrature formulas and their truncated variants are internal
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