Accuracy and Transferability in Machine Learned Potentials for Carbon

In this thesis, we discuss the approach taken to construct an accurate machine learning (ML) model for atomistic simulations of carbon, constructed using the Gaussian approximation potential (GAP) methodology. We begin by discussing the process for constructing a potential for a single phase, graphene. We then extend this to produce a general-purpose potential, named GAP-20, which describes the properties of the bulk crystalline and amorphous phases, crystal surfaces, and defect structures with a high degree of accuracy. We combine structural databases for amorphous carbon and graphene, which we extend substantially by adding suitable configurations, for example, for defects in graphene and other nanostructures. The final potential is fitted to reference data computed using the optB88-vdW density functional theory (DFT) functional. Dispersion interactions, which are crucial to describe multilayer carbonaceous materials, are therefore implicitly included. We additionally account for long-range dispersion interactions using a semianalytical two-body term and show that an improved model can be obtained through an optimization of the manybody smooth overlap of atomic positions descriptor. We rigorously test the potential on lattice parameters, bond lengths, formation energies, and phonon dispersions of numerous carbon allotropes. We compare the formation energies of an extensive set of defect structures, surfaces, and surface reconstructions to DFT reference calculations. The present work demonstrates the ability to combine, in the same ML model, the previously attained flexibility required for amorphous carbon with the high accuracy necessary for crystalline graphene which we introduce in this thesis, thereby providing an interatomic potential that will be applicable to a wide range of applications concerning diverse forms of bulk and nanostructured carbon

Labeled Sampling Consensus A Novel Algorithm For Robustly Fitting Multiple Structures Using Compressed Sampling

The ability to robustly fit structures in datasets that contain outliers is a very important task in Image Processing, Pattern Recognition and Computer Vision. Random Sampling Consensus or RANSAC is a very popular method for this task, due to its ability to handle over 50% outliers. The problem with RANSAC is that it is only capable of finding a single structure. Therefore, if a dataset contains multiple structures, they must be found sequentially by finding the best fit, removing the points, and repeating the process. However, removing incorrect points from the dataset could prove disastrous. This thesis offers a novel approach to sampling consensus that extends its ability to discover multiple structures in a single iteration through the dataset. The process introduced is an unsupervised method, requiring no previous knowledge to the distribution of the input data. It uniquely assigns labels to different instances of similar structures. The algorithm is thus called Labeled Sampling Consensus or L-SAC. These unique instances will tend to cluster around one another allowing the individual structures to be extracted using simple clustering techniques. Since divisions instead of modes are analyzed, only a single instance of a structure need be recovered. This ability of L-SAC allows a novel sampling procedure to be presented “compressing” the required samples needed compared to traditional sampling schemes while ensuring all structures have been found. L-SAC is a flexible framework that can be applied to many problem domains

Multimodal Three Dimensional Scene Reconstruction, The Gaussian Fields Framework

The focus of this research is on building 3D representations of real world scenes and objects using different imaging sensors. Primarily range acquisition devices (such as laser scanners and stereo systems) that allow the recovery of 3D geometry, and multi-spectral image sequences including visual and thermal IR images that provide additional scene characteristics. The crucial technical challenge that we addressed is the automatic point-sets registration task. In this context our main contribution is the development of an optimization-based method at the core of which lies a unified criterion that solves simultaneously for the dense point correspondence and transformation recovery problems. The new criterion has a straightforward expression in terms of the datasets and the alignment parameters and was used primarily for 3D rigid registration of point-sets. However it proved also useful for feature-based multimodal image alignment. We derived our method from simple Boolean matching principles by approximation and relaxation. One of the main advantages of the proposed approach, as compared to the widely used class of Iterative Closest Point (ICP) algorithms, is convexity in the neighborhood of the registration parameters and continuous differentiability, allowing for the use of standard gradient-based optimization techniques. Physically the criterion is interpreted in terms of a Gaussian Force Field exerted by one point-set on the other. Such formulation proved useful for controlling and increasing the region of convergence, and hence allowing for more autonomy in correspondence tasks. Furthermore, the criterion can be computed with linear complexity using recently developed Fast Gauss Transform numerical techniques. In addition, we also introduced a new local feature descriptor that was derived from visual saliency principles and which enhanced significantly the performance of the registration algorithm. The resulting technique was subjected to a thorough experimental analysis that highlighted its strength and showed its limitations. Our current applications are in the field of 3D modeling for inspection, surveillance, and biometrics. However, since this matching framework can be applied to any type of data, that can be represented as N-dimensional point-sets, the scope of the method is shown to reach many more pattern analysis applications

System- and Data-Driven Methods and Algorithms

An increasing complexity of models used to predict real-world systems leads to the need for algorithms to replace complex models with far simpler ones, while preserving the accuracy of the predictions. This two-volume handbook covers methods as well as applications. This first volume focuses on real-time control theory, data assimilation, real-time visualization, high-dimensional state spaces and interaction of different reduction techniques

Modeling small objects under uncertainties : novel algorithms and applications.

