Online Tensor Methods for Learning Latent Variable Models

We introduce an online tensor decomposition based approach for two latent variable modeling problems namely, (1) community detection, in which we learn the latent communities that the social actors in social networks belong to, and (2) topic modeling, in which we infer hidden topics of text articles. We consider decomposition of moment tensors using stochastic gradient descent. We conduct optimization of multilinear operations in SGD and avoid directly forming the tensors, to save computational and storage costs. We present optimized algorithm in two platforms. Our GPU-based implementation exploits the parallelism of SIMD architectures to allow for maximum speed-up by a careful optimization of storage and data transfer, whereas our CPU-based implementation uses efficient sparse matrix computations and is suitable for large sparse datasets. For the community detection problem, we demonstrate accuracy and computational efficiency on Facebook, Yelp and DBLP datasets, and for the topic modeling problem, we also demonstrate good performance on the New York Times dataset. We compare our results to the state-of-the-art algorithms such as the variational method, and report a gain of accuracy and a gain of several orders of magnitude in the execution time.Comment: JMLR 201

Future Computer Requirements for Computational Aerodynamics

Recent advances in computational aerodynamics are discussed as well as motivations for and potential benefits of a National Aerodynamic Simulation Facility having the capability to solve fluid dynamic equations at speeds two to three orders of magnitude faster than presently possible with general computers. Two contracted efforts to define processor architectures for such a facility are summarized

Towards AMR Simulations of Galaxy Formation

Numerical simulations present a fundamental building block of our modern theoretical understanding of the Universe. As such the work in this thesis is primarily concerned with understanding fundamental differences that lie between the different hydrodynamic schemes. In chapter 3 I outline the optimisations I make to the FLASH code to enable larger simulations to be run. These include developing and testing a new FFT gravity solver. With these complete, in chapter 4 I present results from a collaborative code comparison project in which we test a series of different hydrodynamics codes against a suite of demanding test problems with astrophysical relevance. As the problems have known solutions, we can quantify their performance and are able to develop a resolution criteria which allows for the two different types to be reliably compared. In chapter 5 we develop an analytic model for ram pressure stripping of the hot gaseous haloes of galaxies in groups and clusters. We test the model against a suite of hydrodynamic simulations in the SPH GADGET-2 code. To ensure that the spurious suppression of hydrodynamic instabilities by SPH codes does not bias our results, I compare our findings to those obtained with the FLASH AMR code and find excellent agreement. Chapter 6 presents work in which we unambiguously determine the origin of the difference between the entropy cores formed in AMR and SPH codes. By running mergers of model clusters we are able to systematically explore the various proposed mechanisms and determine that turbulent mixing generates the higher entropy cores within AMR codes but is suppressed in SPH codes. The startling differences between the two hydrodynamic schemes presented in chapter 6 leads me to investigate their affect upon different sub-grid physical recipes. In chapter 7 I present the implementation of a sub-grid star formation recipe in FLASH and find strong differences in the way the two codes model pressure laws. I extend the work in chapter 8 by implementing a kinetic supernova feedback mechanism in FLASH and contrasting it with the results from the GADGET-2 code. I find that AMR codes dissipate energy much more efficiently than in SPH codes

Changement de masse des glaciers à l’échelle mondiale par analyse spatiotemporelle de modèles numériques de terrain

Les glaciers de la planète rétrécissent rapidement, et produisent des impacts qui s'étendent de la hausse du niveau de la mer et la modification des risques cryosphériques jusqu'au changement de disponibilité en eau douce. Malgré des avancées significatives durant l'ère satellitaire, l'observation des changements de masse des glaciers est encore entravée par une couverture partielle des estimations de télédétection, et par une faible contrainte sur les erreurs des évaluations associées. Dans cette thèse, nous présentons une estimation mondiale et résolue des changements de masse des glaciers basée sur l'analyse spatio-temporelle de modèles numériques de terrain. Nous développons d'abord des méthodes de statistiques spatio-temporelles pour évaluer l'exactitude et la précision des modèles numériques de terrain, et pour estimer des séries temporelles de l'altitude de surface des glaciers. En particulier, nous introduisons un cadre spatial non stationnaire pour estimer et propager des corrélations spatiales multi-échelles dans les incertitudes d'estimations géospatiales. Nous générons ensuite des modèles numériques de terrain massivement à partir de deux décennies d'archives d'images optiques stéréo couvrant les glaciers du monde entier. À partir de ceux-ci, nous estimons des séries temporelles d'altitude de surface pour tous les glaciers de la Terre à une résolution de 100,m sur la période 2000--2019. En intégrant ces séries temporelles en changements de volume et de masse, nous révélons une accélération significative de la perte de masse des glaciers à l'échelle mondiale, ainsi que des réponses régionalement distinctes qui reflètent des changements décennaux de conditions climatiques. En utilisant une grande quantité de données indépendantes et de haute précision, nous démontrons la validité de notre analyse pour produire des incertitudes robustes et cohérentes à différentes échelles de la structure spatio-temporelle de nos estimations. Nous espérons que nos méthodes favorisent des analyses spatio-temporelles robustes, en particulier pour identifier les sources de biais et d'incertitudes dans les études géospatiales. En outre, nous nous attendons à ce que nos estimations permettent de mieux comprendre les facteurs qui régissent le changement des glaciers et d'étendre nos capacités de prévision de ces changements à toutes échelles. Ces prédictions sont nécessaires à la conception de politiques adaptatives sur l'atténuation des impacts de la cryosphère dans le contexte du changement climatique.The world's glaciers are shrinking rapidly, with impacts ranging from global sea-level rise and changes in freshwater availability to the alteration of cryospheric hazards. Despite significant advances during the satellite era, the monitoring of the mass changes of glaciers is still hampered by a fragmented coverage of remote sensing estimations and a poor constraint of the errors in related assessments. In this thesis, we present a globally complete and resolved estimate of glacier mass changes by spatiotemporal analysis of digital elevation models. We first develop methods based on spatiotemporal statistics to assess the accuracy and precision of digital elevation models, and to estimate time series of glacier surface elevation. In particular, we introduce a non-stationary spatial framework to estimate and propagate multi-scale spatial correlations in uncertainties of geospatial estimates. We then massively generate digital elevation models from two decades of stereo optical archives covering glaciers worldwide. From those, we estimate time series of surface elevation for all of Earth's glaciers at a resolution of 100,m during 2000--2019. Integrating these time series into volume and mass changes, we identify a significant acceleration of global glacier mass loss, as well as regionally-contrasted responses that mirror decadal changes in climatic conditions. Using a large amount of independent, high-precision data, we demonstrate the validity of our analysis to yield robust and consistent uncertainties at different scales of the spatiotemporal structure of our estimates. We expect our methods to foster robust spatiotemporal analyses, in particular to identify sources of biases and uncertainties in geospatial assessments. Furthermore, we anticipate our estimates to advance the understanding of the drivers that govern glacier change, and to extend our capabilities of predicting these changes at all scales. Such predictions are critically needed to design adaptive policies on the mitigation of cryospheric impacts in the context of climate change