Network Decomposition Research Articles

A novel few-sample wind power prediction model based on generative adversarial network and quadratic mode decomposition

With the emergence of various new power systems, accurate wind power prediction plays a critical role in their safety and stability. However, due to the historical wind power data with few samples, it is difficult to ensure the accuracy of power system prediction for new wind farms. At the same time, wind power data show significant uncertainty and fluctuation. To address this issue, it is proposed in this research to build a novel few-sample wind power prediction model based on the least-square generative adversarial network (LSGAN) and quadratic mode decomposition (QMD). Firstly, a small amount of original wind power data are generated to improve the data by least-square generative adversarial network, which solves the error in prediction with limited sample data. Secondly, a quadratic mode decomposition method based on ensemble empirical mode decomposition (EEMD) and variational mode decomposition (VMD) is developed to address the instability of wind power data and extract hidden temporal characteristics. Specifically, ensemble empirical mode decomposition decomposes the data once to obtain a set of intrinsic mode functions (IMFs), and then variational mode decomposition is used to decompose the fuzzy irregular IMF1 function twice. Finally, a bidirectional long short-term memory network (BiLSTM) based on particle swarm optimization (PSO) is applied to predict wind power data. The LSGAN-QMD-PSO-BiLSTM model proposed in this research is verified on a wind farm located in Spain, which indicates that the proposed model achieves the lowest root mean square error (RMSE) and mean absolute error (MAE) errors of 100.6577 and 66.5175 kW, along with the highest R2 of 0.9639.

VWM-DCRNN: A Method of Combining Signal Processing With Deep Learning for Fault Diagnosis in Single-Phase PWM Rectifier

Based on variational mode decomposition and dual model of convolutional recurrent neural network (VMD-DCRNN), a novel diagnosis method is proposed to discover the faults of IGBTs, diodes and series resonant circuit in single-phase pulse width modulation (PWM) AC-DC rectifier, an important part of traction power supply system of high-speed railway. By virtue of the combination of signal processing and deep learning schemes, the multi-scale feature information for fault diagnosis is extracted by regarding the input current of the rectifier and the voltage of dc side as the original signal. More clearly, VMD is adopted to decompose the original signal to a series of intrinsic mode function components (IMFs). Then, the submodel of current is designed to detect the fault types of IGBTs and diodes. Meanwhile, the submodel of voltage is established to identify the fault types of series resonant circuit. These IMFs are fed into DCRNN consisting of the two submodels for training and testing. Finally, the features extracted from the two submodels are integrated and converted to label space to complete fault diagnosis. Experimental results show that the proposed VMD-DCRNN algorithm is superior to the single-channel models, reaching 96.27%.

Convexity Hierarchies in Grid Networks

Several algorithms for path planning in grid networks rely on graph decomposition to reduce the search space size; either by constructing a search data structure on the components, or by using component information for A* guidance. The focus is usually on obtaining components of roughly equal size with few boundary nodes each. In this paper, we consider the problem of splitting a graph into convex components. A convex component is characterized by the property that for all pairs of its members, the shortest path between them is also contained in it. Thus, given a source node, a target node, and a (small) convex component that contains both of them, path planning can be restricted to this component without compromising optimality. We prove that it is NP-hard to find a balanced node separator that splits a given graph into convex components. However, we also present and evaluate heuristics for (hierarchical) convex decomposition of grid networks that perform well across various benchmarks. Moreover, we describe how existing path planning methods can benefit from the computation of convex components. As one main outcome, we show that contraction hierarchies become up to an order of magnitude faster on large grids when the contraction order is derived from a convex graph decomposition.

Dynamics-based reconstruction of the multilayer structure from an aggregated network

Multi-type interactions are common in complex systems. In many cases, we can only observe whether there is a link between two individuals without knowing the type of the link. The distinction of link types within a complex network is crucial for understanding the dynamics on the network especially when the dynamics behave differently on each type of links. We propose in this paper a network decomposition method using propagation time series, which decomposes an aggregated single-layer network into a multilayer network with each layer consisting of links of the same type. We apply the method to various model networks and real networks and find that it works accurately even when diverse network structural characteristics are present. We also investigate the method’s effectiveness and resilience under various restrictions, finding that it is applicable in networks with more than two layers. This work offers an effective and universal framework for untangling the multilayer structure in complex networks.

