Splitting Algorithm Research Articles

Constraining deep mantle anisotropy with shear wave splitting measurements: challenges and new measurement strategies

SUMMARY Determinations of seismic anisotropy, or the dependence of seismic wave velocities on the polarization or propagation direction of the wave, can allow for inferences on the style of deformation and the patterns of flow in the Earth’s interior. While it is relatively straightforward to resolve seismic anisotropy in the uppermost mantle directly beneath a seismic station, measurements of deep mantle anisotropy are more challenging. This is due in large part to the fact that measurements of anisotropy in the deep mantle are typically blurred by the potential influence of upper mantle and/or crustal anisotropy beneath a seismic station. Several shear wave splitting techniques are commonly used that attempt resolve seismic anisotropy in deep mantle by considering the presence of multiple anisotropic layers along a raypath. Examples include source-side S-wave splitting, which is used to characterize anisotropy in the deep upper mantle and mantle transition zone beneath subduction zones, and differential S-ScS and differential SKS-SKKS splitting, which are used to study anisotropy in the D″ layer at the base of the mantle. Each of these methods has a series of assumptions built into them that allow for the consideration of multiple regions of anisotropy. In this work, we systematically assess the accuracy of these assumptions. To do this, we conduct global wavefield modelling using the spectral element solver AxiSEM3D. We compute synthetic seismograms for earth models that include seismic anisotropy at the periods relevant for shear wave splitting measurements (down to 5 s). We apply shear wave splitting algorithms to our synthetic seismograms and analyse whether the assumptions that underpin common measurement techniques are adequate, and whether these techniques can correctly resolve the anisotropy incorporated in our models. Our simulations reveal some inaccuracies and limitations of reliability in various methods. Specifically, explicit corrections for upper mantle anisotropy, which are often used in source-side direct S splitting and S-ScS differential splitting, are typically reliable for the fast polarization direction ϕ but not always for the time lag δt, and their accuracy depends on the details of the upper mantle elastic tensor. We find that several of the assumptions that underpin the S-ScS differential splitting technique are inaccurate under certain conditions, and we suggest modifications to traditional S-ScS differential splitting approaches that lead to improved reliability. We investigate the reliability of differential SKS-SKKS splitting intensity measurements as an indicator for lowermost mantle anisotropy and find that the assumptions built into the splitting intensity formula can break down for strong splitting cases. We suggest some guidelines to ensure the accuracy of SKS-SKKS splitting intensity comparisons that are often used to infer lowermost mantle anisotropy. Finally, we suggest a new strategy to detect lowermost mantle anisotropy which does not rely on explicit upper mantle corrections and use this method to analyse the lowermost mantle beneath east Asia.

A heuristic algorithm for optimal load splitting in hybrid thermally activated building systems

Thermally activated building systems (TABS) integrate high thermal inertia into the heating and cooling system, which has advantages and disadvantages. During sudden fluctuations and high peaks in the energy demand of a building, the thermal comfort may not be efficiently maintained by TABS due to its slow reaction to the control signals. Thus, one solution is to add a complementary fast-reacting emission system to offset the peak loads and guarantee thermal comfort. Conversely, the high thermal inertia of TABS offers peak-shaving and load-shifting opportunities. By optimally exploiting the high thermal inertia of TABS, significant downsizing of the production system can be achieved. Thus, the dynamic behavior of the TABS must be incorporated into the design procedure. Furthermore, the optimal load split between the TABS and the secondary system is a key design consideration. This study reviews the reasons why an appropriate design methodology is not currently available. Moreover, an optimal load splitting algorithm (OLSA) is proposed as a solution, and its performance was verified against a baseline scenario by applying it to nine case studies. The results demonstrate that the OLSA estimated the optimal load split with a maximum error of 9.6%. The application of the OLSA as an easy-to-use tool for the designer was also illustrated. Additionally, the OLSA provided a significant downsizing of the components in the early-stage design (45% in cooling and 38% in heating).

Hybrid dynamic chunk ensemble model for multi-class data streams

In the analysis more specifically in the classification of continuous data stream using machine learning algorithms joint occurrence of concept drift and imbalanced issue becomes more provocative. Also, imbalance issue is again more challenging when the data stream is multi-class with minority class and that is too with data-difficulty factors. Incremental learning with ensemble models found more promising in handling theses issues. But most of the approaches are for two-class data streams which can’t be utilized for multiclass data streams. In this paper we have designed hybrid dynamic chunk ensemble model (HDCEM) for the classification of multi-class insect-data stream for handling imbalance and concept drift issue. To deal with imbalance issue we have proposed effective split bagging algorithm which has achieved better performance on minority class recall and F-measure on arriving dynamic chunks of data from multi-class data stream. HDCEM model can adapt to abrupt and gradual drift because it has combined features of both online and chunk-based learning together. It has achieved average 78% minority class recall in abrupt insect data stream and 71% in gradual drift insect stream.

