Reliable Convergence Research Articles

Optimising Time-Frequency Distributions: A Surface Metrology Approach

Time-frequency signal processing offers a significant advantage over temporal or frequency-only methods, but representations require optimisation for a given signal. Standard practice includes choosing the appropriate time-frequency distribution and fine-tuning its parameters, usually via visual inspection and various measures—the most commonly used ones are based on the Rényi entropies or energy concentration by Stanković. However, a discrepancy between the observed representation quality and reported numerical value may arise when the filter kernel has greater adaptability. Herein, a performance measure derived from the Abbot–Firestone curve similar to the volume parameters in surface metrology is proposed as the objective function to be minimised by the proposed minimalistic differential evolution variant that is parameter-free and uses a population of five members. Tests were conducted on two synthetic signals of different frequency modulations and one real-life signal. The multiform tiltable exponential kernel was optimised according to the Rényi entropy, Stanković’s energy concentration and the proposed measure. The resulting distributions were mutually evaluated using the same measures and visual inspection. The optimiser demonstrated a reliable convergence for all considered measures and signals, while the proposed measure showed consistent alignment of reported numerical values and visual assessments.

Computational Performance of Deep Reinforcement Learning to Find Nash Equilibria

We test the performance of deep deterministic policy gradient—a deep reinforcement learning algorithm, able to handle continuous state and action spaces—to find Nash equilibria in a setting where firms compete in offer prices through a uniform price auction. These algorithms are typically considered “model-free” although a large set of parameters is utilized by the algorithm. These parameters may include learning rates, memory buffers, state space dimensioning, normalizations, or noise decay rates, and the purpose of this work is to systematically test the effect of these parameter configurations on convergence to the analytically derived Bertrand equilibrium. We find parameter choices that can reach convergence rates of up to 99%. We show that the algorithm also converges in more complex settings with multiple players and different cost structures. Its reliable convergence may make the method a useful tool to studying strategic behavior of firms even in more complex settings.

Asynchronous Decomposition Method for the Coordinated Operation of Virtual Power Plants

Virtual Power Plant (VPP) aggregates and coordinates community-owned renewable distributed generations (DGs) and flexibility resources for participating in power system operation. In this paper, the coordinated operation problem of VPPs and the distribution system operator (DSO) is formulated as minimizing the total operational cost constrained by linearized three-phase power flow equations and operational constraints. To preserve the VPPs’ privacy, the DSO needs to coordinate the VPPs in a distributed manner. However, conventional synchronous distributed methods may suffer from communication delays or failures because of the flimsy communication conditions between DSO and VPPs. We propose an asynchronous distributed algorithm that is robust against communication uncertainties. Firstly, a hybrid alternative direction method of multipliers (ADMM) algorithm is developed, which can be applied to convex problems with promising convergence performance. In the hybrid ADMM framework, the delayed or missing data that transmitted from VPPs are compensated by a novel predicting algorithm combining the multi-parameter quadratic programming (MPQP) and autoregressive integrated moving average model (ARIMA). We prove that the proposed algorithm can converge under imperfect communication condition with some mild assumptions. Numerical tests on IEEE 33-bus and IEEE 123-bus systems indicate that the proposed method has more reliable and faster convergence performance than existing asynchronous methods in all cases.

An implicit function formulation for optimization of discretized index-1 differential algebraic systems

A formulation for the optimization of index-1 differential algebraic equation systems (DAEs) is described that uses implicit functions to remove algebraic variables and equations from the optimization problem. The formulation uses the implicit function theorem to calculate derivatives of functions that remain in the optimization problem in terms of a reduced space of variables, allowing it to be solved with second-order nonlinear optimization algorithms. The formulation is shown to lead to more reliable solver convergence when compared with a full-space simultaneous formulation in challenging case studies involving a chemical looping combustion reactor. In a steady state simulation problem, the implicit function formulation solves 82 out of 100 instances, while the full space formulation solves only 42 out of 100 instances. In a dynamic optimization problem, the implicit function formulation solves 189 out of 200 instances, while the full space formulation solves only 152 out of 200 instances.

