Computational Point Of View Research Articles

A non-intrusive data-driven reduced order model for parametrized CFD-DEM numerical simulations

The investigation of fluid-solid systems is very important in a lot of industrial processes. From a computational point of view, the simulation of such systems is very expensive, especially when a huge number of parametric configurations needs to be studied. In this context, we develop a non-intrusive data-driven reduced order model (ROM) built using the proper orthogonal decomposition with interpolation (PODI) method for Computational Fluid Dynamics (CFD) - Discrete Element Method (DEM) simulations. The main novelties of the proposed approach rely in (i) the combination of ROM and FV methods, (ii) a numerical sensitivity analysis of the ROM accuracy with respect to the number of POD modes and to the cardinality of the training set and (iii) a parametric study with respect to the Stokes number. We test our ROM on the fluidized bed benchmark problem. The accuracy of the ROM is assessed against results obtained with the FOM both for Eulerian (the fluid volume fraction) and Lagrangian (position and velocity of the particles) quantities. We also discuss the efficiency of our ROM approach.

Construction of quantile regression using natural gradient descent

Building mathematical models is an important part of developing digital products in various industries, medicine, geology, construction, finance and other areas. Modeling allows optimizing production processes, identifying patterns, predicting time series, classifying objects, and constructing regressions. Quantile regression models are a generalization of median regression and can be used to examine data in depth. Quantile analysis involves estimating model parameters and determining quantile values of the dependent variable for given values of the independent variable. This is done by minimizing the loss function based on quantile values. In contrast to the method of least squares, quantile regression allows to predict the values of the dependent variable more accurately when the values of the independent variable change. That is, quantile regression is more robust. It can be used to solve many problems in various fields of science and business, where it is necessary to more accurately predict the values of the dependent variable under changing conditions. The natural gradient descent is an effective method for constructing regression and has a higher rate of convergence than the classical algorithm. However, in practice this method is quite complicated from a computational point of view, since it requires the calculation of the second derivative. This problem is especially acute when training neural networks, where the number of parameters is much higher than when building classical regression models. The study of methods of regression construction and application of numerical methods are of practical and scientific interest. This paper will look at quantile regression, natural gradient descent and their combination to build mathematical models. Gradient descent is one of the most popular optimization methods and is widely used in machine learning. The natural gradient descent is the preferred method because it is more efficient and has a high rate of convergence. In addition, this method is less vulnerable to hitting local minima and provides more accurate estimates of model parameters. In practice, however, this method is computationally difficult, as it requires the calculation of the second derivative. The article presents an algorithm for model building using natural gradient descent. The essence of using quantile regression in a natural gradient descent is to use a quantile estimate of the loss function instead of the usual estimate used in the least squares method. This allows not only the mean value of the dependent variable, but also more extreme values (e.g., median, 25th percentile, 95th percentile, etc.) to be considered when constructing the model. The resulting method has also been compared with other popular quantile regression-supported gradient descent methods on open data sets of different dimensionality, both in terms of the number of factors and the number of observations. In addition, the possibilities of further development and optimization of this method will be discussed.

Performance Assessment Comparison between Physically Based and Regression Hydrological Modelling: Case Study of the Euphrates–Tigris Basin

This paper presents two hydrological models developed for the Euphrates–Tigris Basin in Turkey. The first model is a linear regression-based model allowing the estimation of streamflow based on available hydroclimatic data (precipitation, temperature, evapotranspiration, etc.) with the use of clustering analysis. The second model consists of an elevation-based semi-distributed hydrological model (HBV model), allowing process-based modelling of the watershed. A set of performance metrics identified the HBV model as the best performance in terms of predicting streamflow (NSE = 0.752), while the RCA4-EU regression model of CORDEX showed the most robust performance. The results show the potential of regression models from a computational and data point of view in being integrated into physically based models wherein a hybrid approach might be beneficial. The comparison of conceptual models with statistical analyses of streamflow shows the potential of regression analysis when the regions are clustered in hydro-meteorologically homogeneous groups. The employment of the conceptual model HBV also provides significantly robust streamflow estimation for the region, which is especially important in estimating the hydropower potential of the region’s near future.

