Good Convergence Properties Research Articles

Inversion learning of turbulent thermal diffusion for film cooling

Film cooling is a typical three-dimensional fluid phenomenon, where the coolant with lower temperature is ejected from discrete holes to protect metal walls from being burnt by the hot mainstream. It is a great challenge for Reynolds-averaged Navier–Stokes (RANS) methods to accurately predict the coolant coverage on the wall because the turbulent thermal diffusion tends to be under-predicted due to inherent assumptions behind RANS models. In this paper, a framework of integrated field inversion and machine learning is built to enhance RANS prediction of turbulent thermal diffusion. A neural network (NN) is trained in this framework to predict the spatially varying turbulent Prandtl number (Prt) and to improve the prediction of RANS models. The temperature distribution obtained from the large eddy simulation is used as the learning target, and the discrete adjoint method is used as the inverse model that helps calculate derivatives of mean square error of the temperature distribution to NN parameters. The training process of NN shows good convergence properties. The results show that the obtained NN effectively increases the insufficient turbulent thermal diffusion by predicting much lower Prt than the commonly used value of 0.9. The NN-enhanced RANS provides significant improvements on predicting experimental temperature distributions compared with general RANS models not only on the training data but also on the unseen testing data. In addition, the obtained NN can be implemented into general-purpose software with minimal effort and no numerical stability problem.

Set-membership affine projection algorithm based on the percentage change of the error signal and variable projection order

Nowadays, the use of adaptive filters plays an important role in multiple signal processing applications, such as active noise control, acoustic echo cancellers, system identifiers, channel equalizer, among others. Until date, many of the existing adaptive algorithms such as affine projection algorithms offer a high convergence speed. However, its computational cost is also high. Currently, several authors make extraordinary efforts to reduce its computational cost to be used in practical applications. In this paper, we propose a new set-membership affine projection algorithm based on the percentage change of the error signal and variable projection order (SMAP-PC-VO). Specifically, we propose two techniques to create this algorithm; 1) the new algorithm uses an error bound, which is obtained by calcuting the percentage change of the error signal, to avoid the computation of the variance of additive noise, since in existing approaches this parameter determines the error bound. In practical applications, the computation of the variance of additive noise is infeasible since this signal is not available; 2) we propose a new method to dynamically modify the projection order in the new algorithm. As a consequence, its computational cost is reduced. To demonstrate its performance, the proposed algorithm was successfully tested in different environments for system identification and active noise control for headphone applications. The simulation results demonstrate that the proposed algorithm presents good convergence properties. In addition, the proposed algorithm exhibits a low overall computational complexity.

Derivative-free trust region optimization for robust well control under geological uncertainty

A Derivative-Free Trust-Region (DFTR) algorithm is proposed to solve the robust well control optimization problem under geological uncertainty. Derivative-Free (DF) methods are often a practical alternative when gradients are not available or are unreliable due to cost function discontinuities, e.g., caused by enforcement of simulation-based constraints. However, the effectiveness of DF methods for solving realistic cases is heavily dependent on an efficient sampling strategy since cost function calculations often involve time-consuming reservoir simulations. The DFTR algorithm samples the cost function space around an incumbent solution and builds a quadratic polynomial model, valid within a bounded region (the trust-region). A minimization of the quadratic model guides the method in its search for descent. Because of the curvature information provided by the model-based routine, the trust-region approach is able to conduct a more efficient search compared to other sampling methods, e.g., direct-search approaches. DFTR is implemented within FieldOpt, an open-source framework for field development optimization, and is tested in the Olympus benchmark against two other types of methods commonly applied to production optimization: a direct-search (Asynchronous Parallel Pattern Search) and a population-based (Particle Swarm Optimization). Current results show that DFTR has improved performance compared to the model-free approaches. In particular, the method presented improved convergence, being capable to reach solutions with higher NPV requiring comparatively fewer iterations. This feature can be particularly attractive for practitioners who seek ways to improve production strategies while using an ensemble of full-fledged models, where good convergence properties are even more relevant.