Dissipative symmetry-protected topological order

In this work, we investigate the interplay between dissipation and symmetry-protected topological order. We considered the one-dimensional spin-1 Affleck-Kennedy-Lieb-Tasaki model interacting with an environment where the dissipative dynamics are described by the Lindladian master equation. The Markovian dynamics is solved by the implementation of a tensor network algorithm for mixed states in the thermodynamic limit. We observe that, for time-reversal symmetric dissipation, the resulting steady state has topological signatures even if being a mixed state. This is seen in finite string-order parameters as well as in the degeneracy pattern of singular values in the tensor network decomposition of the reduced density matrix. We also show that such features do not appear for nonsymmetric dissipation. Our work opens the way toward a generalized and more practical definition of symmetry-protected topological order for mixed states induced by dissipation.

A Taxonomic Survey of Physics-Informed Machine Learning

Physics-informed machine learning (PIML) refers to the emerging area of extracting physically relevant solutions to complex multiscale modeling problems lacking sufficient quantity and veracity of data with learning models informed by physically relevant prior information. This work discusses the recent critical advancements in the PIML domain. Novel methods and applications of domain decomposition in physics-informed neural networks (PINNs) in particular are highlighted. Additionally, we explore recent works toward utilizing neural operator learning to intuit relationships in physics systems traditionally modeled by sets of complex governing equations and solved with expensive differentiation techniques. Finally, expansive applications of traditional physics-informed machine learning and potential limitations are discussed. In addition to summarizing recent work, we propose a novel taxonomic structure to catalog physics-informed machine learning based on how the physics-information is derived and injected into the machine learning process. The taxonomy assumes the explicit objectives of facilitating interdisciplinary collaboration in methodology, thereby promoting a wider characterization of what types of physics problems are served by the physics-informed learning machines and assisting in identifying suitable targets for future work. To summarize, the major twofold goal of this work is to summarize recent advancements and introduce a taxonomic catalog for applications of physics-informed machine learning.

Investigation of proper orthogonal decomposition for echo state networks

Echo State Networks (ESN) are a type of Recurrent Neural Network that yields promising results in representing time series and nonlinear dynamic systems. Although they are equipped with a very efficient training procedure, Reservoir Computing strategies, such as the ESN, require high-order networks, i.e., many neurons, resulting in a large number of states that are magnitudes higher than the number of model inputs and outputs. A large number of states not only makes the time-step computation more costly but also may pose robustness issues, especially when applying ESNs to problems such as Model Predictive Control (MPC) and other optimal control problems. One way to circumvent this complexity issue is through Model Order Reduction strategies such as the Proper Orthogonal Decomposition (POD) and its variants (POD-DEIM), whereby we find an equivalent lower order representation to an already trained high dimension ESN. To this end, this work aims to investigate and analyze the performance of POD methods in Echo State Networks, evaluating their effectiveness through the Memory Capacity (MC) of the POD-reduced network compared to the original (full-order) ESN. We also perform experiments on two numerical case studies: a NARMA10 difference equation and an oil platform containing two wells and one riser. The results show that there is little loss of performance comparing the original ESN to a POD-reduced counterpart and that the performance of a POD-reduced ESN tends to be superior to a normal ESN of the same size. Also, the POD-reduced network achieves speedups of around 80% compared to the original ESN.

Asymptotic dimension of minor-closed families and Assouad–Nagata dimension of surfaces

The asymptotic dimension is an invariant of metric spaces introduced by Gromov in the context of geometric group theory. In this paper, we study the asymptotic dimension of metric spaces generated by graphs and their shortest path metric and show their applications to some continuous spaces. The asymptotic dimension of such graph metrics can be seen as a large scale generalisation of weak diameter network decomposition which has been extensively studied in computer science. We prove that every proper minor-closed family of graphs has asymptotic dimension at most 2, which gives optimal answers to a question of Fujiwara and Papasoglu and (in a strong form) to a problem raised by Ostrovskii and Rosenthal on minor excluded groups. For some special minorclosed families, such as the class of graphs embeddable in a surface of bounded Euler genus, we prove a stronger result and apply this to show that complete Riemannian surfaces have Assouad–Nagata dimension at most 2. Furthermore, our techniques allow us to determine the asymptotic dimension of graphs of bounded layered treewidth and graphs with any fixed growth rate, which are graph classes that are defined by purely combinatorial notions and properly contain graph classes with some natural topological and geometric flavours.