Active Shape Models (ASM), Active Appearance Models (AAM) and Active Tensor Models (ATM) are common approaches to model elastic (deformable) objects. These models require an ensemble of shapes and textures, annotated by human experts, in order identify the model order and parameters. A candidate object may be represented by a weighted sum of basis generated by an optimization process. These methods have been very effective for modeling deformable objects in biomedical imaging, biometrics, computer vision and graphics. They have been tried mainly on objects with known features that are amenable to manual (expert) annotation. They have not been examined on objects with severe ambiguities to be uniquely characterized by experts. This dissertation presents a unified approach for modeling, detecting, segmenting and categorizing small objects under uncertainty, with focus on lung nodules that may appear in low dose CT (LDCT) scans of the human chest. The AAM, ASM and the ATM approaches are used for the first time on this application. A new formulation to object detection by template matching, as an energy optimization, is introduced. Nine similarity measures of matching have been quantitatively evaluated for detecting nodules less than 1 em in diameter. Statistical methods that combine intensity, shape and spatial interaction are examined for segmentation of small size objects. Extensions of the intensity model using the linear combination of Gaussians (LCG) approach are introduced, in order to estimate the number of modes in the LCG equation. The classical maximum a posteriori (MAP) segmentation approach has been adapted to handle segmentation of small size lung nodules that are randomly located in the lung tissue. A novel empirical approach has been devised to simultaneously detect and segment the lung nodules in LDCT scans. The level sets methods approach was also applied for lung nodule segmentation. A new formulation for the energy function controlling the level set propagation has been introduced taking into account the specific properties of the nodules. Finally, a novel approach for classification of the segmented nodules into categories has been introduced. Geometric object descriptors such as the SIFT, AS 1FT, SURF and LBP have been used for feature extraction and matching of small size lung nodules; the LBP has been found to be the most robust. Categorization implies classification of detected and segmented objects into classes or types. The object descriptors have been deployed in the detection step for false positive reduction, and in the categorization stage to assign a class and type for the nodules. The AAMI ASMI A TM models have been used for the categorization stage. The front-end processes of lung nodule modeling, detection, segmentation and classification/categorization are model-based and data-driven. This dissertation is the first attempt in the literature at creating an entirely model-based approach for lung nodule analysis

Digital Image Processing

This book presents several recent advances that are related or fall under the umbrella of 'digital image processing', with the purpose of providing an insight into the possibilities offered by digital image processing algorithms in various fields. The presented mathematical algorithms are accompanied by graphical representations and illustrative examples for an enhanced readability. The chapters are written in a manner that allows even a reader with basic experience and knowledge in the digital image processing field to properly understand the presented algorithms. Concurrently, the structure of the information in this book is such that fellow scientists will be able to use it to push the development of the presented subjects even further

Multiscale analysis of geometric planar deformations: application to wild animals electronic tracking and satellite ocean observation data

International audienceThe development of animal tracking technologies (including for instance GPS and ARGOS satellite systems) and the increasing resolution of remote sensing observations call for tools extracting and describing the geometric patterns along a track or within an image over a wide range of spatial scales. Whereas shape analysis has largely been addressed over the last decades, the multiscale analysis of the geometry of opened planar curves has received little attention. We here show that classical multiscale techniques cannot properly address this issue and propose an original wavelet-based scheme. To highlight the generic nature of our multiscale wavelet technique, we report applications to two different observation datasets, namely wild animal movement paths recorded by electronic tags and satellite observations of sea surface geophysical fields

