443 research outputs found

    Towards large-scale accurate Kohn-Sham DFT for the cost of tight-binding

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    PhD ThesisDensity functional theory (DFT) is a widely used ab initio quantum mechanical method to study the properties of materials. Over the past 20 years a huge amount of work has been done developing codes that are able to tackle calculations containing large numbers of atoms. AIMPRO, a DFT code which uses Gaussian type orbitals (GTO) as a basis set, uses a filtration methodology which makes calculations with a few thousand atoms routinely possible on desktop machines. Previous implementations of filtration have focused on the time saving aspect of the methodology and performed calculations on structures containing only atoms from a small subset of the periodic table. In this thesis a novel basis set generation routine is presented and the filtration methodology is modified and expanded to include most of the atoms in the periodic table. The focus of this work lies in demonstrating the potential gains in accuracy, in addition to efficiency, available through use of the filtration algorithm and shows that results comparable to codes using systematic basis set can be achieved for each of the elements considered across the periodic table. Two huge advantages present themselves using this scheme; firstly, the time to solution is essentially decoupled from the basis size; secondly, basis sets that would be unstable in a conventional calculation can be used allowing for more accurate calculations. The work presented here is assessed using a recently developed benchmark, the ∆-test. This, together with the increases in speed previously demonstrated, shows that a filtered basis calculation can now achieve the accuracy of a plane wave calculation at the asymptotic cost, with respect to system size, of a tight-binding calculation, enabling Kohn-Sham calculations of unprecedented size to be performed at the basis set limi

    O(N) methods in electronic structure calculations

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    Linear scaling methods, or O(N) methods, have computational and memory requirements which scale linearly with the number of atoms in the system, N, in contrast to standard approaches which scale with the cube of the number of atoms. These methods, which rely on the short-ranged nature of electronic structure, will allow accurate, ab initio simulations of systems of unprecedented size. The theory behind the locality of electronic structure is described and related to physical properties of systems to be modelled, along with a survey of recent developments in real-space methods which are important for efficient use of high performance computers. The linear scaling methods proposed to date can be divided into seven different areas, and the applicability, efficiency and advantages of the methods proposed in these areas is then discussed. The applications of linear scaling methods, as well as the implementations available as computer programs, are considered. Finally, the prospects for and the challenges facing linear scaling methods are discussed.Comment: 85 pages, 15 figures, 488 references. Resubmitted to Rep. Prog. Phys (small changes

    Advances of Machine Learning in Materials Science: Ideas and Techniques

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    In this big data era, the use of large dataset in conjunction with machine learning (ML) has been increasingly popular in both industry and academia. In recent times, the field of materials science is also undergoing a big data revolution, with large database and repositories appearing everywhere. Traditionally, materials science is a trial-and-error field, in both the computational and experimental departments. With the advent of machine learning-based techniques, there has been a paradigm shift: materials can now be screened quickly using ML models and even generated based on materials with similar properties; ML has also quietly infiltrated many sub-disciplinary under materials science. However, ML remains relatively new to the field and is expanding its wing quickly. There are a plethora of readily-available big data architectures and abundance of ML models and software; The call to integrate all these elements in a comprehensive research procedure is becoming an important direction of material science research. In this review, we attempt to provide an introduction and reference of ML to materials scientists, covering as much as possible the commonly used methods and applications, and discussing the future possibilities.Comment: 80 pages; 22 figures. To be published in Frontiers of Physics, 18, xxxxx, (2023

    Connected Attribute Filtering Based on Contour Smoothness

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    Policy space abstraction for a lifelong learning agent

