Set Of Sample Points Research Articles

A Multi-Fidelity Bayesian Optimization Approach for Constrained Multi-Objective Optimization Problems

Abstract In this paper, a multi-fidelity Bayesian optimization approach is presented to tackle computationally expensive constrained multiobjective optimization problems (MOPs). The proposed approach consists of a three-stage optimization framework designed to search for promising candidate points. In the first stage, an acquisition function is proposed to identify a feasible solution if none is available in the current set of sampling points. Subsequently, a new multi-fidelity weighted expected hypervolume improvement function is developed to find better solutions. In the third stage, a constrained weighted lower confidence bound acquisition function is presented to enhance the constraint predictions and refine the solutions near the constraint boundary. Additionally, a filter strategy is suggested to determine whether constraint updating is necessary, aiming to save computational resources and improve optimization efficiency. Moreover, to expedite the optimization process, a parallel optimization approach is further developed based on the suggested three-stage optimization framework. To achieve this, a multi-fidelity influence function is introduced, allowing the proposed approach to determine a desired number of candidate points within a single iteration. Lastly, the proposed approach is demonstrated through six numerical benchmark examples, which verifies its significant advantages in addressing expensive constrained MOPs. Besides, the proposed approach is applied to the multiobjective optimization of a metamaterial vibration isolator, resulting in the attainment of satisfactory solutions.

MPP-net: Multi-perspective perception network for dense video captioning

Applying deformable transformer for dense video captioning has achieved great success recently. However, deformable transformer only explores local-perspective perception by attending to a small set of key sampling points, which will make the decoder short-sighted and generate semantically incoherent and contradictory dense captions for a long video. In this paper, we propose a novel Multi-Perspective Perception Network to improve this problem. We first introduce a hierarchical temporal-spatial summary method to generate global-perspective summary context for each decoder layer and avoid redundant information. Then our new designed multi-perspective attention encourages the model to selectively incorporate the multi-perspective perception feature. Finally, we propose a novel multi-perspective generator to perform both multi-perspective feature fusion and caption generation. Experiments show that our proposed model outperforms previously published methods and achieves a competitive performance on ActivityNet Captions and YouCook2. The design of our model also shows the universality of other visual tasks that we obtain comparable results by applying our model for Object Detection and Paragraph Video Captioning.

Stochastic representation of many-body quantum states

The quantum many-body problem is ultimately a curse of dimensionality: the state of a system with many particles is determined by a function with many dimensions, which rapidly becomes difficult to efficiently store, evaluate and manipulate numerically. On the other hand, modern machine learning models like deep neural networks can express highly correlated functions in extremely large-dimensional spaces, including those describing quantum mechanical problems. We show that if one represents wavefunctions as a stochastically generated set of sample points, the problem of finding ground states can be reduced to one where the most technically challenging step is that of performing regression—a standard supervised learning task. In the stochastic representation the (anti)symmetric property of fermionic/bosonic wavefunction can be used for data augmentation and learned rather than explicitly enforced. We further demonstrate that propagation of an ansatz towards the ground state can then be performed in a more robust and computationally scalable fashion than traditional variational approaches allow.

Adapting the centred simplex gradient to compensate for misaligned sample points

Abstract The centred simplex gradient (CSG) is a popular gradient approximation technique in derivative-free optimization. Its computation requires a perfectly symmetric set of sample points and is known to provide an accuracy of $\mathcal {O}(\varDelta ^2)$, where $\varDelta $ is the radius of the sampling set. In this paper, we consider the situation where the set of sample points is not perfectly symmetric. By adapting the formula for the CSG to compensate for the misaligned points, we define a new Adapted-CSG. We study the error bounds and the numerical stability of the Adapted-CSG. We also present numerical examples to demonstrate its properties relative to each new parameter and make a comparison to an alternative method.

Dynamic reconfiguration of AC/DC hybrid distribution network considering non-ideal linear BES model

The charging and discharging process of battery energy storage (BES) directly affects its cycle aging. Therefore, considering the cycle aging cost and demand response of BES, this paper proposes a dynamic reconfiguration method of AC/DC hybrid distribution network. By sampling the operation area of charging and discharging power, the BES model in the non-ideal state is reconstructed into a linear model in the convex envelope set of sampling points. On this basis, the cycle aging cost models based on the cumulative throughput and discharge depth are established respectively, and the AC/DC hybrid distribution network reconfiguration model with the minimum comprehensive cost is constructed, and the mixed integer second-order cone programming method is used to solve it. The effectiveness and economy of the proposed reconfiguration method for AC/DC hybrid distribution network are verified by simulation on a modified 33-bus and 70-bus system.