Finite-Volume Method Enables Simulation of Induced Seismicity

This article, written by JPT Technology Editor Chris Carpenter, contains highlights of paper SPE 203903, “A Collocated Finite-Volume Scheme for High-Performance Simulation of Induced Seismicity in Geoenergy Applications,” by A. Novikov, D.V. Voskov, SPE, and M. Khait, SPE, Delft University of Technology, et al. The paper has not been peer reviewed. In the complete paper, the authors develop a collocated finite-volume method (FVM) to study induced seismicity as a result of pore-pressure fluctuations. A discrete system is obtained based on a fully implicit coupled description of flow, elastic deformation, and contact mechanics at fault surfaces on a fully unstructured mesh. The cell-centered collocated scheme leads to convenient integration of the different physical equations because the unknowns share the same discrete locations on the mesh. Additionally, a multipoint flux approximation is formulated in a general procedure to treat heterogeneity, anisotropy, and cross-derivative terms for both flow and mechanics equations. Introduction The FVM has become an essential tool for flow and transport simulation because of its local conservation property. For mechanical deformation, however, the conservation property does not have the same importance. Nonetheless, the FVM is still an attractive choice because it represents conservation laws in integral form more naturally. Some authors in the literature use fixed-stress splitting algorithms to decouple mechanics and flow equations. These are a form of sequential implicit solution schemes and often lead to more-efficient simulations than fully implicit (FI) simulation. However, sequential schemes introduce certain restrictions on timestep sizes. On the other hand, FI schemes provide unconditionally convergent solutions and are more-robust and -convenient approaches for investigation of complex multiphysical problems. Although the FI approach does not imply any restriction on timestep size, it requires an efficient linear equation solution strategy for high-resolution models. In this study, the authors develop a collocated FI multipoint FVM scheme for poromechanics simulation of faulted reservoirs. The scheme can be used to solve poromechanics problems on unstructured polyhedral grids with minimal degrees of freedom per cell. It is also capable of considering material heterogeneity while preserving mass and momentum balances. This scheme is extended to consider discontinuities in displacements at faults. The developed algorithms have been embedded into the open-source Delft Advanced Research Terra Simulator (DARTS).

Convergence analysis of the stochastic reflected forward–backward splitting algorithm

We propose and analyze the convergence of a novel stochastic algorithm for solving monotone inclusions that are the sum of a maximal monotone operator and a monotone, Lipschitzian operator. The propose algorithm requires only unbiased estimations of the Lipschitzian operator. We obtain the rate $${\mathcal {O}}(log(n)/n)$$ in expectation for the strongly monotone case, as well as almost sure convergence for the general case. Furthermore, in the context of application to convex–concave saddle point problems, we derive the rate of the primal–dual gap. In particular, we also obtain $${\mathcal {O}}(1/n)$$ rate convergence of the primal–dual gap in the deterministic setting.

Feasibility study of multi-site split learning for privacy-preserving medical systems under data imbalance constraints in COVID-19, X-ray, and cholesterol dataset

It seems as though progressively more people are in the race to upload content, data, and information online; and hospitals haven’t neglected this trend either. Hospitals are now at the forefront for multi-site medical data sharing to provide ground-breaking advancements in the way health records are shared and patients are diagnosed. Sharing of medical data is essential in modern medical research. Yet, as with all data sharing technology, the challenge is to balance improved treatment with protecting patient’s personal information. This paper provides a novel split learning algorithm coined the term, “multi-site split learning”, which enables a secure transfer of medical data between multiple hospitals without fear of exposing personal data contained in patient records. It also explores the effects of varying the number of end-systems and the ratio of data-imbalance on the deep learning performance. A guideline for the most optimal configuration of split learning that ensures privacy of patient data whilst achieving performance is empirically given. We argue the benefits of our multi-site split learning algorithm, especially regarding the privacy preserving factor, using CT scans of COVID-19 patients, X-ray bone scans, and cholesterol level medical data.

