Sparse Systems Solving on GPUs with GMRES

International audienceScientific applications very often rely on solving one or more linear systems. When matrices are sparse, iterative methods are preferred to direct ones. Nevertheless, the value of non zero elements and their distribution (i.e. the sketch of the matrix) greatly influence the efficiency of those methods (in terms of computation time, number of iterations, result precision) or simply prevent the convergence. Among iterative methods, GMRES is often chosen when dealing with general non symmetric matrices. Indeed its convergence is very fast and more stable than the biconjugate gradient. Furthermore, it is mainly based on mathematical operations (matrix-vector and dot products, norms, $\ldots$) that can be heavily parallelized and is thus a good candidate to implement a solver for sparse systems on Graphics Processing Units (GPU). This paper presents a GMRES method for such an architecture. It is based on the modified Gram-Schmidt approach and is very similar to that of Sparselib. Our version uses restarting and a very basic preconditioning. For its implementation, we have based our code on CUBLAS and SpMV libraries, in order to achieve a good performance whatever the matrix sizes and their sketch are. Our experiments exhibit encouraging results on the comparison between Central Processing Units (CPU) and GPU executions in double precision, obtaining a speedup ranging from 8 up-to 23 for a large variety of problems

Etude de la déshydratation mécanique assistée thermiquement

Ce travail s'inscrit dans un contexte général qui concerne les procédés de Séparation Liquide Solide (SLS) et plus particulièrement une technique de déshydratation mécanique : la filtration/compression. L'objectif de ce travail est d'étudier l'effet d'un apport thermique localisé sur l'opération de filtration compression. Une synthèse bibliographique a permis de dégager les aspects importants des mécanismes de filtration et de compression en relation avec la structure des gâteaux. Une part importante du travail de thèse a consisté en la conception et la réalisation d'un outil expérimental instrumenté permettant d'effectuer une opération de filtration/compression avec apport thermique au niveau du piston et/ou au niveau du support du media filtrant. La démarche suivie a consisté à faire évoluer une cellule classique de filtration-compression, pour permettre l'insertion des éléments chauffants et des capteurs adaptés. Cette évolution a nécessité notamment l'adjonction en avant du piston d'une pièce circulaire (appelée pseudo piston) destinée à protéger le capteur de pression placé à la surface du piston et à accueillir une résistance chauffante. L'étude expérimentale a été réalisée avec des suspensions de Talc et de Kaolin. Les résultats obtenus ont montré une réelle efficacité d'un apport thermique localisé au niveau du media filtrant pour améliorer la cinétique de séparation. En effet, une diminution de la viscosité du filtrat dans la zone la plus résistive du procédé (partie basse du gâteau et media filtrant) permet d'accélérer de fa on significative la filtration relativement à une opération de filtration effectuée à température homogène. Pendant la compression, une modification de la structure du gâteau (effondrement) s'opère lorsque la température au niveau du media filtrant atteint la température d'ébullition du liquide. Cet effondrement est rapide à l'échelle de la compression mécanique et son amplitude dépend des conditions opératoires et de la compressibilité du gâteau. De plus, ce phénomène permet d'obtenir rapidement des niveaux de siccité élevés. Les mécanismes complexes mis en jeu résultent d'un couplage fort entre mécanique et thermique et n'ont pas encore été interprétés. Les résultats très encourageants obtenus à partir de suspensions modèles permettent d'envisager d'étendre l'étude à des suspensions formant des gâteaux extrêmement compressibles comme les boues biologiques floculées.This work deals with liquid solid separation processes and specially with a technique of mechanical dehydration : filtration/expression. The aim of this work is to study the effects of a local thermal supply on the filtration expression process. A bibliographic synthesis brought out important aspects of the filtration expression mechanisms and cake structuring. A significant part of this work concerns the design of an experimental rig which allows to perform filtration/expression tests with a local thermal supply at filter medium and/or at cake surface level. The design step consisted in developing a classical filtration expression cell by adding a circular piece ahead of the piston (called pseudo piston) which protects the pressure sensor placed at the piston surface and receives a heat component. Talc and Kaolin suspensions were used for the experimental study. Results obtained showed a great efficacy of a heat supply at filter medium level to enhance the separation kinetic. Indeed, a reduction of the filtrate viscosity in the more resistive part of the process (lower part of the cake and filter medium) enables to accelerate significantly the filtration compared to a test performed at homogeneous temperature. During expression, a modification of the cake structure (cake collapse) occurs when temperature of filter medium reaches temperature of liquid boiling. This cake collapse is quick at the expression scale and depends on experimental conditions and cake compressibility. Moreover, this phenomena enables to reach high dry matter content. Complex mechanisms involved come from a great coupling between thermal and mechanical effects and don't have any interpretation for the moment. Results obtained with rutile suspensions enable to extend the study to suspensions forming extremely compressible cakes such as flocculated biological sludge