Point normal orientation and surface reconstruction by incorporating isovalue constraints to Poisson equation

Oriented normals are common pre-requisites for many geometric algorithms based on point clouds, such as Poisson surface reconstruction. However, it is not trivial to obtain a consistent orientation. In this work, we bridge orientation and reconstruction in the implicit space and propose a novel approach to orient point cloud normals by incorporating isovalue constraints to the Poisson equation. In implicit surface reconstruction, the reconstructed shape is represented as an isosurface of an implicit function defined in the ambient space. Therefore, when such a surface is reconstructed from a set of sample points, the implicit function values at the points should be close to the isovalue corresponding to the surface. Based on this observation and the Poisson equation, we propose an optimization formulation that combines isovalue constraints with local consistency requirements for normals. We optimize normals and implicit functions simultaneously and solve for a globally consistent orientation. Thanks to the sparsity of the linear system, our method can work on an average laptop with reasonable computational time. Experiments show that our method can achieve high performance in non-uniform and noisy data and manage varying sampling densities, artifacts, multiple connected components, and nested surfaces. The source code is available at https://github.com/Submanifold/IsoConstraints.

Assessing Search and Unsupervised Clustering Algorithms in Nested Sampling.

Nested sampling is an efficient method for calculating Bayesian evidence in data analysis and partition functions of potential energies. It is based on an exploration using a dynamical set of sampling points that evolves to higher values of the sampled function. When several maxima are present, this exploration can be a very difficult task. Different codes implement different strategies. Local maxima are generally treated separately, applying cluster recognition of the sampling points based on machine learning methods. We present here the development and implementation of different search and clustering methods on the nested_fit code. Slice sampling and the uniform search method are added in addition to the random walk already implemented. Three new cluster recognition methods are also developed. The efficiency of the different strategies, in terms of accuracy and number of likelihood calls, is compared considering a series of benchmark tests, including model comparison and a harmonic energy potential. Slice sampling proves to be the most stable and accurate search strategy. The different clustering methods present similar results but with very different computing time and scaling. Different choices of the stopping criterion of the algorithm, another critical issue of nested sampling, are also investigated with the harmonic energy potential.

A non-linear Kalman filter for track parameters estimation in high energy physics

The Kalman Filter is a widely used approach for the linear quadratic estimation of dynamical systems and is frequently employed within nuclear and particle physics experiments for the reconstruction of charged particle trajectories, known as tracks. Implementations of this formalism often make assumptions on the linearity of the underlying dynamic system and the Gaussian nature of the process noise and measurement model, which are violated in a number of track reconstruction applications. This paper introduces an implementation of a Non-Linear Kalman Filter (NLKF) within the ACTS track reconstruction toolkit. The NLKF addresses the issue of non-linearity by using a set of representative sample points during the projection of the track state to the measurement. In a typical use case, the NLKF outperforms the so-called Extended Kalman Filter in the accuracy and precision of the track parameter estimates obtained, with an increase in CPU time below a factor of two. It is therefore a promising approach for use in applications where precise estimation of track parameters is a key concern.

Lorentz-covariant sampling theory for fields

Sampling theory is a discipline in communications engineering involved with the exact reconstruction of continuous signals from discrete sets of sample points. From a physics perspective, this is interesting in relation to the question of whether spacetime is continuous or discrete at the Planck scale, since in sampling theory we have functions which can be viewed as equivalently residing on a continuous or discrete space. Further, it is possible to formulate analogues of sampling which yield discreteness without disturbing underlying spacetime symmetries. In particular, there is a proposal for how this can be adapted for Minkowski spacetime. Here we will provide a detailed examination of the extension of sampling theory to this context. We will also discuss generally how spacetime symmetries manifest themselves in sampling theory, which at the surface seems in conflict with the fact that the discreteness of the sampling is not manifestly covariant. Specifically, we will show how the symmetry of a function space with a sampling property is equivalent to the existence of a family of possible sampling lattices related by the symmetry transformations.

Investicioni portfolio zasnovan na probabilističkoj višekriterijumskoj optimizaciji i uniformnom dizajnu za eksperimente sa varijacijama

Introduction/purpose: In this paper, a new approach to solving the portfolio investment problem is formulated to handle simultaneous optimization of both maximizing the rate of return and minimizing the variance of the rate of return. Probability - based multi - objective optimization is combined with uniform design for experiments with mixtures to conduct processing. Methods: Preliminarily, probability - based multi - objective optimization is employed to synthesize the bi-objective problem of simultaneous optimization of both maximizing the rate of return and minimizing the variance of the rate of return into a single objective one of the total preferable probability of each alternative scenario. The total preferable probability is the product of all partial preferable probabilities of each performance utility; subsequently, the method of uniform design for experiments with mixtures is used to create a set of effective sampling points for the portfolio investment problem to provide discretization in data processing and simplifying treatment, of which the proportion xi follows the constraint condition of xl + x2 + x3．．．+ xs = 1 with the total number of variables s for xi. Results: The new approach is used to deal with the portfolio Investment problem that is, in essence, simultaneous optimization of both maximizing the rate of return and minimizing the variance of the rate of return, which leads to reasonable consequences. The results are with the quality of rationality from the respect of the probability theory for simultaneous optimization of multiple objectives. Conclusion: This method naturally reflects the essence of the portfolio investment problem and opens a new way of solving the relevant problem.