Spatial pricing of ride-sourcing services in a congested transportation network

We investigate the impacts of spatial pricing for ride-sourcing services in a Stackelberg framework considering traffic congestion. In the lower level, we use combined distribution and assignment approaches to explicitly capture the interactions between drivers’ relocation, riders’ mode choice, and all travelers’ routing decisions. In the upper level, a single transportation network company (TNC) determines spatial pricing strategies to minimize imbalance in a two-sided market. We show the existence of the optimal pricing strategies for locational imbalance minimization, and propose effective algorithms with reliable convergence properties. Furthermore, the optimal pricing is unique and can be solved in a convex reformulation when waiting time is small compared to travel time. We conduct numerical experiments on different scales of transportation networks with different TNC objectives to generate policy insights on how spatial pricing could impact transportation systems.

Hypergraph clustering based on modularity feature projection for high-order relationship community detection of microorganisms.

Microbial community is an important part of organisms or ecosystems to maintain health and stability. Analyzing the interaction of microorganisms in the ecosystem and mining the co-occurrence module of the microbial community can deepen the understanding of microbial community function. This could also improve the ability to manipulate the microbial community, thus provide new means for ecological restoration, disease treatment and drug development. Instead of the investigations of pairwise relationships, more and more studies have realized that the higher-order interactions may play important roles in explaining the diversity and complexity of the community. In this study, a hypergraph clustering (HCMFP) based on modularity feature projection is proposed to detect the microbial community in higher-order interaction network among microbes. Specifically, HCMFP uses information entropy to mine the higher-order logical relationships among microbes, and constructs a hypergraph learning model based on modularity feature projection to detect the microbial community. The experimental results show that compared with other methods, HCMFP has better clustering performance and reliable convergence speed. The proposed method is an effective tool for high-order organizations in microbial interaction network. The code and data in this study is freely available at https://github.com/Mayingjun20179/ HCMFP.

Context-aware reinforcement learning for course recommendation

Online course recommendation is an extremely relevant ingredient for the efficiency of e-learning. The current recommendation methods cannot guarantee the effectiveness and accuracy of course recommendation, especially when a user has enrolled in many different courses. Because these methods fail to distinguish the most relevant historical courses, which can contribute to predicting the target course that indeed reflects the user’s interests from her sequential learning behaviors. In this paper, we propose a context-aware reinforcement learning method, named Hierarchical and Recurrent Reinforcement Learning (HRRL), to efficiently reconstruct user profiles for course recommendation. The key ingredient of our scheme is the novel interaction between an attention-based recommendation model and a profile reviser with Recurrent Reinforcement Learning (RRL) that exploits temporal context. To this aim, a contextual policy gradient with approximation is proposed for RRL. By employing RRL in hierarchical tasks of revising user profiles, the proposed HRRL model enables reliable convergence in revising policy learning and improves the recommendation accuracy. We demonstrate the effectiveness of our proposed method by experiments on two open online courses datasets. Empirical results show that HRRL significantly outperforms state-of-the-art baselines.

Searching Method of Critical Slip Surface of Slope Based on Improved Wolf Swarm Algorithm

Determining the critical sliding surface and calculating the safety factor of slope stability are the key problems of slope stability analysis. Firstly, according to the characteristics of the existing wolf swarm algorithm, an improved wolf swarm algorithm is proposed, which abandons the assumption of a circular sliding surface. Then, a multipoint spline curve is introduced to describe the shape of a slope sliding surface. The optimization of the curve can determine the critical slip surface of slope and avoid falling into the local optimum. This method is programmed and implemented in Python, and then, accuracy and reliability are verified through typical slope cases and engineering examples, and the sensitivity analysis of factors that have great influence is carried out. The research results show that the slope sliding surface search method based on the improved wolf swarm algorithm can effectively and quickly determine the critical sliding surface of the slope. Compared with traditional methods, it has higher convergence accuracy and reliability. It provides an effective method for slope stability analysis.