A model-based performance test for forest classifiers on remote-sensing imagery

Ambiguity between forest types on remote-sensing imagery is a major cause of errors found in accuracy assessments of forest inventorymaps. This paper presents a methodology, based on forest plot inventory, ground measurements and simulated imagery, for systematically quantifying these ambiguities in the sense of the minimum distance (MD), maximum likelihood (ML), and frequency-based (FB) classifiers. The method is tested with multi-spectral IKONOS images acquired on areas containing six major communities (oak, pine, fir, primary and secondary high tropical forests, and avocado plantation) of the National Forest Inventory (NFI) map in Mexico. A structural record of the canopy and optical measurements (leaf area index and soil reflectance) were performed on one plot of each class. Intra-class signal variation was modelled using the Discrete Anisotropic Radiative Transfer (DART) simulator of remote-sensing images. Atmospheric conditions were inferred from ground measurements on reference surfaces and leaf optical properties of each forest type were derived from the IKONOS forest signal. Next, all forest types were simulated, using a common environmental configuration, in order to quantify similarity among all forest types, according to MD, ML and FB classifiers. Classes were considered ambiguous when their dissimilarity was smaller than intra-class signal variation. DART proved useful in approximating the pixel value distribution and the ambiguity pattern measured on real forest imagery. In the case study, the oak forest and the secondary tropical forest were both distinguishable from all other classes using an MD classifier in a 25 m window size, whereas pine and primary tropical forests were ambiguous with three other classes using MD. By contrast, only two pairs of classes were found ambiguous for the ML classifier and only one for the FB classifier in that same window size. The avocado plantation was confounded with the primary tropical forest for all classifiers, presumably because the reflectance of both types of forest is governed by a deep canopy and a similar shadow area. We confronted the results of this study with the confusion matrix from the accuracy assessment of the NFI map. An asset of this model-basedmethod is its applicability to a variety of sensor types, eco-zones and class definitions

A cost effective AFM setup, combining interferometry and FPGA

International audienceAtomic force microscopes (AFM) provide high resolution images of surfaces. In this paper, we focus on an interferometry method for estimation of deflections in arrays of cantilever in quasi-static regime. We propose a novel complete solution with a least square based algorithm to determine interference fringe phases and its optimized FPGA implementation. Simulations and real tests show very good results and open perspectives for real-time estimation and control of cantilever arrays in the dynamic regime

Fast Autofocusing using Tiny Transformer Networks for Digital Holographic Microscopy

The numerical wavefront backpropagation principle of digital holography confers unique extended focus capabilities, without mechanical displacements along z-axis. However, the determination of the correct focusing distance is a non-trivial and time consuming issue. A deep learning (DL) solution is proposed to cast the autofocusing as a regression problem and tested over both experimental and simulated holograms. Single wavelength digital holograms were recorded by a Digital Holographic Microscope (DHM) with a 10$\mathrm{x}$ microscope objective from a patterned target moving in 3D over an axial range of 92 $\mu$m. Tiny DL models are proposed and compared such as a tiny Vision Transformer (TViT), tiny VGG16 (TVGG) and a tiny Swin-Transfomer (TSwinT). The experiments show that the predicted focusing distance $Z_R^{\mathrm{Pred}}$ is accurately inferred with an accuracy of 1.2 $\mu$m in average in comparison with the DHM depth of field of 15 $\mu$m. Numerical simulations show that all tiny models give the $Z_R^{\mathrm{Pred}}$ with an error below 0.3 $\mu$m. Such a prospect would significantly improve the current capabilities of computer vision position sensing in applications such as 3D microscopy for life sciences or micro-robotics. Moreover, all models reach state of the art inference time on CPU, less than 25 ms per inference