Accelerated continuous time quantum Monte Carlo method with machine learning

We investigate the Hubbard model on the triangular lattice at half-filling using the dynamical cluster approximation (DCA) and dual fermion (DF) methods in combination with continuous-time quantum Monte carlo (CT QMC) and semiclassical approximation (SCA) methods. We study the one-particle properties and nearest-neighbor spin correlations using the DCA method. We calculate the spectral functions using the CT QMC and SCA methods. The spectral function in the SCA and obtained by analytic continuation of the Pade approximation in CT QMC are in good agreement. We determine the metal-insulator transition (MIT) and the hysteresis associated with a first-order transition in the double occupancy and nearest-neighbor spin correlation functions as a function of temperature. As a further check, we employ the DF method and discuss the advantages and limitation of the dynamical mean field theory (DMFT), DCA and recently developed DF methods by comparing Green's functions. We find an enhancement of antiferromagnetic (AF) correlations and provide evidence for magnetically ordered phases by calculating the spin susceptibility.

Dynamical mean-field theory (DMFT) is one of the most widely-used methods to treat accurately electron correlation effects in ab-initio real material calculations. Many modern large-scale implementations of DMFT in electronic structure codes involve solving a quantum impurity model with a Continuous-Time Quantum Monte Carlo (CT-QMC) solver. The main advantage of CT-QMC is that, unlike standard quantum Monte Carlo approaches, it is able to generate the local Green's functions of the correlated system on an arbitrarily fine imaginary time grid, and is free of any systematic errors. In this work, we extend a hybrid QMC solver proposed by Khatami et al. and Rost et al. to a multi-orbital context. This has the advantage of enabling impurity solver QMC calculations to scale linearly with inverse temperature and permit its application to d and f band materials. In addition, we present a novel Green's function processing scheme which generates accurate quasi-continuous imaginary time solutions of the impurity problem which overcome errors inherent to standard QMC approaches. This solver and processing scheme are incorporated into a full DFT+DMFT calculation using the CASTEP DFT code. Benchmark calculations for strontium vanadate properties are presented.

The applicability of Green's function (GF) and Feynman path-integral quantum Monte Carlo (QMC) methods for the simulation of cyclic networks with (4n + 2) and 4n (n = 1, 2, 3, …) electrons is analysed. Both QMC techniques are employed in simulations on the basis of the simple Huckel Hamiltonian which is exclusively defined by nearest-neighbour hopping elements. In addition we have used the Pariser-Parr-Pople (PPP) Hamiltonian to perform GF QMC simulations. The electronic energies E derived by the QMC methods are compared either with Huckel molecular orbital (HMO) results or exact configuration interaction data where (π) electronic correlations are fully taken into account. A sign problem occurs in QMC simulations of 4n annulenes. This leads to an error in the total energy in the standard formulations of the employed QMC techniques, which is enhanced with decreasing ring size. A simple modification in the QMC formalisms is suggested to avoid the numerical uncertainties caused by the sign problem in 4n annu...

We present a guiding principle for designing fermionic Hamiltonians and quantum MonteCarlo (QMC) methods that are free from the infamous sign problem by exploiting the Lie groups and Lie algebras that appear naturally in the MonteCarlo weight of fermionic QMC simulations. Specifically, rigorous mathematical constraints on the determinants involving matrices that lie in the split orthogonal group provide a guideline for sign-free simulations of fermionic models on bipartite lattices. This guiding principle not only unifies the recent solutions of the sign problem based on the continuous-time quantum MonteCarlo methods and the Majorana representation, but also suggests new efficient algorithms to simulate physical systems that were previously prohibitive because of the sign problem.

Efficient continuous time quantum Monte Carlo (CT-QMC) algorithms that do not suffer from time discretization errors have become the state-of-the-art for most discrete quantum models. They have not been widely used yet for fermionic quantum lattice models, such as the Hubbard model, due to a suboptimal scaling of $O(\beta^3)$ with inverse temperature $\beta$, compared to the linear scaling of discrete time algorithms. Here we present a CT-QMC algorithms for fermionic lattice models that matches the scaling of discrete-time methods but is more efficient and free of time discretization errors. This provides an efficient simulation scheme that is free from the systematic errors opening an avenue to more precise studies of large systems at low temperatures.