Fine scale reconstruction (VIC#) by implementing additional constraints and coarse-grid approximation into VIC+\u2009

This study proposes a method that complements Vortex-In-Cell plus (VIC+) (Schneiders and Scarano, Exp Fluids 57:139, 2016), a data assimilation technique that reconstructs a dense flow field from sparse particle tracks. Here, the focus is on the treatment of boundary conditions. In the VIC+ method, the choice of boundary conditions significantly affects a large part of the inner domain through their role as Dirichlet boundary conditions of the Poisson equations. By nature, there are particle tracks on one side of the boundaries, and often, due to experimental limitations, the track density is low, just close to the boundaries. This lack of data near the boundaries leads to a poor iterative update of the boundary condition for VIC+. Overall, the VIC+ method tends to be sensitive about the specific choice of the initial conditions, including the inner domain and the boundaries. Without prior flow information, a large padded volume has been proposed to achieve stable and reliable convergence, at the cost of a large number of additional unknowns that need to be optimized. The present method pursues the following concepts to resolve the above issues: use of the smallest possible padding size, reconstruction starting with “all zero” initial conditions, and progressive correction of the boundary conditions by considering the continuity law and the Navier–Stokes equation. These physical laws are incorporated as additional terms in the cost function, which so far only contained the disparity between PTV measurements and the VIC+ reconstruction. Here, the Navier–Stokes equation allows an instantaneous pressure field to be optimized simultaneously with the velocity and acceleration fields. Moreover, the scale parameters in VIC+ are redefined to be directly computed from PTV measurement instead of using the initial condition, and new scaling factors for the additional cost function terms are introduced. A coarse-grid approximation is employed in order to both improve reconstruction stability and save computation time. It provides a subsequent finer-grid with its low-resolution result as an initial condition while the interrogation volume slightly shrinks. A numerical assessment is conducted using synthetic PTV data generated from the direct numerical simulation data of forced isotropic turbulence from the Johns Hopkins Turbulence Database. Improved reconstructions, especially near the volume boundary, are achieved while the virtues of VIC+ are preserved. As an experimental assessment, the existing data from a time-resolved water jet is processed. Two reconstruction domains with different sizes are considered to compare the boundary of the smaller domain with the inside of the larger one. Visible enhancements near the boundary of the smaller domain are observed for this new approach in time-varying flow fields despite the limited input from PTV data.Graphical abstract

Sample-Efficient Adaptive Calibration of Quantum Networks Using Bayesian Optimization

All physical systems employed for quantum information tasks must act as unbiased carriers of encoded quantum states. Ensuring such indistinguishability of information carriers is a major challenge in many quantum information applications, including advanced quantum communication protocols. For photons, the workhorses of quantum communication networks, it is difficult to obtain and maintain their indistinguishability because of environment-induced transformations and loss imparted by communication channels, especially in noisy scenarios. Conventional strategies to mitigate these transformations often require hardware or software overhead that is restrictive (e.g., adding noise), infeasible (e.g., on a satellite), or time-consuming for deployed networks. Here we propose and develop resource-efficient Bayesian optimization techniques to rapidly and adaptively calibrate the indistinguishability of individual photons for quantum networks using only information derived from their measurement. To experimentally validate our approach, we demonstrate the optimization of Hong-Ou-Mandel interference between two photons--a central task in quantum networking-- finding rapid, efficient, and reliable convergence towards maximal photon indistinguishability in the presence of high loss and shot noise. We expect our resource-optimized and experimentally friendly methodology will allow fast and reliable calibration of indistinguishable quanta, a necessary task in distributed quantum computing, communications, and sensing, as well as for fundamental investigations.