Adaptive Erasure Coded Fault Tolerant Linear System Solver

As parallel and distributed systems scale, fault tolerance is an increasingly important problem—particularly on systems with limited I/O capacity and bandwidth. Erasure coded computations address this problem by augmenting a given problem instance with redundant data and then solving the augmented problem in a fault oblivious manner in a faulty parallel environment. In the event of faults, a computationally inexpensive procedure is used to compute the true solution from a potentially fault-prone solution. These techniques are significantly more efficient than conventional solutions to the fault tolerance problem. In this article, we show how we can minimize, to optimality, the overhead associated with our problem augmentation techniques for linear system solvers. Specifically, we present a technique that adaptively augments the problem only when faults are detected. At any point in execution, we only solve a system whose size is identical to the original input system. This has several advantages in terms of maintaining the size and conditioning of the system, as well as in only adding the minimal amount of computation needed to tolerate observed faults. We present, in detail, the augmentation process, the parallel formulation, and evaluation of performance of our technique. Specifically, we show that the proposed adaptive fault tolerance mechanism has minimal overhead in terms of FLOP counts with respect to the original solver executing in a non-faulty environment, has good convergence properties, and yields excellent parallel performance. We also demonstrate that our approach significantly outperforms an optimized application-level checkpointing scheme that only checkpoints needed data structures.

Deep Reinforcement Learning-Based Accurate Control of Planetary Soft Landing.

Planetary soft landing has been studied extensively due to its promising application prospects. In this paper, a soft landing control algorithm based on deep reinforcement learning (DRL) with good convergence property is proposed. First, the soft landing problem of the powered descent phase is formulated and the theoretical basis of Reinforcement Learning (RL) used in this paper is introduced. Second, to make it easier to converge, a reward function is designed to include process rewards like velocity tracking reward, solving the problem of sparse reward. Then, by including the fuel consumption penalty and constraints violation penalty, the lander can learn to achieve velocity tracking goal while saving fuel and keeping attitude angle within safe ranges. Then, simulations of training are carried out under the frameworks of Deep deterministic policy gradient (DDPG), Twin Delayed DDPG (TD3), and Soft Actor Critic (SAC), respectively, which are of the classical RL frameworks, and all converged. Finally, the trained policy is deployed into velocity tracking and soft landing experiments, results of which demonstrate the validity of the algorithm proposed.

Trial and Error Learning for Dynamic Distributed Channel Allocation in Random Medium

This paper considers the problem of fully distributed channel allocation in clustered wireless networks when the propagation medium is random. We extend here the existing Trial and Error (TE) framework developed in the deterministic case and for which strong convergence properties hold. We prove that using directly this solution in the random context leads to unsatisfactory solutions. Then we propose an adaptation of the original Trial and Error Learning (TEL) algorithm, called Robust TEL (RTEL), assuming that the random channel effects translate into a bounded stochastic disturbance of the utility function. The solution consists in introducing thresholds in the transitions of the TEL’s Finite State Controller (FSC). We prove that this new solution restores the good convergence property inherited from the TEL. Furthermore, we provide analysis of the stochastic utilities in the Rayleigh fading case in order to check the bounded assumption. Finally, we develop an online algorithm that dynamically estimates the optimal threshold values to adapt to the instantaneous disturbance. Numerical results corroborate our theoretical claims.

Renormalization group optimized λϕ4 pressure at next-to-next-to-leading order

We investigate the renormalization group optimized perturbation theory (RGOPT) at the next-to-next-to-leading order (NNLO) for the thermal scalar field theory. From comparing three thus available successive RGOPT orders, we illustrate the efficient resummation and very good apparent convergence properties of the method. In particular, the remnant renormalization scale dependence of thermodynamical quantities is drastically improved as compared to both standard perturbative expansions and other related resummation methods, such as the screened perturbation theory. Our present results thus constitute a useful first NNLO illustration in view of NNLO applications of this approach to the more involved thermal QCD.

Uni-Cycle Genetic Algorithm to Improve the Adaptive Equalizer Performance

In this contribution, a novel uni-cycle Genetic Algorithm (GA) is proposed as a learning tool to optimize the coefficients of an adaptive linear equalizer. The meaning of evolution concept is understood quite different in comparison with the regular GA, originally not designed to solve dynamic optimization problems: just like in nature, where the environmental conditions tend to evolve, the channel state is a subject to continuous change so does the optimal set of equalizer coefficients, represented by the individuals’ chromosomes in the proposed uni-cycle GA. The algorithm is designed with the aim to work in the real time. To meet such requirement, it considers only one generation per one signaling interval. As the results of the simulation study show, the proposed solution achieves superior performance over the Least Mean Square (LMS) algorithm. Furthermore, the uni-cycle GA possesses good convergence properties and a fast-tracking capability.

