Renormalization group flows of Hamiltonians using tensor networks

A renormalization group flow of Hamiltonians for two-dimensional classical partition functions is constructed using tensor networks. Similar to tensor network renormalization ([G. Evenbly and G. Vidal, Phys. Rev. Lett. 115, 180405 (2015)], [S. Yang, Z.-C. Gu, and X.-G Wen, Phys. Rev. Lett. 118, 110504 (2017)]) we obtain approximate fixed point tensor networks at criticality. Our formalism however preserves positivity of the tensors at every step and hence yields an interpretation in terms of Hamiltonian flows. We emphasize that the key difference between tensor network approaches and Kadanoff's spin blocking method can be understood in terms of a change of local basis at every decimation step, a property which is crucial to overcome the area law of mutual information. We derive algebraic relations for fixed point tensors, calculate critical exponents, and benchmark our method on the Ising model and the six-vertex model.Comment: accepted version for Phys. Rev. Lett, main text: 5 pages, 3 figures, appendices: 9 pages, 1 figur

Development of a stochastic computational fluid dynamics approach for offshore wind farms

In this paper, a method for stochastic analysis of an offshore wind farm using computational fluid dynamics (CFD) is proposed. An existing offshore wind farm is modelled using a steady-state CFD solver at several deterministic input ranges and an approximation model is trained on the CFD results. The approximation model is then used in a Monte-Carlo analysis to build joint probability distributions for values of interest within the wind farm. The results are compared with real measurements obtained from the existing wind farm to quantify the accuracy of the predictions. It is shown that this method works well for the relatively simple problem considered in this study and has potential to be used in more complex situations where an existing analytical method is either insufficient or unable to make a good prediction

Core-periphery organization of complex networks

Networks may, or may not, be wired to have a core that is both itself densely connected and central in terms of graph distance. In this study we propose a coefficient to measure if the network has such a clear-cut core-periphery dichotomy. We measure this coefficient for a number of real-world and model networks and find that different classes of networks have their characteristic values. For example do geographical networks have a strong core-periphery structure, while the core-periphery structure of social networks (despite their positive degree-degree correlations) is rather weak. We proceed to study radial statistics of the core, i.e. properties of the n-neighborhoods of the core vertices for increasing n. We find that almost all networks have unexpectedly many edges within n-neighborhoods at a certain distance from the core suggesting an effective radius for non-trivial network processes

The role of emotional variables in the classification and prediction of collective social dynamics

We demonstrate the power of data mining techniques for the analysis of collective social dynamics within British Tweets during the Olympic Games 2012. The classification accuracy of online activities related to the successes of British athletes significantly improved when emotional components of tweets were taken into account, but employing emotional variables for activity prediction decreased the classifiers' quality. The approach could be easily adopted for any prediction or classification study with a set of problem-specific variables.Comment: 16 pages, 9 figures, 2 tables and 1 appendi

Theoretical Interpretations and Applications of Radial Basis Function Networks

Medical applications usually used Radial Basis Function Networks just as Artificial Neural Networks. However, RBFNs are Knowledge-Based Networks that can be interpreted in several way: Artificial Neural Networks, Regularization Networks, Support Vector Machines, Wavelet Networks, Fuzzy Controllers, Kernel Estimators, Instanced-Based Learners. A survey of their interpretations and of their corresponding learning algorithms is provided as well as a brief survey on dynamic learning algorithms. RBFNs' interpretations can suggest applications that are particularly interesting in medical domains

Deep Learning Applied to the Asteroseismic Modeling of Stars with Coherent Oscillation Modes

We develop a novel method based on machine learning principles to achieve optimal initiation of CPU-intensive computations for forward asteroseismic modeling in a multi-D parameter space. A deep neural network is trained on a precomputed asteroseismology grid containing about 62 million coherent oscillation-mode frequencies derived from stellar evolution models. These models are representative of the core-hydrogen burning stage of intermediate-mass and high-mass stars. The evolution models constitute a 6D parameter space and their predicted low-degree pressure- and gravity-mode oscillations are scanned, using a genetic algorithm. A software pipeline is created to find the best fitting stellar parameters for a given set of observed oscillation frequencies. The proposed method finds the optimal regions in the 6D parameters space in less than a minute, hence providing the optimal starting point for further and more detailed forward asteroseismic modeling in a high-dimensional context. We test and apply the method to seven pulsating stars that were previously modeled asteroseismically by classical grid-based forward modeling based on a $\chi^2$ statistic and obtain good agreement with past results. Our deep learning methodology opens up the application of asteroseismic modeling in +6D parameter space for thousands of stars pulsating in coherent modes with long lifetimes observed by the $Kepler$ space telescope and to be discovered with the TESS and PLATO space missions, while applications so far were done star-by-star for only a handful of cases. Our method is open source and can be used by anyone freely.Comment: Accepted for publication in PASP Speciale Volume on Machine Learnin

Artificial Neural Network in Cosmic Landscape

In this paper we propose that artificial neural network, the basis of machine learning, is useful to generate the inflationary landscape from a cosmological point of view. Traditional numerical simulations of a global cosmic landscape typically need an exponential complexity when the number of fields is large. However, a basic application of artificial neural network could solve the problem based on the universal approximation theorem of the multilayer perceptron. A toy model in inflation with multiple light fields is investigated numerically as an example of such an application.Comment: v2, add some new content