A distributed newton method for processing signals defined on the large-scale networks

In the graph signal processing (GSP) framework, distributed algorithms are highly desirable in processing signals defined on large-scale networks. However, in most existing distributed algorithms, all nodes homogeneously perform the local computation, which calls for heavy computational and communication costs. Moreover, in many real-world networks, such as those with straggling nodes, the homogeneous manner may result in serious delay or even failure. To this end, we propose active network decomposition algorithms to select non-straggling nodes (normal nodes) that perform the main computation and communication across the network. To accommodate the decomposition in different kinds of networks, two different approaches are developed, one is centralized decomposition that leverages the adjacency of the network and the other is distributed decomposition that employs the indicator message transmission between neighboring nodes, which constitutes the main contribution of this paper. By incorporating the active decomposition scheme, a distributed Newton method is employed to solve the least squares problem in GSP, where the Hessian inverse is approximately evaluated by patching a series of inverses of local Hessian matrices each of which is governed by one normal node. The proposed algorithm inherits the fast convergence of the second-order algorithms while maintains low computational and communication cost. Numerical examples demonstrate the effectiveness of the proposed algorithm.

An open-source program for spatial decomposition of bus transit networks

Comparing transit operations and performance over time is often challenging due to changes in route identifiers and service patterns. It is particularly difficult if the analysis period spans a major network design change where bus routes are realigned and renamed. This paper presents a new open-source software package that simplifies longitudinal transit performance analysis by decomposing a bus network into block-length segments that remain stable over time. The package then matches transit networks across time periods using segment geometry rather than potentially unstable route or stop identifiers. This package provides an efficient method for transit planners, advocacy groups, policy makers and urban scientists to analyze changes in transit performance over time without any prior knowledge of network design changes.

Time series forecasting based on a novel ensemble‐based network and variational mode decomposition

AbstractStatistical and computational intelligence methods contain weaknesses in handling nonlinearity, non‐stationarity and noise. This research develops a novel decomposition ensemble‐based network named VMD‐DENetwork for time series forecasting over different horizons. A robust decomposition technique called variational mode decomposition (VMD) is applied to decompose the input sequence into several intrinsic modes in a non‐recursive manner. The optimal number of intrinsic modes is selected based on a comprehensive analysis to ensure the stability of the framework. The proposed DENetwork is developed based on stacking architecture and constitutes heterogeneous learners to model the nonlinear and complex relationships. It combines a convolutional neural network, long short‐term memory and an extreme learning machine. A firefly optimization algorithm is adopted for utilizing hyperparameters of the proposed model to enhance the efficiency of VMD‐DENetwork. The forecasting performance is verified by using six real‐world data sets from the New York Mercantile and International Petroleum Exchange. The final obtained results are compared with several peer‐advanced algorithms using the root mean squared error (RMSE), mean absolute error (MAE), Theil inequality coefficient (TIC) and correlation coefficient (R) metrics. The experimental results confirm that the proposed model demonstrates outstanding prediction performance. The employed optimization algorithm is compared with three frequently used bio‐inspired optimization algorithms, and their performance is tested using standard CEC benchmarks.

Spatial-spectral-temporal connective tensor network decomposition for thick cloud removal

Thick cloud removal is a fundamental and challenging remote sensing image processing problem, which is beneficial to subsequent analysis and application. Fortunately, multi-temporal remote sensing images (MTRSIs) contain highly correlated spatial–spectral–temporal (SST) information that makes it possible to solve the thick cloud removal problem. To explore the rich SST relationships of MTRSIs effectively and efficiently, this paper proposes a semi-blind thick cloud removal method via SST connective tensor network decomposition (SSTC-CR). Specifically, the proposed model performs the subspace representation along the spectral mode of the image at each time node, and then introduces the tensor network decomposition to characterize the intrinsic relationship of the fourth-order tensor consisting of all intrinsic images under subspace representation. Besides, we develop a proximal alternating minimization-based algorithm to tackle the newly-built thick cloud removal model. In the developed algorithm, we integrate the cloud removal and mask refinement by updating optimization variables and the cloud masks alternately. Extensive numerical experiments on simulated and real-world MTRSIs substantiate that the proposed method outperforms other state-of-the-art tensor modeling and deep learning-based methods, especially for color protection. The code is available at https://github.com/zhaoxile/SSTC_CR.