Investigating GNSS PPP\u2013RTK with external ionospheric constraints

Real-Time Kinematic Precise Point Positioning (PPP–RTK) is inextricably linked to external ionospheric information. The PPP–RTK performances vary much with the accuracy of ionospheric information, which is derived from different network scales, given different prior variances, and obtained under different disturbed ionospheric conditions. This study investigates the relationships between the PPP–RTK performances, in terms of precision and convergence time, and the accuracy of external ionospheric information. The statistical results show that The Time to First Fix (TTFF) for the PPP–RTK constrained by Global Ionosphere Map (PPP–RTK-GIM) is about 8–10 min, improved by 20%–50% as compared with that for PPP Ambiguity Resolution (PPP-AR) whose TTFF is about 13–16 min. Additionally, the TTFF of PPP–RTK is 4.4 min, 5.2 min, and 6.8 min, respectively, when constrained by the external ionospheric information derived from different network scales, e.g. small-, medium-, and large-scale networks, respectively. To analyze the influences of the optimal prior variances of external ionospheric delay on the PPP–RTK results, the errors of 0.5 Total Electron Content Unit (TECU), 1 TECU, 3 TECU, and 5 TECU are added to the initial ionospheric delays, respectively. The corresponding convergence time of PPP–RTK is less than 1 min, about 3, 5, and 6 min, respectively. After adding the errors, the ionospheric information with a small variance leads to a long convergence time and that with a larger variance leads to the same convergence time as that of PPP-AR. Only when an optimal prior variance is determined for the ionospheric delay in PPP–RTK model, the convergence time for PPP–RTK can be shorten greatly. The impact of Travelling Ionospheric Disturbance (TID) on the PPP–RTK performances is further studied with simulation. It is found that the TIDs increase the errors of ionospheric corrections, thus affecting the convergence time, positioning accuracy, and reliability of PPP–RTK.

Novel design of weighted differential evolution for parameter estimation of Hammerstein-Wiener systems

IntroductionKnacks of evolutionary computing paradigm-based heuristics has been exploited exhaustively for system modeling and parameter estimation of complex nonlinear systems due to their legacy of reliable convergence, accurate performance, simple conceptual design ease implementation ease and wider applicability. ObjectivesThe aim of the presented study is to investigate in evolutionary heuristics of weighted differential evolution (WDE) to estimate the parameters of Hammerstein-Wiener model (HWM) along with comparative evaluation from state-of-the-art counterparts. The objective function of the HWM for controlled autoregressive systems is efficaciously formulated by approximating error in mean square sense by computing difference between true and estimated parameters. MethodsThe adjustable parameters of HWM are estimated through heuristics of WDE and genetic algorithms (GAs) for different degrees of freedom and noise levels for exhaustive, comprehensive, and robust analysis on multiple autonomous trials. ResultsComparison through sufficient large number of graphical and numerical illustrations of outcomes for single and multiple execution of WDE and GAs through different performance measuring metrics of precision, convergence and complexity proves the worth and value of the designed WDE algorithm. Statistical assessment studies further prove the efficacy of the proposed scheme. ConclusionExtensive simulation based experimentations on measure of central tendency and variance authenticate the effectiveness of the designed methodology WDE as precise, efficient, stable, and robust computing platform for system identification of HWM for controlled autoregressive scenarios.

High sensitivity fault location technology for distribution networks considering measurement error

Accurately identifying weak fault characteristics is a critical issue for locating high impedance faults (HIFs) in distribution networks. Due to the measurement error of current sensors, the weak fault signals are easily submerged by the measurement noise interference. Nonetheless, the impact of measurement error is rarely considered explicitly. The present work addresses this issue by proposing a weak fault characteristics extraction algorithm based on an adaptive Fourier decomposition method (FDM) that can effectively suppress noise interference, and accurately locate faults with high sensitivity. First, the generalized Fourier expansion method is applied to obtain a series of independent and uncorrelated Fourier intrinsic band functions (FIBFs) adaptively by decomposing the noisy zero sequence current (ZSC) signal sampled from current sensors. Then, the FIBFs are employed to construct a set of Fourier-Hilbert spectra, which are utilized to map the noisy ZSC into a series of frequency distributions that includes the weak fault characteristic information of the HIF. The proposed density-distance search scheme can quickly identify the frequency center of gravity on both sides of the fault point to achieve reliable convergence of the clustering algorithm. Numerical simulations and field testing demonstrate that the proposed method can accurately locate HIFs with high sensitivity. Moreover, the observability and reliability of the distribution networks are improved.