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    This thesis is concerned with policy space abstractions that concisely encode alternative ways of making decisions; dealing with discovery, learning, adaptation and use of these abstractions. This work is motivated by the problem faced by autonomous agents that operate within a domain for long periods of time, hence having to learn to solve many different task instances that share some structural attributes. An example of such a domain is an autonomous robot in a dynamic domestic environment. Such environments raise the need for transfer of knowledge, so as to eliminate the need for long learning trials after deployment. Typically, these tasks would be modelled as sequential decision making problems, including path optimisation for navigation tasks, or Markov Decision Process models for more general tasks. Learning within such models often takes the form of online learning or reinforcement learning. However, handling issues such as knowledge transfer and multiple task instances requires notions of structure and hierarchy, and that raises several questions that form the topic of this thesis – (a) can an agent acquire such hierarchies in policies in an online, incremental manner, (b) can we devise mathematically rigorous ways to abstract policies based on qualitative attributes, (c) when it is inconvenient to employ prolonged trial and error learning, can we devise alternate algorithmic methods for decision making in a lifelong setting? The first contribution of this thesis is an algorithmic method for incrementally acquiring hierarchical policies. Working with the framework of options - temporally extended actions - in reinforcement learning, we present a method for discovering persistent subtasks that define useful options for a particular domain. Our algorithm builds on a probabilistic mixture model in state space to define a generalised and persistent form of ‘bottlenecks’, and suggests suitable policy fragments to make options. In order to continuously update this hierarchy, we devise an incremental process which runs in the background and takes care of proposing and forgetting options. We evaluate this framework in simulated worlds, including the RoboCup 2D simulation league domain. The second contribution of this thesis is in defining abstractions in terms of equivalence classes of trajectories. Utilising recently developed techniques from computational topology, in particular the concept of persistent homology, we show that a library of feasible trajectories could be retracted to representative paths that may be sufficient for reasoning about plans at the abstract level. We present a complete framework, starting from a novel construction of a simplicial complex that describes higher-order connectivity properties of a spatial domain, to methods for computing the homology of this complex at varying resolutions. The resulting abstractions are motion primitives that may be used as topological options, contributing a novel criterion for option discovery. This is validated by experiments in simulated 2D robot navigation, and in manipulation using a physical robot platform. Finally, we develop techniques for solving a family of related, but different, problem instances through policy reuse of a finite policy library acquired over the agent’s lifetime. This represents an alternative approach when traditional methods such as hierarchical reinforcement learning are not computationally feasible. We abstract the policy space using a non-parametric model of performance of policies in multiple task instances, so that decision making is posed as a Bayesian choice regarding what to reuse. This is one approach to transfer learning that is motivated by the needs of practical long-lived systems. We show the merits of such Bayesian policy reuse in simulated real-time interactive systems, including online personalisation and surveillance

    Large-scale local-orbital DFT calculations of Si - Ge core - shell nanowires

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    Nanowires, represent the smallest device dimensionality for efficient transport of electrons and other more exotic quasiparticles. Among a plethora of applications identified, research directed towards field-effect transistors (FETs), the building blocks of next-generation computer processors, is of utmost importance considering current 7 nm FET technologies are expected to be the limit of “top-down” manufacturing techniques. Characterisation of the mechanical and electronic properties of nanowires, by conventional electronic structure techniques, have coincidentally reached a limit due to the maximum simulation sizes they are capable of. CONQUEST is a code capable of simulation of millions of atoms using O(N) methods and thousands of atoms using Hamiltonian diagonalisation with a pseudo-atomic orbital basis. Physical quantities calculated using CONQUEST do not exhibit systematic convergence using PAO basis sets, unlike plane-wave codes, so we quantify PAO basis sizes needed to achieve comparable accuracy to plane-wave calculations for a variety of bulk and molecular systems with varying chemical environments. Implementation of the stress tensor, presented in this thesis, resulted in the discovery of slow stress convergence with respect to density matrix localisation. We quantify the O(N) simulation parameters necessary to achieve stress calculations to a required accuracy. We present the first study of experimentally relevant, surface reconstructed, Si (core) - Ge (shell) nanowires. Vegard’s law, used to quantify experimental results and as an approximation in theoretical calculations, has been found to poorly describe our nanowires and we assess the relative error due to its usage. Young’s modulus is shown to decrease with increasing shell deposition and dependent on relative nanowire composition. Poisson ratios, also correlated to composition, exhibit anisotropy. Shell deposition induced strain has been mapped by our method and shows strong anisotropy in different bonding directions. Our nanowires exhibit a direct-to-indirect band gap transition with intrinsic uniaxial strains > 0.5% and effective hole masses 50% smaller than similar unreconstructed nanowires. Finally, valence band offsets which are responsible for the formation of hole gases, were found to be double that of unreconstructed models
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