Elegant Iterative Methods for Solving a Nonlinear Matrix Equation X-A* eX A=I

The nonlinear matrix equation was solved by Gao (2016) via standard fixed point method. In this paper, three more elegant iterative methods are proposed to find the approximate solution of the nonlinear matrix equation namely: Newton’s method; modified fixed point method and a combination of Newton’s method and fixed point method. The convergence of Newton’s method and modified fixed point method are derived. Comparative numerical experimental results indicate that the new developed algorithms have both less computational time and good convergence properties when compared to their respective standard algorithms.
 Keywords: Hermitian positive definite solution; nonlinear matrix equation; modified fixed point method; iterative method

Isogeometric collocation discretizations for acoustic wave problems

The acoustic wave problem is here discretized by collocation isogeometric analysis (IGA) in space and Newmark schemes of first and second order in time. A numerical study in the plane on both Cartesian and NURBS domains investigates the convergence rate of the proposed collocation Newmark-IGA method and its dependence on the main isogeometric parameters, the mesh size h, the spline polynomial degree p, the spline regularity k, and on the time step size Δt. In addition, a Ricker wavelet propagation test is accurately reproduced. The stability thresholds in time of the proposed method depend linearly on h and inversely on p. Therefore, the proposed collocation Newmark-IGA method retains the good convergence and stability properties of standard Galerkin IGA and spectral element discretizations of acoustic problems, as well as the high computational efficiency of collocation methods due to matrix sparsity and fast function evaluation.

Optimal measurement budget allocation for Kalman prediction over a finite time horizon by genetic algorithms

In this paper, we address the problem of optimal measurement budget allocation to estimate the state of a linear discrete-time dynamical system over a finite horizon. More precisely, our aim is to select the measurement times in order to minimize the variance of the estimation error over a finite horizon. In addition, we investigate the closely related problem of finding a trade-off between number of measurements and signal to noise ratio.First, the optimal measurement budget allocation problem is reduced to a deterministic combinatorial program. Then, we propose a genetic algorithm implementing a count preserving crossover to solve it. On the theoretical side, we provide a one-dimensional analysis that indicates that the benefit of using irregular measurements grows when the system is unstable or when the process noise becomes important. Then, using the duality between estimation and control, we show that the problem of selecting optimal control times for a linear quadratic regulator can be reduced to our initial problem.Finally, numerical implementations demonstrate that using measurement times optimized by our genetic algorithm gives better estimate than regularly spaced measurements. Our method is applied to a discrete version of a continuous-time system and the impact of the discretization time step is studied. It reveals good convergence properties, showing that our method is well suited to both continuous-time and discrete-time setups.

Analytical modeling and optimization of new Ku‐band tunable square waveguide iris‐post polarizer

AbstractA novel design of the polarizer based on a square waveguide with four posts and four irises for Ku‐band 10.7–12.8 GHz is proposed. The main advantage of the developed polarizer design is the option to tune its polarization characteristics by variation of the posts height. The equivalent circuit of the polarizer has been obtained using scattering and transfer matrices technique. Using this model, the polarization and matching characteristics of the suggested polarizer were optimized simultaneously using the trust region method. This method is reliable and robust since it provides good convergence properties. The novelty of this study lies in the use of a new waveguide polarizer structure based on a combination of irises and posts. Posts enable fine‐tuning of the polarizer performance, while irises promote wide operating frequency band. The following simulated characteristics of the optimal polarizer design were obtained: VSWR for the main modes of horizontal and vertical polarization is less than 1.47, the differential phase shift is within 90° ± 2.6°, the axial is less than 0.46 dB, and the XPD is higher than 32 dB in the operating frequency range. A developed polarizer can be applied in antenna feeds for satellite communication and radar systems.