Different Experimental and Numerical Models to Analyse Emptying Processes in Pressurised Pipes with Trapped Air

In hydraulic engineering, some researchers have developed different mathematical and numerical tools for a better understanding of the physical interaction between water flow in pipes with trapped air during emptying processes, where they have made contributions on the use of simple and complex models in different application cases. In this article, a comparative study of different experimental and numerical models existing in the literature for the analysis of trapped air in pressurised pipelines subjected to different scenarios of emptying processes is presented, where different authors have develope, experimental, one-dimensional mathematical and complex computational fluid dynamics (CFD) models (two-dimensional and three-dimensional) to understand the level of applicability of these models in different hydraulic scenarios, from the physical and computational point of view. In general, experimental, mathematical and CFD models had maximum Reynolds numbers ranging from 2670 to 20,467, and it was possible to identify that the mathematical models offered relevant numerical information in a short simulation time on the order of seconds. However, there are restrictions to visualise some complex hydraulic and thermodynamic phenomena that CFD models are able to illustrate in detail with a numerical resolution similar to the mathematical models, and these require simulation times of hours or days. From this research, it was concluded that the knowledge of the information offered by the different models can be useful to hydraulic engineers to identify physical and numerical elements present in the air–water interaction and computational conditions necessary for the development of models that help decision-making in the field of hydraulics of pressurised pipelines.

Gradient-based descent linesearch to solve interval-valued optimization problems under gH-differentiability with application to finance

In this article, gradient based descent line search scheme is proposed to solve interval optimization problems under generalized Hukuhara differentiability. The innovation and importance of these concepts are presented from practical and computational point of view. The necessary condition for existence of critical point is presented in inclusion form of interval-valued gradient, without transforming it into real valued function. Suitable efficient descent direction is chosen based on the monotonic property of the interval-valued function and specific interval ordering. Mathematical convergence of the scheme is proved under the assumption of Inexact line search for interval optimization problem. The theoretical developments are implemented with a set of interval test problems in different dimensions. A possible application in finance is provided and solved by our proposed scheme.

Oxidative dehydrogenation of alcohols on gold: An experimental and computational study on the role of water and the alcohol chain length

The oxidative dehydrogenation of primary alcohols promoted by gold nanoparticles was investigated from an experimental and computational viewpoint to derive a plausible reaction mechanism and to understand the role of water and alcohol chain length in the elementary steps. The influence of water in reaction kinetics and product distribution was determined in a laboratory-scale microreactor adding water to the reaction mixture in different amounts. DFT calculations revealed that the presence of water on the catalyst surface is beneficial to assist the key step in alcohol oxidation i.e., oxygen activation by protonation. The calculations were performed for primary alcohols ranging from methanol to butanol to understand the role of the alkyl chain length on the catalytic activity and to clarify experimental observations. General conclusions were drawn on the influence of temperature on product distribution when employing a typical support material for gold nanoparticles, Al2O3. The combination of experiments and theory has been useful to improve the knowledge of alcohol oxidation promoted by gold.

A nuanced understanding of the doping of poly(3,4-ethylenedioxythiophene) with tosylate

The conducting polymer poly(3,4-ethylenedioxythiophene) (known as PEDOT) is routinely fabricated into doped thin films for investigation of its inherent properties as well as for a range of applications. Fabrication of PEDOT is often achieved via oxidative polymerisation, where the conducting polymer is polymerised and doped (oxidised) to yield a conductive polymer thin film. The oxidiser and the polymerisation temperature are two parameters that may influence the properties and performance of the resultant PEDOT thin film. In this study, the role of temperature for the chemical polymerisation of PEDOT using the oxidiser iron tosylate is investigated from a computational and experimental viewpoint. While computations of the doping energetics suggest increasing doping with increasing temperature, x-ray photoelectron spectroscopy of fabricated PEDOT thin films indicate doping is much more complicated. With the aid of computations of the spatial distribution functions for tosylate in PEDOT, experiments indicate that two different populations of tosylate anions exist in the PEDOT matrix. Their relative populations change as a function of the polymerisation temperature. Therefore, polymerisation temperature plays a critical role in tailoring the properties of PEDOT in pursuit of being fit-for-purpose for the desired application.