Correlation-Consistent Gaussian Basis Sets for Solids Made Simple.

The rapidly growing interest in simulating condensed-phase materials using quantum chemistry methods calls for a library of high-quality Gaussian basis sets suitable for periodic calculations. Unfortunately, most standard Gaussian basis sets commonly used in molecular simulation show significant linear dependencies when used in close-packed solids, leading to severe numerical issues that hamper the convergence to the complete basis set (CBS) limit, especially in correlated calculations. In this work, we revisit Dunning's strategy for construction of correlation-consistent basis sets and examine the relationship between accuracy and numerical stability in periodic settings. We find that limiting the number of primitive functions avoids the appearance of problematic small exponents while still providing smooth convergence to the CBS limit. As an example, we generate double-, triple-, and quadruple-ζ correlation-consistent Gaussian basis sets for periodic calculations with Goedecker-Teter-Hutter (GTH) pseudopotentials. Our basis sets cover the main-group elements from the first three rows of the periodic table. Especially for atoms on the left side of the periodic table, our basis sets are less diffuse than those used in molecular calculations. We verify the fast and reliable convergence to the CBS limit in both Hartree-Fock and post-Hartree-Fock (MP2) calculations, using a diverse test set of 19 semiconductors and insulators.

Difference-based Equivalent Static Load Method with adaptive time selection and local stiffness adaption

Structural optimization of crash-related problems usually involves nonlinearities in geometry, material, and contact. The Equivalent Static Load (ESL) method provides a method to solve such problems. It has previously been extended to employ an individual Finite Element model describing the deformed geometry at each considered time step under the name Difference-based Equivalent Static Load (DiESL) method. This paper demonstrates how an appropriate selection of the time steps in each cycle can further improve the convergence behavior of the DiESL method. It is shown that the adaptive selection of time steps leads to better objective values and more reliable convergence to the presumed global optimum. Furthermore, the DiESL extension enables the adaption of path-dependent structural properties of the original nonlinear problem like material stiffness in each linear auxiliary load case. In this paper, an adaption of the Young’s modulus on element level in the linear auxiliary problem corresponding to the local plasticization in the nonlinear dynamic problem is successfully implemented. Here, the test examples indicate that an observable improvement can only be obtained if neither the elements in the elastic nor in the plastic range are dominating the structure’s behavior.

Autonomous parafoil precision landing using convex real-time optimized guidance and control

To overcome the limitations of current parafoil precision landing capabilities, an efficient real-time convex optimized guidance and control strategy is presented. The parafoil guidance problem is non-convex in essence and it can be solved with a sequence of convex problems, each of those converging in polynomial time to a feasible solution of the approximated original problem. Our approach shows reliable and fast numerical convergence through in-flight recalculation of time of flight and a new optimal trajectory to cope with time-varying dynamics. The efficiency of our strategy is demonstrated via a comparative analysis of the existing X-38 in-flight demonstrated guidance and control system. Exhaustive Monte Carlo simulations show performance improvements of about one order of magnitude. The concept proposed is simple, yet general, as it scales to any atmospheric parafoil landing system and allows efficient implementation relying only on the turn rate saturation information for the parafoil model.

Performance comparison of r2SCAN and SCAN metaGGA density functionals for solid materials via an automated, high-throughput computational workflow