A Cybersecurity Knowledge Graph Completion Method for Penetration Testing

Penetration testing is an effective method of making computers secure. When conducting penetration testing, it is necessary to fully understand the various elements in the cyberspace. Prediction of future cyberspace state through perception and understanding of cyberspace can assist defenders in decision-making and action execution. Accurate cyberspace detection information is the key to ensuring successful penetration testing. However, cyberspace situation awareness still faces the following challenges. Due to the limited detection capability, the information obtained from cyberspace detection intelligence is incomplete. There are some errors in the cyberspace detection intelligence, which may mislead the penetration testing workers. The knowledge graph can store and manage the cybersecurity data. In order to ensure the integrity and accuracy of cyberspace information, we design a knowledge graph completion model called CSNT to complete cybersecurity data. CSNT uses the BiLSTM to capture the interaction information between entities and relationships. It models the relationship between entities by combining the neural network and tensor decomposition. The Pearson Mix Net is designed to control the generation of joint vectors. We also design a novel self-distillation strategy to reduce catastrophic forgetting during model training. After learning the relationship pattern between entities in the cyberspace detection intelligence, the model can be used to mine the knowledge not found in the cybersecurity detection intelligence and correct the erroneous records. Experiments show that our method has certain advantages for the knowledge graph completion.

Uniqueness of Clearing Payment Matrices in Financial Networks

We study bankruptcy problems in financial networks in the presence of general bankruptcy laws. The set of clearing payment matrices is shown to be a lattice, which guarantees the existence of a greatest clearing payment and a least clearing payment. Multiplicity of clearing payment matrices is both a theoretical and a practical concern. We present a new condition for uniqueness that generalizes all the existing conditions proposed in the literature. Our condition depends on the decomposition of the financial network into strongly connected components. A strongly connected component that contains more than one agent is called a cycle, and the involved agents are called cyclical agents. If there is a cycle without successors, then one of the agents in such a cycle should have a strictly positive endowment. The division rule used by a cyclical agent with a strictly positive endowment should be positive monotonic, and the rule used by a cyclical agent with a zero endowment should be strictly monotonic. Because division rules involving priorities are not positive monotonic, uniqueness of the clearing payment matrix is a much bigger concern for such division rules than for proportional ones. As a final contribution of the paper, we exhibit the relationship between the uniqueness of clearing payment matrices and the continuity of bankruptcy rules, a property that is very much desired for stability of financial systems. Funding: This research was supported by the Higher Education Institutional Excellence Program 2020 of the Ministry of Innovation and Technology in the framework of the “Financial and Public Services” research project [Grant TKP2020-IKA-02] at Corvinus University of Budapest. P. Csóka received funding from the National Research, Development and Innovation Office [Grants K-120035 and K-138826].

A multiscale model for multiaxial inelastic behavior of elastomeric particulate composites

This article addresses the problem of the multiscale constitutive representation of the multiaxial inelastic behavior of elastomeric particulate composites. A fully three-dimensional model is proposed within a micromechanical treatment to describe the multiaxial inelastic response in relation to the reinforcement mechanisms. A network decomposition based on the tube confinement theory is used to consider the combined effects of multiaxiality and inelasticity. The near-field direct interactions between the particles and the rubber networks are physically described using the Eshelby inclusion theory. The capabilities of the microstructure-based model are evaluated for different modes of deformation over a wide range of filler concentrations. It is found being able to successfully reproduce the significant features of the multiaxial macro-response upon monotonic and cyclic loading sequences. Important insights about the effective role of the reinforcement mechanisms on the multiaxial dissipation are revealed.

NOVEL ACCESSIBILITY METRICS BASED ON HIERARCHICAL DECOMPOSITION OF TRANSPORT NETWORKS

Scientific analysis of public transport systems at the urban, regional, and national levels is vital in this contemporary, highly connected world. Quantifying the accessibility of nodes (locations) in a transport network is considered a holistic measure of transportation and land use and an important research area. In recent years, complex networks have been employed for modeling and analyzing the topology of transport systems and services networks. However, the design of network hierarchy-based accessibility measures has not been fully explored in transport research. Thus, we propose a set of three novel accessibility metrics based on the k-core decomposition of the transport network. Core-based accessibility metrics leverage the network topology by eliciting the hierarchy while accommodating variations like travel cost, travel time, distance, and frequency of service as edge weights. The proposed metrics quantify the accessibility of nodes at different geographical scales, ranging from local to global. We use these metrics to compute the accessibility of geographical locations connected by air transport services in India. Finally, we show that the measures are responsive to changes in the topology of the transport network by analyzing the changes in accessibility for the domestic air services network for both pre-covid and post-covid times.