First Principles Investigations of Novel Condensed Matter Materials

The advent of very fast computing power has led to the positioning of theoretical investigations of condensed matter materials as a core part of research in this area. Often the results of such numerical and computational investigations serve as reliable guide for future experimental exploration of new materials and has led to the discovery of numerous materials. In this thesis, state-of-the-art first principles calculations have been applied to investigate the structural, electronic and dynamical properties of some novel condensed matter materials. The novelty of these compounds stems from the fact that they challenge our previous knowledge of the chemistry of chemical reactions that support the formation and stability of chemical compounds and can therefore expand our frontier of knowledge in the quest for scientific understanding of new atypical compounds in high pressure physics. In the first project, the long sought post-Cmcm phase of the cadmium telluride is characterized with the application of first principles metadynamics method. It has a monoclinic unit cell and the P21/m space group. Enthalpy calculation confirms this phase transition sequence and further predicts a P21/m to P4/nmm transition near 68 GPa. Interestingly, the enthalpies of CdTe compounds are found to be higher than the enthalpy sum of its constituents Cd and Te at pressures higher than 34 GPa which is an indication that the com-pound should decompose above this pressure point. However, dynamical stability revealed in the phonon dispersion relations prevents the decomposition of CdTe at high pressure. This suggests that CdTe becomes a high-enthalpy compound at high pressure. The second project is directed towards the prediction of stable helium-hydrogen compound. In spite of extensive experimental and theoretical work, a general agreement on the crystal structure and stability of the helium-hydrogen system is lacking. In this study, the possibility of helium forming stable compound with hydrogen is investigated by using first principles structure search method. A stable helium hydrogen compound formed at ambient conditions is found. It belongs to the triclinic P-1 space group, having He(H2)3stoichiometry. Topological analysis of electron density at the bond critical points shows there exists a quantifiable level of bonding interaction between helium and hydrogen in the P-1 structure. At ambient pressure, the compound is characterized and stabilized by interactions with strength typical of van der Waals interaction that increases with pressure. This current results provide a case of weak interaction in a mixed hydrogen-helium system, offering insights for the evolution of interiors of giant planets such as Jupiter and Saturn. In the final project, a machine learning potential is successfully created for sodium based on the Gaussian process regression method and weighted atom-centered symmetry functions representation of the potential energy surface. Here, sodium potential energy surface is described using different relevant data sets that represent several regions of the potential energy surface with each data set consisting of three element groups which are total energies, inter-atomic forces, and stress tensors of the cell, which were constructed from density functional theory calculations. It is demonstrated that by learning from the underlying density functional theory results, the trained machine learning potential is able to reproduce important properties of all available sodium phases with an exceptional accuracy in comparison to those computed using density functional theory. In combination with the metadynamics method, this well trained machine learning potential is applied to large simulation boxes containing1024 and 3456 sodium atoms in the cI16 phase. These large-scale simulations reveal a notable phase transition at 150 K and 120 GPa with an impressive capturing of the rearrangements of atomic configurations involved in the transition process that may not be evident in asmall-scale simulation. Without a doubt, this work shows that applying machine learning methods to condensed matter systems will lead to significant increase in our understanding of important processes such as atomic rearrangements, growth and nucleation process in crystal formation and phase transition

Saliency for Image Description and Retrieval

We live in a world where we are surrounded by ever increasing numbers of images. More often than not, these images have very little metadata by which they can be indexed and searched. In order to avoid information overload, techniques need to be developed to enable these image collections to be searched by their content. Much of the previous work on image retrieval has used global features such as colour and texture to describe the content of the image. However, these global features are insufficient to accurately describe the image content when different parts of the image have different characteristics. This thesis initially discusses how this problem can be circumvented by using salient interest regions to select the areas of the image that are most interesting and generate local descriptors to describe the image characteristics in that region. The thesis discusses a number of different saliency detectors that are suitable for robust retrieval purposes and performs a comparison between a number of these region detectors. The thesis then discusses how salient regions can be used for image retrieval using a number of techniques, but most importantly, two techniques inspired from the field of textual information retrieval. Using these robust retrieval techniques, a new paradigm in image retrieval is discussed, whereby the retrieval takes place on a mobile device using a query image captured by a built-in camera. This paradigm is demonstrated in the context of an art gallery, in which the device can be used to find more information about particular images. The final chapter of the thesis discusses some approaches to bridging the semantic gap in image retrieval. The chapter explores ways in which un-annotated image collections can be searched by keyword. Two techniques are discussed; the first explicitly attempts to automatically annotate the un-annotated images so that the automatically applied annotations can be used for searching. The second approach does not try to explicitly annotate images, but rather, through the use of linear algebra, it attempts to create a semantic space in which images and keywords are positioned such that images are close to the keywords that represent them within the space