A new self-adaptive iterative method for variational inclusion problems on Hadamard manifolds with applications

The objective of this work is to design a new iterative method based on Armijo’s type-modified extragradient method for solving the inclusion problem $$\varvec{(A+B)^{-1}(0)}$$ , where $$\varvec{A}$$ is a maximal monotone vector field and $$\varvec{B}$$ is a continuous monotone vector field. The proposed method requires one projection at each iteration, reducing the cost of computational viewpoint and improving the convergence rate. A convergence theorem is established for the proposed extragradient method, significantly improving existing results. We provide concrete examples of Hadamard manifolds and convergency for numerical confirmation. Moreover, we demonstrate convergence results for the variational inequality problems in which the vector field’s monotonicity can be removed.

Implicit Annealing in Kernel Spaces: A Strongly Consistent Clustering Approach.

Kernel k-means clustering is a powerful tool for unsupervised learning of non-linearly separable data. Its merits are thoroughly validated on a suite of simulated datasets and real data benchmarks that feature nonlinear and multi-view separation. Since the earliest attempts, researchers have noted that such algorithms often become trapped by local minima arising from the non-convexity of the underlying objective function. In this paper, we generalize recent results leveraging a general family of means to combat sub-optimal local solutions to the kernel and multi-kernel settings. Called Kernel Power k-Means, our algorithm uses majorization-minimization (MM) to better solve this non-convex problem. We show that the method implicitly performs annealing in kernel feature space while retaining efficient, closed-form updates. We rigorously characterize its convergence properties both from computational and statistical points of view. In particular, we characterize the large sample behavior of the proposed method by establishing strong consistency guarantees as well as finite-sample bounds on the excess risk of the estimates through modern tools in learning theory. The proposal's efficacy is demonstrated through an array of simulated and real data experiments.

Computationally efficient methodology of 3D thermal-hydraulic analysis of Diagnostic Shielding Module #2 of ITER Equatorial Port #11

The process of design justification of Diagnostic Shielding Modules (DSMs) of port plugs of the International Thermonuclear Experimental Reactor (ITER) includes a stage of thermal-hydraulic computational analysis. The ITER tokamak operates in a pulsation mode that means the nuclear heating affecting DSMs is unsteady, and transient analysis is required. Three-dimensional (3D) approaches for fully coupled thermal-hydraulic analysis, which imply simultaneous computations for fluid and solid parts of a 3D DSM model, lead typically to “heavy” numerical models being very expensive from the computational point of view, especially for transient simulations. In order to significantly reduce the consumption of computational resources, the present 3D thermal-hydraulic analysis of DSM #2 of ITER Equatorial Port #11 was performed using one-way coupling. Firstly, steady-state CFD computations of turbulent flow were performed for the front part of DSM cooling system, which is a high-density network of channels of complex geometry. Obtained in CFD analysis map of wall shear stress on surface of channels was then converted into a map of local heat transfer coefficient using a simple and conservative approach based on known empirical correlations for turbulent flow in a circular pipe. For the back part of DSM cooling system, which basically consist of many relatively long channels, an individual (single) value of heat transfer coefficient for each of the channels was directly evaluated using empirical correlation. The heat transfer coefficient maps obtained for both parts of DSM cooling system were used finally as a boundary condition in transient thermal analysis of the solid part of the DSM model. Details and justifications of the described computationally-efficient methodology are presented.