Improving the accuracy of bathymetry using the combined neural network and gravity wavelet decomposition method with altimetry derived gravity data

The wide range of bathymetry models can be estimated using the marine gravity information derived from satellite altimetry. However, due to nonlinear factors influences such as isostasy effects, the bathymetry estimated by gravity anomaly and vertical gravity gradient is not satisfactory. Therefore, to improve the accuracy of bathymetry estimation, a combined neural network and gravity information wavelet decomposition (CNNGWD) method is proposed based on wavelet decomposition and correlation analysis. Next, the bathymetry of the Manila Trench area is estimated using the CNNGWD method and multilayer neural network (MNN) method, respectively. Then, the shipborne sounding data and international bathymetric models such as ETOPO1 and GEBCO_2021 are separately used to evaluate the accuracy of the inversion models. The results show that the root mean square errors (RMSE) of the difference between the bathymetric model one (BM1) estimated by CNNGWD method and the shipborne sounding data is 59.90 m, the accuracy is improved by 12.45%, 64.70% and 28.68% compared with the bathymetric model two (BM2) which estimated by MNN, ETOPO1 and GEBCO, respectively. Finally, by analyzing the bathymetric accuracy shift with depth, the BM1 has lower RMSE at depths ranging from 1000 m to 3000 m. Furthermore, BM1 shows dominance in flat troughs and rugged ridge regions.

Observability Decomposition of Boolean Control Networks

This article investigates the observability decomposition of Boolean control networks (BCNs) under the algebraic frame based on the semitensor product of matrices. First, the definition for the observability decomposition of BCNs is proposed, which is consistent with the observability decomposition of traditional linear control systems. Then, by using the vertex partition method, a necessary and sufficient vertex partition condition for the observability decomposition of BCNs is proposed. Next, an algorithm is designed for the analysis and realization of observability decomposition. Finally, a biological example and a counterexample are analyzed to illustrate the obtained results.

Mode interpretation and force prediction surrogate model of flow past twin cylinders via machine learning integrated with high-order dynamic mode decomposition

Understanding and modeling the flow field and force development over time for flow past twin tandem cylinders can promote insight into underlying physical laws and efficient engineering design. In this study, a new surrogate model, based on a convolutional neural network and higher-order dynamic mode decomposition (CNN-HODMD), is proposed to predict the unsteady fluid force time history specifically for twin tandem cylinders. Sampling data are selected from a two-dimensional direct numerical simulation flow solution over twin tandem cylinders at different aspect ratios (AR = 0.3–4), gap spacing (L* = 1–8), and Re = 150. To promote insight into underlying physical mechanisms and better understand the surrogate model, the HODMD analysis is further employed to decompose the flow field at selected typical flow regimes. Results indicate that CNN-HODMD performs well in discovering a suitable low-dimensional linear representation for nonlinear dynamic systems via dimensionality augment and reduction technique. Therefore, the CNN-HODMD surrogate model can efficiently predict the time history of lift force at various AR and L* within 5% error. Moreover, fluid forces, vorticity field, and power spectrum density of twin cylinders are investigated to explore the physical properties. It was found three flow regimes (i.e., overshoot, reattachment, and coshedding) and two wake vortex patterns (i.e., 2S and P). It was found the lift force of the upstream cylinder for AR < 1 is more sensitive to the gap increment, while the result is reversed for the downstream cylinder. It was found that the fluctuating component of the wake of cylinders decreases with increasing AR at L* = 1. Moreover, flow transition was observed at L* = 4.

Wind turbine output power forecasting based on temporal convolutional neural network and complete ensemble empirical mode decomposition with adaptive noise

ABSTRACT Predicting the output power of the wind turbine accurately is an important means to ensure the stable operation of the wind power system. More and more deep learning methods are currently applied to the prediction of the output power, but few of them pay attention to the non-stationarity of the output power, which leads to a decrease in the prediction accuracy. In this study, a hybrid forecasting model that combines complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN) and temporal convolutional neural network (TCN) is developed to predict the output power. First, the CEEMDAN method is used to decompose the original output power sequence into several sub-sequences of different frequencies. Then, the TCN model is used to predict each sub-sequence. Finally, the sum of the prediction results is used as the predicted value of the output power. Take a wind turbine in Shanghai as an example, the experimental results show that the CEEMDAN-TCN model has the highest prediction accuracy when compared with the current mainstream deep learning models. Compared with the single TCN, the mean square error (MSE) predicted by the CEEMDAN-TCN model is reduced by 17%, and the root mean square error (RMSE) is reduced by 11%.