Electronic structure calculations by quantum Monte Carlo methods

The possibilities and problems to predict excited-state acidities and basicities in water with electronic structure calculations combined with a continuum solvation model are investigated for a test set of photoacids and photobases. Different error sources, like errors in the ground-state values, the excitation energies in solution for the neutral and (de-)protonated species, basis set effects, and contributions beyond implicit solvation are investigated and their contributions to the total error in are discussed. Density functional theory in combination with the conductor like screening model for real solvents and an empirical linear Gibbs free energy relationship are used to predict the ground-state values. For the test set, this approach gives more accurate values for the acids than for the bases. Time-dependent density-functional theory (TD-DFT) and second-order wave function methods in combination with the conductor like screening model are applied to compute excitation energies in water. Some TD-DFT functionals fail for several species to predict correctly the order of the lowest excitations. Where experimental data for absorption maxima in water is available, the implicit solvation model leads with the applied electronic structure methods in most cases for the excitation energies in water to an overestimation for the protonated and to an underestimation for the deprotonated species. The magnitude and sign of the errors depend on the hydrogen bond donating and accepting ability of the solute. We find that for aqueous solution this results generally in an underestimation in the changes from the ground to the excited state for photoacids and an overestimation for photobases.

We present a strategy to alleviate the sign problem in continuous-time quantum Monte Carlo (CTQMC) simulations of the dynamical-mean-field-theory (DMFT) equations for the spin-orbit-coupled multiorbital Hubbard model. We first identify the combinations of rotationally invariant Hund coupling terms present in the relativistic basis which lead to a severe sign problem. Exploiting the fact that the average sign in CTQMC depends on the choice of single-particle basis, we propose a bonding-antibonding basis $V_{j3/2\mathrm{BA}}$ which shows an improved average sign compared to the widely used relativistic basis for most parameter sets investigated. We then generalize this procedure by introducing a stochastic optimization algorithm that exploits the space of single-particle bases and show that $V_{j3/2\mathrm{BA}}$ is very close to optimal within the parameter space investigated. Our findings enable more efficient DMFT simulations of materials with strong spin-orbit coupling.

Chapter 1 Path-integral quantum Monte Carlo studies of the vibrational properties of crystals

We report a study of metal-insulator transition of a strongly correlated two-band Hubbard model using a dynamical mean-field theory approach. We find that the Mott transition appears at half filling even at $T=0$ in contrast to the one-band Hubbard model. The transition is characterized by the development of a ``Kondo-like'' peak near Fermi level. We also find a signature of the coexistence of metallic and antiferromagnetic phases from the study of the single-particle Green's function and the magnetic long-range order due to the superexchange coupling between the correlated electrons. We then suggest the relevance of our results to the metal-insulator transition and the recent angle-resolved photoemission measurements of ${\mathrm{NiS}}_{2\ensuremath{-}x}{\mathrm{Se}}_{x}.$ We also study the effect of carrier doping and the comparison of our findings with the experimental results suggests the possible importance of departures from stoichiometry associated with the Se substitution. The relevance of our results to high-temperature superconductivity is also discussed.