On circulant and skew-circulant splitting algorithms for (continuous) Sylvester equations

We present a circulant and skew-circulant splitting (CSCS) iterative method for solving large sparse continuous Sylvester equations AX+XB=C, where the coefficient matrices A and B are Toeplitz matrices. A theoretical study shows that if the circulant and skew-circulant splitting factors of A and B are positive semi-definite (not necessarily Hermitian), and at least one factor is positive definite, then the CSCS method converges to the unique solution of the Sylvester equation. In addition, our analysis gives an upper bound for the convergence factor of the CSCS iteration which depends only on the eigenvalues of the circulant and skew-circulant splitting matrices. A computational comparison with alternative methods reveals the efficiency and reliability of the proposed method.

Distributed Proximal Splitting Algorithms with Rates and Acceleration

We analyze several generic proximal splitting algorithms well suited for large-scale convex nonsmooth optimization. We derive sublinear and linear convergence results with new rates on the function value suboptimality or distance to the solution, as well as new accelerated versions, using varying stepsizes. In addition, we propose distributed variants of these algorithms, which can be accelerated as well. While most existing results are ergodic, our nonergodic results significantly broaden our understanding of primal–dual optimization algorithms.

The multiscale perturbation method for two-phase reservoir flow problems

In this work we formulate and test a new procedure, the Multiscale Perturbation Method for Two-Phase Flows (MPM-2P), for the fast, accurate and naturally parallelizable numerical solution of two-phase, incompressible, immiscible displacement in porous media approximated by an operator splitting method. The proposed procedure is based on domain decomposition and combines the Multiscale Perturbation Method (MPM) [Ali, et al., Appl. Math. and Comput., 387 (2020) pp. 125023] with the Multiscale Robin Coupled Method (MRCM) [Guiraldello, et al., J. Comput. Phys., 355 (2018) pp. 1-21]. When an update of the velocity field is called for by the operator splitting algorithm, the MPM-2P may provide, depending on the magnitude of a dimensionless algorithmic parameter, an accurate and computationally inexpensive approximation for the velocity field by reusing previously computed multiscale basis functions. Thus, a full update of all multiscale basis functions required by the MRCM for the construction of a new velocity field is avoided.There are two main steps in the formulation of the MPM-2P. Initially, for each subdomain one local boundary value problem with trivial Robin boundary conditions is solved (instead of a full set of multiscale basis functions, that would be required by the MRCM). Then, the solution of an inexpensive interface problem provides the velocity field on the skeleton of the decomposition of the domain. The resulting approximation for the velocity field is obtained by downscaling.We consider challenging two-phase flow problems, with high-contrast permeability fields and water-oil finger growth in homogeneous media. Our numerical experiments show that the use of the MPM-2P gives exceptional speed-up - almost 90% of reduction in computational cost - of two-phase flow simulations. Hundreds of MRCM solutions can be replaced by inexpensive MPM-2P solutions, and water breakthrough can be simulated with very few updates of the MRCM set of multiscale basis functions.

OPK_SNCA: Optimized prior knowledge via sparse non-convex approach for cone-beam X-ray luminescence computed tomography imaging

BackgroundThe development of Cone-beam X-ray luminescence computed tomography (CB-XLCT) has allowed the quantitative in-depth biological imaging, but with a greatly ill-posed and ill-conditioned inverse problem. Although the predefined permissible source region (PSR) is a widely used way to alleviate the problem for CB-XLCT imaging, how to obtain the accurate PSR is still a challenge for the process of inverse reconstruction. MethodsWe proposed an optimized prior knowledge via a sparse non-convex approach (OPK_SNCA) for CB-XLCT imaging. Firstly, non-convex Lp-norm optimization model was employed for copying with the inverse problem, and an iteratively reweighted split augmented lagrangian shrinkage algorithm was developed to obtain a group of sparse solutions based on different non-convex p values. Secondly, a series of permissible regions (PRs) with different discretized mesh was further achieved, and the intersection operation was implemented on the group of PRs to get a reasonable PSR. After that, the final PSR was adopted as an optimized prior knowledge to enhance the reconstruction quality of inverse reconstruction. ResultsBoth simulation experiments and in vivo experiment were performed to evaluate the efficiency and robustness of the proposed method. ConclusionsThe experimental results demonstrated that our proposed method could significantly improve the imaging quality of the distribution of X-ray-excitable nanophosphors for CB-XLCT.