Approximate oblique dual frames

In representations using frames, oblique duality appears in situations where the analysis and the synthesis has to be done in different subspaces. In some cases, we cannot obtain an explicit expression for the oblique duals and in others there exists only one oblique dual frame which has not the properties we need. Also, in practice the computations are not exact. To give a solution to these problems, in this work we introduce and investigate the notion of approximate oblique dual frames first in the setting of separable Hilbert spaces. We present several properties and provide different characterizations of approximate oblique dual frames. We focus then on approximate oblique dual frames in shift-invariant subspaces of L2(R) and give different conditions on the generators that assure their existence. The importance of approximate oblique dual frames from a numerical and computational point of view is illustrated with an example of frame sequences generated by B-splines, where the previous results are used to construct approximate oblique dual frames which have better attributes than the exact ones. We provide an expression for the approximation error and study its behaviour.

Вычислительная эффективность интерполированных полосно-заграждающих фильтров для нечетных спектральных зон

Interpolated band stop FIR filters are excluded. A block diagram of an interpolated band stop FIR filter for odd spectral regions is proposed. The use of the proposed maximum allowable value of the filter coefficient in comparison with the reference filter calculated by the classical method, namely the maximum allowable value of the quantitative limitation to the computing resource. For the proposed structure, relations are obtained to determine the coefficient of computational efficiency and the coefficient of increase in the number of registers. In the proposed work, the following values were determined: the optimal interpolation coefficient, the maximum coefficient of computational efficiency and the coefficient of increase in the number of registers at the optimal interpolation coefficient. In the obtained relations for the synthesis of the interpolated band-stop FIR filter, the values of the stop band and the central frequency of the rejection are used. We also compared the interpolated band stop filter for odd spectral zones, synthesized according to the proposed structure, and the reference band stop filter calculated by the classical method. As a result of the study, it was found that the proposed nature is used under specific conditions. The obtained structure of the interpolated band stop FIR filter is optimal from a computational point of view, however, the calculated structure is not universal. The main limitation for the application of the resulting structure is the discreteness of switching between spectral zones and the need for fine tuning of the center rejection frequency.

MAQA: a quantum framework for supervised learning

Quantum machine learning has the potential to improve traditional machine learning methods and overcome some of the main limitations imposed by the classical computing paradigm. However, the practical advantages of using quantum resources to solve pattern recognition tasks are still to be demonstrated. This work proposes a universal, efficient framework that can reproduce the output of a plethora of classical supervised machine learning algorithms exploiting quantum computation’s advantages. The proposed framework is named Multiple Aggregator Quantum Algorithm (MAQA) due to its capability to combine multiple and diverse functions to solve typical supervised learning problems. In its general formulation, MAQA can be potentially adopted as the quantum counterpart of all those models falling into the scheme of aggregation of multiple functions, such as ensemble algorithms and neural networks. From a computational point of view, the proposed framework allows generating an exponentially large number of different transformations of the input at the cost of increasing the depth of the corresponding quantum circuit linearly. Thus, MAQA produces a model with substantial descriptive power to broaden the horizon of possible applications of quantum machine learning with a computational advantage over classical methods. As a second meaningful addition, we discuss the adoption of the proposed framework as hybrid quantum–classical and fault-tolerant quantum algorithm.

The environment as a frontier of efficiency in tissue P systems with communication rules

Originally, in P systems the environment plays a passive role; that is, it can only receive objects, without having the ability to send objects to the system. Later, tissue P systems were introduced, where the cells are located in the environment in the sense that they can communicate between each other but also with the environment. In fact, a special alphabet was introduced as a way to symbolize the chemical elements available in it and that can interact with the cells. In the framework of membrane computing, all the objects of this alphabet are present in the environment with an arbitrary multiplicity at the beginning of the computation; that is, there are enough objects of this type in the environment to fire the rules that can be fired by these objects. From the computational complexity point of view, it seems to be a very strong ingredient, since it adds a virtually infinite number of objects to the system in the whole computation. In this paper, we demonstrate that the behaviour of this special alphabet can be simulated by a generation stage ruled by evolutional communication rules and/or division/separation rules, such that the ability of these systems to efficiently solve presumably hard problems is not changed if the environment does not play an active role.