With the popularization of machine learning (ML) techniques and the increased chipset’s performance, the application of ML to pedestrian localization systems has received significant attention in the last years. Several survey papers have attempted to provide a state-of-the-art overview, but they usually limit their scope to a particular type of positioning system or technology. In addition, they are written from the point of view of ML techniques and their practice, not from the point of view of the localization system and the specific problems that ML techniques can help to solve. This article is intended to offer a comprehensive state-of-the-art survey of the ML techniques that have been adopted over the last ten years to improve the performance of pedestrian localization systems, addressing the applicability of ML techniques in this domain, along with the main localization strategies. It concludes by indicating the underlying open issues and challenges associated with the existing systems, and possible future directions in which ML techniques could improve the performance of pedestrian localization systems. Among other open issues, most previous authors have focused their attention on position estimation accuracy, which wastes the potential of ML techniques to improve other performance parameters (e.g., response time, computational complexity, robustness, scalability or energy efficiency). This study shows that there is a strong trend towards the application of supervised learning. Consequently, there are many potential research opportunities in the use of other learning types, such as unsupervised and reinforcement learning, to improve the performance of pedestrian localization systems.

Machine Learning (ML) techniques are pervasive tools in various emerging commercial applications, but have to be accommodated by powerful computer systems to process very large data. Although general-purpose CPUs and GPUs have provided straightforward solutions, their energy-efficiencies are limited due to their excessive supports for flexibility. Hardware accelerators may achieve better energy-efficiencies, but each accelerator often accommodates only a single ML technique (family). According to the famous No-Free-Lunch theorem in the ML domain, however, an ML technique performs well on a dataset may perform poorly on another dataset, which implies that such accelerator may sometimes lead to poor learning accuracy. Even if regardless of the learning accuracy, such accelerator can still become inapplicable simply because the concrete ML task is altered, or the user chooses another ML technique.In this study, we present an ML accelerator called PuDianNao, which accommodates seven representative ML techniques, including k-means, k-nearest neighbors, naive bayes, support vector machine, linear regression, classification tree, and deep neural network. Benefited from our thorough analysis on computational primitives and locality properties of different ML techniques, PuDianNao can perform up to 1056 GOP/s (e.g., additions and multiplications) in an area of 3.51 mm^2, and consumes 596 mW only. Compared with the NVIDIA K20M GPU (28nm process), PuDianNao (65nm process) is 1.20x faster, and can reduce the energy by 128.41x.

Machine learning (ML) techniques have numerous applications in many fields, including healthcare, medicine, finance, marketing, and cyber security. For example, ML techniques are being applied to determine whether to give a loan to a customer or whether the computing system has been attacked. However, the ML techniques themselves may be subject to attacks and may discriminate when determining who should get the loan. Therefore, the ML techniques have to be secure, ensure privacy of the individuals, incorporate fairness and be accurate. Such collection of ML techniques has come to be known as trustworthy machine learning (trustworthy ML). This article describes an architecture to support scalable trustworthy ML and describes the features that have to be incorporated into the ML techniques to ensure that they are trustworthy.

A comprehensive review on detection of plant disease using machine learning and deep learning approaches

Code smells are considered symptoms of poor implementation choices, which may hamper the software maintainability. Hence, code smells should be detected as early as possible to avoid software quality degradation. Unfortunately, detecting code smells is not a trivial task. Some preliminary studies investigated and concluded that machine learning (ML) techniques are a promising way to better support smell detection. However, these techniques are hard to be customized to promote an early and accurate detection of specific smell types. Yet, ML techniques usually require numerous code examples to be trained (composing a relevant dataset) in order to achieve satisfactory accuracy. Unfortunately, such a dependency on a large validated dataset is impractical and leads to late detection of code smells. Thus, a prevailing challenge is the early customized detection of code smells taking into account the typical limited training data. In this direction, this paper reports a study in which we collected code smells, from ten active projects, that were actually refactored by developers, differently from studies that rely on code smells inferred by researchers. These smells were used for evaluating the accuracy regarding early detection of code smells by using seven ML techniques. Once we take into account such smells that were considered as important by developers, the ML techniques are able to customize the detection in order to focus on smells observed as relevant in the investigated systems. The results showed that all the analyzed techniques are sensitive to the type of smell and obtained good results for the majority of them, especially JRip and Random Forest. We also observe that the ML techniques did not need a high number of examples to reach their best accuracy results. This finding implies that ML techniques can be successfully used for early detection of smells without depending on the curation of a large dataset.