Alpha -Firmly nonexpansive operators on metric spaces

We extend to p-uniformly convex spaces tools from the analysis of fixed point iterations in linear spaces. This study is restricted to an appropriate generalization of single-valued, pointwise averaged mappings. Our main contribution is establishing a calculus for these mappings in p-uniformly convex spaces, showing in particular how the property is preserved under compositions and convex combinations. This is of central importance to splitting algorithms that are built by such convex combinations and compositions, and reduces the convergence analysis to simply verifying that the individual components have the required regularity pointwise at fixed points of the splitting algorithms. Our convergence analysis differs from what can be found in the previous literature in that the regularity assumptions are only with respect to fixed points. Indeed we show that, if the fixed point mapping is pointwise nonexpansive at all cluster points, then these cluster points are in fact fixed points, and convergence of the sequence follows. Additionally, we provide a quantitative convergence analysis built on the notion of gauge metric subregularity, which we show is necessary for quantifiable convergence estimates. This allows one for the first time to prove convergence of a tremendous variety of splitting algorithms in spaces with curvature bounded from above.

A family of split kernel adaptive filtering algorithms for nonlinear stereophonic acoustic echo cancellation

A family of split kernel adaptive filtering algorithms for nonlinear stereophonic acoustic echo cancellation

Conservation laws with discontinuous flux function on networks: a splitting algorithm

<abstract><p>In this article, we present an extension of the splitting algorithm proposed in [<xref ref-type="bibr" rid="b22">22</xref>] to networks of conservation laws with piecewise linear discontinuous flux functions in the unknown. We start with the discussion of a suitable Riemann solver at the junction and then describe a strategy how to use the splitting algorithm on the network. In particular, we focus on two types of junctions, i.e., junctions where the number of outgoing roads does not exceed the number of incoming roads (dispersing type) and junctions with two incoming and one outgoing road (merging type). Finally, numerical examples demonstrate the accuracy of the splitting algorithm by comparisons to the exact solution and other approaches used in the literature.</p></abstract>

Post hoc deconvolution of human mitochondrial DNA mixtures by EMMA 2 using fine-tuned Phylotree nomenclature

In this paper we present a new algorithm for splitting (partial) human mitogenomes into components with high similarity to haplogroup motifs of Phylotree. The algorithm reads a (partial) mitogenome coded by the differences to the reference (rCRS) and outputs the estimated haplogroups of the putative components. The algorithm requires no special information on the raw data of the sequencing process and is therefore suited for the post hoc analysis of mixtures of any sequencing technology. The software EMMA 2 implementing the algorithm will be made available via the EMPOP (https://empop.online) database and extends the nine years old software EMMA for haplogrouping single mitogenomes to mixtures with at most three components.

МОДЕЛИРОВАНИЕ РАСЩЕПЛЕНИЯ ПАССАЖИРОПОТОКА ПО ВИДАМ ТРАНСПОРТА МЕТОДОМ ВЗВЕШЕННЫХ ГРУППОВЫХ ОЦЕНОК

The paper considers methods for modeling passenger traffic splitting at presence on a route of various competing modes of transport. The authors suggest a method based on a hypothesis that passengers of various population groups make decisions based on assessment of importance of route (mode of transport) parameters such as ride time, cost and comfort. On the first stage of the study with the use of data on average income of the population the authors split passengers on groups and for each group they determine coefficients of criteria significance. The algorithm of modeling passenger traffic splitting allows analysing attractiveness for population of newly introduced routes and validity of fares at increase of comfort.