EEG-Based BCIs on Motor Imagery Paradigm Using Wearable Technologies: A Systematic Review.

In recent decades, the automatic recognition and interpretation of brain waves acquired by electroencephalographic (EEG) technologies have undergone remarkable growth, leading to a consequent rapid development of brain-computer interfaces (BCIs). EEG-based BCIs are non-invasive systems that allow communication between a human being and an external device interpreting brain activity directly. Thanks to the advances in neurotechnologies, and especially in the field of wearable devices, BCIs are now also employed outside medical and clinical applications. Within this context, this paper proposes a systematic review of EEG-based BCIs, focusing on one of the most promising paradigms based on motor imagery (MI) and limiting the analysis to applications that adopt wearable devices. This review aims to evaluate the maturity levels of these systems, both from the technological and computational points of view. The selection of papers has been performed following the Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA), leading to 84 publications considered in the last ten years (from 2012 to 2022). Besides technological and computational aspects, this review also aims to systematically list experimental paradigms and available datasets in order to identify benchmarks and guidelines for the development of new applications and computational models.

CLUSTERIZATION OF DATA ARRAYS BASED ON THE MODIFIED GRAY WOLF ALGORITHM

Context. The task of clustering arrays of multidimensional data, the main goal of which is to find classes of observations that are homogeneous in the sense of the accepted metric, is an important part of the intelligent data analysis of Data Mining. From a computational point of view, the problem of clustering turns into the problem of finding local extrema of a multiextreme function, which are repeatedly started from different points of the original data array. To speed up the process of finding these extrema using the ideas of evolutionary optimization, which includes algorithms inspired by nature, swarm algorithms, population algorithms, etc.
 Objective. The purpose of the work is to introduce a procedure for clustering data arrays based on the improved gray wolf algorithm.
 Method. A method of clustering data arrays based on the modified gray wolf algorithm is introduced. The advantage of the proposed approach is a reduction in the time of solving optimization problems in conditions where clusters are overlap. A feature of the proposed method is computational simplicity and high speed, due to the fact that the entire array is processed only once, that is, eliminates the need for multi-era self-learning, implemented in traditional fuzzy clustering algorithms.
 Results. The results of the experiments confirm the effectiveness of the proposed approach in clustering problems under the condition of classes that overlap and allow us to recommend the proposed method for use in practice to solve problems of automatic clustering big data.
 Conclusions. A method of clustering data arrays based on the modified gray wolf algorithm is introduced. The advantage of the proposed approach is the reduction of time for solving optimization problems. The results of the experiments confirm the effectiveness of the proposed approach in clustering problems under the conditions of overlapping clusters.

Latent dirichlet allocation for double clustering (LDA-DC): discovering patients phenotypes and cell populations within a single Bayesian framework

BackgroundCurrent clinical routines rely more and more on “omics” data such as flow cytometry data from host and microbiota. Cohorts variability in addition to patients’ heterogeneity and huge dimensions make it difficult to understand underlying structure of the data and decipher pathologies. Patients stratification and diagnostics from such complex data are extremely challenging. There is an acute need to develop novel statistical machine learning methods that are robust with respect to the data heterogeneity, efficient from the computational viewpoint, and can be understood by human experts.ResultsWe propose a novel approach to stratify cell-based observations within a single probabilistic framework, i.e., to extract meaningful phenotypes from both patients and cells data simultaneously. We define this problem as a double clustering problem that we tackle with the proposed approach. Our method is a practical extension of the Latent Dirichlet Allocation and is used for the Double Clustering task (LDA-DC). We first validate the method on artificial datasets, then we apply our method to two real problems of patients stratification based on cytometry and microbiota data. We observe that the LDA-DC returns clusters of patients and also clusters of cells related to patients’ conditions. We also construct a graphical representation of the results that can be easily understood by humans and are, therefore, of a big help for experts involved in pre-clinical research.