Entanglement rearrangement in self-consistent nuclear structure calculations

Background: Entanglement plays a central role in a diverse array of increasingly important research areas, including quantum computation, simulation, measurement, sensing, and communication. Extensive suites of investigations have been performed to better understand entanglement in atomic and molecular quantum many-body systems, while the exploration of entanglement in the structure of nuclei and their reactions is presently in its infancy.Purpose: The goal of this work is to begin investigating the entanglement properties of nuclei from first-principles nuclear many-body calculations. We attempt to identify common features and emergent structures of entanglement that could ultimately lead to new and natural many-body schemes. With an eye toward quantum accelerators in future hybrid-supercomputers, criteria for partitioning nuclear many-body calculations into quantum and classical components may provide advantages in future large-scale computations. Along the way we look for explanations of the relative success of phenomenological models such as the nuclear shell model, and for better ways to match to low-energy nuclear effective field theories and lattice QCD calculations to nuclear many-body techniques that are based upon entanglement.Method: We explore the entanglement between single-particle states in $^{4}\mathrm{He}$ and $^{6}\mathrm{He}$. The patterns of entanglement emerging from different single-particle bases are compared, and possible links with the convergence of observables are explored, in particular, ground-state energies. The nuclear wave functions are obtained by performing active-space no-core configuration-interaction calculations using a two-body nucleon-nucleon interaction derived from chiral effective field theory. Entanglement measures within single-particle bases exhibiting different degrees of complexity are determined, in particular, harmonic oscillator (HO), Hartree-Fock (HF), natural (NAT) and variational natural (VNAT) bases. Specifically, single-orbital entanglement entropy, two-orbital mutual information, and negativity are studied.Results: The entanglement structures in $^{4}\mathrm{He}$ and $^{6}\mathrm{He}$ are found to be more localized within NAT and VNAT bases than within a HO basis for the optimal HO parameters we have worked with. In particular a core-valence structure clearly emerges from the full no-core calculation of $^{6}\mathrm{He}$. The two-nucleon mutual information shows that the VNAT basis, which typically exhibits good convergence properties, effectively decouples the active and inactive spaces.Conclusions: Measures of one- and two-nucleon entanglement are found to be useful in analyzing the structure of nuclear wave functions, in particular the efficacy of basis states, and may provide useful metrics toward developing more efficient schemes for ab initio computations of the structure and reactions of nuclei, and quantum many-body systems more generally.

Microarchitecture-dependent nonlinear bending analysis for cellular plates with prismatic corrugated cores via an anisotropic strain gradient plate theory of first-order shear deformation

This study focuses on the microarchitecture-dependent nonlinear bending behavior of cellular plates with equitriangularly prismatic microarchitectures by adopting a dimensionally and constitutively reduced strain gradient plate model. The strain energy formulation is based on the dimension reduction of the first-order shear deformation plate theory along with von Kármán’s nonlinear strain relations and anisotropic strain gradient theory. The classical and higher-order constitutive parameters are obtained according to the recently published homogenization results for a corresponding linear plate model. The corresponding finite element simulations, numerically solving the anisotropic strain gradient plate problems, rely on a nonstandard, higher-order, six-node triangular element showing good convergence properties. Comparisons between the proposed (2D) strain gradient shear deformation plate model and the corresponding (3D) detailed full-field reference models demonstrate for a variety of cellular plate structures that the accuracy of the proposed approach is at a very good level with relatively low computational costs. A diverse set of numerical examples is provided in order to investigate the size-dependent nonlinear structural response of cellular plates having different numbers of microarchitectural layers, midsurface shapes and boundary conditions.

A Cournot game model for integrated energy service transaction in electric-gas coupled market

Based on the analysis of the game behaviours of multi-energy players, for the purpose of maximining the utility of market entities, this study establishes a Cournot game model in the electricity-gas coupled market for multi-energy players, which include the pricing model of multi-energy players in Leader-Follower mode and the operation optimization model between multi-energy players and local energy system based on Stackelberg game. Through the example analysis, it is demonstrated that the master-slave model has good convergence properties and plays a vital role in the interaction process between different decision-making bodies and find the optimal strategy, which can provide important reference information for the decision-makers and has certain practical value.

Effective Two-Stage Image Segmentation: A New Non-Lipschitz Decomposition Approach with Convergent Algorithm

Image segmentation is an important median level vision topic. Accurate and efficient multiphase segmentation for images with intensity inhomogeneity is still a great challenge. We present a new two-stage multiphase segmentation method trying to tackle this, where the key is to compute an inhomogeneity-free approximate image. For this, we propose to use a new non-Lipschitz variational decomposition model in the first stage. The minimization problem is solved by an iterative support shrinking algorithm. By assuming that the subproblem at each iteration is exactly solved, we show the global convergence of the iterative algorithm and a lower bound theory of the image gradient of the iterative sequence, which indicates that the generated approximate image (inhomogeneity-corrected component) is with very neat edges and suitable for the following thresholding operation. Implementation details based on the alternating direction method of multipliers for the strongly convex subproblems are also given. In the second stage, the segmentation is done by applying a widely used simple thresholding technique to the piecewise constant approximation. Numerical experiments indicate good convergence properties and effectiveness of our method in multiphase segmentation for either clean or noisy homogeneous and inhomogeneous images. Both visual and quantitative comparisons with some state-of-the-art approaches demonstrate the performance advantages of our non-Lipschitz-based method.