Chain-based machine learning for full PVT data prediction

Building machine learning (ML) models based on pressure-volume-temperature (PVT) data is of paramount importance to capture trends and predict fluid behavior in a very heterogeneous and highly nonlinear thermodynamic system. PVT samples stored in an oil company database are often not complete and might be missing properties; both black oil and compositional. Before delving into building optimized fluid models, it is required to have a clean and structured PVT database complete with all the required properties. We present multiple novel algorithms developed to accurately predict a complete set of black oil and compositional properties within a PVT database. The proposed methodology consists of predicting properties in series, starting from a minimal set of data (black oil and compositional) and obtaining a complete set of data for all PVT samples. The order through which this is completed relies on benefiting from the existing data to predict missing data starting from the highest correlating data to the lowest. We also honored the physical nature of correlations between properties, and consequently, ranked properties for prediction as this leads to less error propagation. In addition, we have implemented data clustering prior to training ML models. Clustering is used to categorize the fluid samples into families based on the collective behavior of their different features, and hence, improve the quality of the PVT samples' properties prediction using machine learning. Several options are tested where clustering is performed using black oil properties only, compositional properties, or a combined set of black oil and compositional properties and the clustering scenario leading to the least prediction error is adopted. We have trained ML models to generically predict all black oil and compositional properties resulting from laboratory experiments, including molecular weights (MW) and mole fractions of heavy fractions (any set of heavy fractions) from the mole fractions of all the commonly available components up to C7+ and molecular weight of C7+. The massive data set used in this paper enabled comprehensive testing of the developed algorithms and provided striking accuracy of the predicted PVT properties; especially the compositional ones. Despite all the significant efforts shown in the literature concerning predicting PVT properties, the missing link is a systematic methodology to complete PVT samples' properties in a consistent manner. Furthermore, the focus in the literature is mainly on forecasting black oil properties; compositional properties are scarcely considered. Algorithms developed in this paper address these two limitations and are tested using a uniquely large data set available for onshore and offshore fields and reservoirs in Abu Dhabi. No previous algorithms, to the best of our knowledge, are tested on such a large data set. • Systematic, chain-based, methodology to complete PVT samples' compositional and black oil properties in a consistent manner. • Clustering to categorize fluid samples based on their thermodynamic behavior and reveal deep insights of these categories. • Application of the proposed algorithms for compositional splitting was a powerful illustration of the proposed algorithms. • Algorithms are tested using a uniquely large data set available for onshore and offshore fields and reservoirs in Abu Dhabi.

Algorithmic and analytical approach to the proximal split feasibility problem and fixed point problem

In this paper, we investigate the proximal split feasibility algorithm and fixed point problem in Hilbert spaces. We propose an iterative algorithm for finding a common element of the solution of the proximal split feasibility algorithm and fixed point of an L-Lipschitz pseudocontractive operator. We demonstrate that the considered algorithm converges strongly to a common point of the investigated problems under some mild conditions.

L2 Regularization Model with Removal of Gaussian Noise

In order to remove Gaussian noise from images, a Gaussian noise image restoration method based on the L2 norm regularization model was proposed. The L2 norm is selected as the data fidelity term and the gradient operator and wavelet frame as the regularization term to suppress the image ladder effect and protect the image edge details. Since the objective function of the model is a large convex function, the solving process is very tedious. The split Bregman iterative algorithm and alternate direction multiplier method are combined to restore the image. The experimental results show that show that the alternate direction multiplier method can effectively reduce the difficulty of solving the restoration model, and the image recovered by using this model has a higher peak signal-to-n ratio and better structural similarity and can get a clearer image.

Panchromatic Side Sparsity Model-Based Deep Unfolding Network for Pansharpening

Deep learning (DL) recently receives state-of-the-art results in pansharpening. However, most of the existing pansharpening neural networks are purely data-driven, without taking account of the characteristics of the pansharpening task. To address this issue, we propose a novel deep unfolding network for pansharpening that combines the insight of the variational optimization (VO) model and the capability of deep neural network (DNN). We first develop a panchromatic side sparsity (PASS) prior-based VO model for pansharpend image reconstruction, which is formulated as the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\ell _{1}-\ell _{1}$ </tex-math></inline-formula> minimization. In particular, the PASS prior is defined using the transform sparsity, which can alleviate the influences of the irregular outliers between the multispectral (MS) and panchromatic (PAN) images. The iterations of half-quadratic splitting algorithm for solving the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\ell _{1}-\ell _{1}$ </tex-math></inline-formula> minimization are then deeply unfolded into a DNN, referred as PASS-Net. To capture the nonlinear relationship between MS and PAN images, the linear transforms used in PASS prior are extended into the subnetworks in PASS-Net. Moreover, a pair of learnable downsampling and upsampling modules are designed to realize the downsampling and upsampling operations, which can improve the flexibility. The experimental results on different satellite datasets confirm that PASS-Net is superior to some representational traditional methods and state-of-the-art DL-based methods.

Low-Gain Stability of Projected Integral Control for Input-Constrained Discrete-Time Nonlinear Systems

We consider the problem of zeroing an error output of a nonlinear discrete-time system in the presence of constant exogenous disturbances, subject to hard convex constraints on the input signal. The design specification is formulated as a variational inequality, and we adapt a forward-backward splitting algorithm to act as an integral controller which ensures that the input constraints are met at each time step. We establish a low-gain stability result for the closed-loop system when the plant is exponentially stable, generalizing previously known results for integral control of discrete-time systems. Specifically, it is shown that if the composition of the plant equilibrium input-output map and the integral feedback gain is strongly monotone, then the closed-loop system is exponentially stable for all sufficiently small integral gains. The method is illustrated via application to a four-tank process.