Distributed iterative reweighted least squares algorithm for high-resolution finite-frequency traveltime velocity inversion using VSP data

Seismic traveltime between a source-receiver pair is a finite-frequency phenomenon. The velocity information at all points inside the first Fresnel zone is contained inside the traveltime. Therefore, finite-frequency traveltime velocity inversion (FFTVI) is able to invert velocity with finer structures than that can be obtained by ray-based tomography. Since FFTVI is a global inversion, its cost is lower than full waveform inversion. The implementation in this paper mainly focuses on the numerical aspects of FFTVI. We analyze the characteristics of FFTVI from the computational point of view. A parallel version, Iterative Reweighted Least Squares (IRLS) is designed for solving a large linear system in the memories of computer clusters. This implementation not only yields the accurate inversion of velocity at arbitrary grids and with an arbitrary acquisition geometry, but also is able to mitigate the impacts of traveltime picks with large uncertainties. The proposed workflow and parallel algorithm are demonstrated on synthetic VSP examples designed from a land project.

On Kosloff Tal-Ezer least-squares quadrature formulas

In this work, we study a global quadrature scheme for analytic functions on compact intervals based on function values on quasi-uniform grids of quadrature nodes. In practice it is not always possible to sample functions at optimal nodes that give well-conditioned and quickly converging interpolatory quadrature rules at the same time. Therefore, we go beyond classical interpolatory quadrature by lowering the degree of the polynomial approximant and by applying auxiliary mapping functions that map the original quadrature nodes to more suitable fake nodes. More precisely, we investigate the combination of the Kosloff Tal-Ezer map and least-squares approximation (KTL) for numerical quadrature: a careful selection of the mapping parameter ensures stability of the scheme, a high accuracy of the approximation and, at the same time, an asymptotically optimal ratio between the degree of the polynomial and the spacing of the grid. We will investigate the properties of this KTL quadrature and focus on the symmetry of the quadrature weights, the limit relations for the mapping parameter, as well as the computation of the quadrature weights in the standard monomial and in the Chebyshev bases with help of a cosine transform. Numerical tests on equispaced nodes show that a static choice of the map’s parameter improve the results of the composite trapezoidal rule, while a dynamic approach achieves larger stability and faster convergence, even when the sampling nodes are perturbed. From a computational point of view the proposed method is practical and can be implemented in a simple and efficient way.

An immersed Crouzeix–Raviart finite element method in 2D and 3D based on discrete level set functions

This paper is devoted to the construction and analysis of immersed finite element (IFE) methods in three dimensions. Different from the 2D case, the points of intersection of the interface and the edges of a tetrahedron are usually not coplanar, which makes the extension of the original 2D IFE methods based on a piecewise linear approximation of the interface to the 3D case not straightforward. We address this coplanarity issue by an approach where the interface is approximated via discrete level set functions. This approach is very convenient from a computational point of view since in many practical applications the exact interface is often unknown, and only a discrete level set function is available. As this approach has also not be considered in the 2D IFE methods, in this paper we present a unified framework for both 2D and 3D cases. We consider an IFE method based on the traditional Crouzeix–Raviart element using integral values on faces as degrees of freedom. The novelty of the proposed IFE is the unisolvence of basis functions on arbitrary triangles/tetrahedrons without any angle restrictions even for anisotropic interface problems, which is advantageous over the IFE using nodal values as degrees of freedom. The optimal bounds for the IFE interpolation errors are proved on shape-regular triangulations. For the IFE method, optimal a priori error and condition number estimates are derived with constants independent of the location of the interface with respect to the unfitted mesh. The extension to anisotropic interface problems with tensor coefficients is also discussed. Numerical examples supporting the theoretical results are provided.