Spanish validation and factor structure of the Prenatal Distress Questionnaire Revised (NuPDQ)

ABSTRACT Background: Due to an absence of maternal stress being measured in routine prenatal care by clinicians, prenatal stress has become a serious problem which is associated with poorer obstetric outcomes, as well as worse maternal and infant health. For that reason, the aim of this study was the translation, validation and adaptation of Prenatal Distress Questionnaire Revised (NuPDQ) in a Spanish sample. Methods: Three-hundred and seventy-one pregnant women were assessed using the NuPDQ, the Prenatal Distress Questionnaire, Perceived Stress Scale and the Connor–Davidson Resilience Scale. The NuPDQ was translated into Spanish by the backtranslation method and administered to participants. Results: A confirmatory factor analysis revealed the established unidimensional structure to be a poor fit to data with the Spanish version. An exploratory factor analysis suggested a five-factor structure with 14 items. The instrument had good reliability, convergent and discriminant validity psychometric properties. Conclusions: The five-factor 14-item NuPDQ is useful to assess pregnancy-specific stress in Spanish pregnant women. It may be appropriate to use this instrument in order to identify pregnant women with high pregnancy-specific stress to try to prevent negative consequences derived from those high levels.

Fully implicit multiple graphics processing units’ schemes for hypersonic flows with lower upper symmetric Gauss-Seidel preconditioner on unstructured non-orthogonal grids

The paper discusses the simulation of the hypersonic flow problems on unstructured grids using fully implicit scheme and the analysis of the orthogonal corrections on the quality of heat fluxes on the surfaces of the bodies subject to hypersonic flow. The governing equations are the Navier-Stokes equations for viscous calorically perfect gas. Second order finite volume discretization is applied to the problem on arbitrary unstructured grids with implicit temporal treatment. The problem is solved using the Newton-Raphson method. Such methods require the solution of large linear systems with iterative solvers and require a preconditioning operator to converge. In this paper a well known Lower-Upper Symmetric Gauss Seidel (LU-SGS) preconditioner is applied. The new method is based on the tricky reordering for the factored Jacobi matrix that allows one to execute block triangular matrix solvers on GPUs in parallel without the loss of algebraic properties of the original non-factored operator. Good convergence properties are demonstrated for large scale problems of external aerodynamics with implicit Courant number around 1000 - 10000 for flows with Mach number around 13-25. The influence of the non-orthogonal corretions on the fluxes for highly scewed anisotropic grids is demonstrated at Mach numbers around 20. It is shown that the non-orthogonality corrections are of the second infinitesimal order compared to the effects of the shock fix influence on the heat fluxes on the body.

Overlapping Schwarz methods for isogeometric analysis based on generalized B-splines

Generalized B-splines (GB-splines) are a special class of Tchebycheff B-splines that are smooth piecewise function with sections in more general spaces. GB-splines allow for an exact representation of conic sections as well as transcendental curves and thus they become very attractive for geometrical modeling and numerical simulation. In this paper, we present overlapping Schwarz preconditioners for elliptic problems discretized with isogeometric analysis based on GB-splines. An h-analysis of the proposed preconditioners shows an optimal convergence rate bound that is scalable in the number of subdomains and that is linear in the ratio between subdomain and overlap sizes. Numerical results in two- and three-dimensional tests confirm this analysis and also illustrate the good convergence properties of the preconditioner with respect to the discretization parameters, the domain deformation and the jumping coefficients.

Hybrid Riemannian conjugate gradient methods with global convergence properties

This paper presents Riemannian conjugate gradient methods and global convergence analyses under the strong Wolfe conditions. The main idea of the proposed methods is to combine the good global convergence properties of the Dai–Yuan method with the efficient numerical performance of the Hestenes–Stiefel method. One of the proposed algorithms is a generalization to Riemannian manifolds of the hybrid conjugate gradient method of the Dai and Yuan in Euclidean space. The proposed methods are compared well numerically with the existing methods for solving several Riemannian optimization problems. Python implementations of the methods used in the numerical experiments are available at https://github.com/iiduka-researches/202008-hybrid-rcg .