Computational materials discovery efforts utilize hundreds or thousands of density functional theory calculations to predict material properties. Historically, such efforts have performed calculations at the generalized gradient approximation (GGA) level of theory due to its efficient compromise between accuracy and computational reliability. However, high-throughput calculations at the higher metaGGA level of theory are becoming feasible. The strongly constrained and appropriately normed (SCAN) metaGGA functional offers superior accuracy to GGA across much of chemical space, making it appealing as a general-purpose metaGGA functional, but it suffers from numerical instabilities that impede its use in high-throughput workflows. The recently developed ${\mathrm{r}}^{2}\mathrm{SCAN}$ metaGGA functional promises accuracy similar to SCAN in addition to more robust numerical performance. However, its performance compared to SCAN has yet to be evaluated over a large group of solid materials. In this paper, we compared ${\mathrm{r}}^{2}\mathrm{SCAN}$ and SCAN predictions for key properties of approximately 6000 solid materials using a newly developed high-throughput computational workflow. We find that ${\mathrm{r}}^{2}\mathrm{SCAN}$ predicts formation energies more accurately than SCAN and PBEsol for both strongly and weakly bound materials and that ${\mathrm{r}}^{2}\mathrm{SCAN}$ predicts systematically larger lattice constants than SCAN. We also find that ${\mathrm{r}}^{2}\mathrm{SCAN}$ requires modestly fewer computational resources than SCAN and offers significantly more reliable convergence. Thus, our large-scale benchmark confirms that ${\mathrm{r}}^{2}\mathrm{SCAN}$ has delivered on its promises of numerical efficiency and accuracy, making it a preferred choice for high-throughput metaGGA calculations.

Proxy-Based Deep Learning Framework for Spectral–Spatial Hyperspectral Image Classification: Efficient and Robust

Deep convolutional networks have been extensively deployed in hyperspectral image (HSI) classification. Reaching for high accuracy, the existing deep-learning-based methods commonly deepen or widen their networks for better performance, which brings higher computational complexity and the risk of overfitting. Although the introduction of the residual module and batch-normalization reduces the generalization degradation in complex networks, the mainstream methods still suffer from low robustness to the noise. To tackle these issues, a compact proxy-based deep learning framework is proposed to perform highly accurate HSI classification with superb efficiency and robustness. In this article: 1) novel deep proxies are integrated to replace the dense classifier layers in conventional networks, which represents specific classes in deep embedding space and enables fast and reliable convergence; 2) the proxy-based feature embedding is studied in distance metric and similarity metric, and compatible dual-metric loss functions are designed for further optimized embedding distribution, which leads to more robust generalization; and 3) state-of-the-art performance and robustness are demonstrated by the proposed framework on mainstream HSI data sets with the minimal network scale and time complexity.

Intelligent computing based supervised learning for solving nonlinear system of malaria endemic model

<abstract><p>A repeatedly infected person is one of the most important barriers to malaria disease eradication in the population. In this article, the effects of recurring malaria re-infection and decline in the spread dynamics of the disease are investigated through a supervised learning based neural networks model for the system of non-linear ordinary differential equations that explains the mathematical form of the malaria disease model which representing malaria disease spread, is divided into two types of systems: Autonomous and non-autonomous, furthermore, it involves the parameters of interest in terms of Susceptible people, Infectious people, Pseudo recovered people, recovered people prone to re-infection, Susceptible mosquito, Infectious mosquito. The purpose of this work is to discuss the dynamics of malaria spread where the problem is solved with the help of Levenberg-Marquardt artificial neural networks (LMANNs). Moreover, the malaria model reference datasets are created by using the strength of the Adams numerical method to utilize the capability and worth of the solver LMANNs for better prediction and analysis. The generated datasets are arbitrarily used in the Levenberg-Marquardt back-propagation for the testing, training, and validation process for the numerical treatment of the malaria model to update each cycle. On the basis of an evaluation of the accuracy achieved in terms of regression analysis, error histograms, mean square error based merit functions, where the reliable performance, convergence and efficacy of design LMANNs is endorsed through fitness plot, auto-correlation and training state.</p></abstract>

Filtering variational quantum algorithms for combinatorial optimization

Current gate-based quantum computers have the potential to provide a computational advantage if algorithms use quantum hardware efficiently. To make combinatorial optimization more efficient, we introduce the filtering variational quantum eigensolver which utilizes filtering operators to achieve faster and more reliable convergence to the optimal solution. Additionally we explore the use of causal cones to reduce the number of qubits required on a quantum computer. Using random weighted MaxCut problems, we numerically analyze our methods and show that they perform better than the original VQE algorithm and the quantum approximate optimization algorithm. We also demonstrate the experimental feasibility of our algorithms on a Quantinuum trapped-ion quantum processor powered by Honeywell.