Open-Set Recognition Model Based on Negative-Class Sample Feature Enhancement Learning Algorithm

In order to solve the problem that the F1-measure value and the AUROC value of some classical open-set classifier methods do not exceed 40% in high-openness scenarios, this paper proposes an algorithm combining negative-class feature enhancement learning and a Weibull distribution based on an extreme value theory representation method, which can effectively reduce the risk of open space in open-set scenarios. Firstly, the solution uses the negative-class sample feature enhancement learning algorithm to generate the negative sample point set of similar features and then compute the corresponding negative-class sample feature segmentation hypersphere. Secondly, the paired Weibull distributions from positive and negative samples are established based on the corresponding negative-class sample feature segmentation hypersphere of each class. Finally, solutions for non-linear multi-class classifications are constructed by using the Weibull and reverse Weibull distributions. Experiments on classic open datasets such as the open dataset of letter recognition, the Caltech256 open dataset, and the CIFAR100 open dataset show that when the openness is greater than 60%, the performance of the proposed method is significantly higher than other open-set support vector classifier algorithms, and the average is more than 7% higher.

Multi-objective optimization of the geometric parameters of a pressure-swirl nozzle

ABSTRACT The geometric parameters of the pressure-swirl nozzle demonstrate a significant effect on the atomization performance such as the spray cone angle and mass flow rate. However, these objectives are incompatible, and obtaining a nozzle geometric parameter that optimizes all the atomization performances is difficult. The effectiveness of the nozzle optimization process is typically low, resulting in high costs. To this purpose, an enhanced CBSO-Kriging surrogate model was developed to solve this expensive black box problem, and the spray cone angle and mass flow rate were optimized using a multi-objective optimization algorithm. Firstly, the optimal Latin hypercube sampling method was used to generate 65 sets of sample points, and the corresponding response values were calculated using CFD simulation. The established surrogate model of atomization performance can predict the atomization characteristics of the nozzle with arbitrary shape. The correlation between the key geometric parameters and the spray cone angle and the mass flow rate was determined on this basis. Then, to find the optimal geometric parameters for the nozzle, the NSGA-II algorithm was used. In comparison to the initial model, the optimization results show that the spray cone angle and mass flow rate increased by 4.26% and 37.74%, respectively.

Finite element model updating through derivative-free optimization algorithm

Finite element (FE) model of updating is the process of calibrating model parameters to improve the accuracy of numerical prediction. This goal is usually achieved by solving an optimization problem with the objective function measuring the misfit between simulated responses and experimental data. The sensitivity method is the predominate class of algorithms to FE model updating problems, and has opened a wide range of applications. However, this method often suffers from large errors due to linearization. To address this challenge, this paper proposes to utilize the unscented Kalman inversion (UKI) method to solve the FE model updating problems in a derivative-free manner. As an iterative optimization method, the UKI determines the new iterate using function values at a set of sample points rather than the derivative information. Implementation details, such as handling constraints during the optimization process, are presented in the paper. To validate the proposed UKI, model updating of a pedestrian bridge is conducted using the simulated and experimental data. Both validation examples show that the UKI is a competitive method for solving FE model updating problems.

Terrain matching positioning method for underwater vehicles based on curvature discrimination

Terrain matching positioning technology is used to locate underwater vehicles by the terrain information. The traditional method uses all real-time bathymetric points to traverse the underwater prior map, which has a large calculation amount and high complexity. To improve computational efficiency while ensuring accuracy, we represent the terrain matching positioning method based on the local terrain features and the global search technology in this paper. Firstly, the Moving Least Square (MLS) method is used to construct the MLS surface of the multi-beam bathymetric terrain. Then, a shape operator related to the principal curvatures is employed to reflect the curvedness of the MLS surface at each bathymetric point. Next, a Local Curvature Binary Discrimination (LCBD) method is proposed to describe the shape of local MLS surface with a LCBD descriptor, and divide the points satisfying the LCBD situations into the sampling point set. Finally, the Genetic Algorithm (GA) is introduced to replace the traditional traversal method (TM) to search the optimal estimated position of vehicle from the underwater prior map. The experimental results show that the proposed method can quickly locate the vehicle without affecting the accuracy, and the efficiency is improved by more than 80% compared with the traditional method.

Theoretical formulation/development of signal sampling with an equal arc length using the frame theorem

Nonuniform sampling with equal arc length intervals can be found in shape measurements with contact sensor arrays. In this study, the conditions of nonuniform spatial sampling with an equal arc length interval are derived from two frame theorems. First, for general nonuniform sampling, the condition is that the equal arc length interval of the sensors should be less than frac{1}{4Omega }. Second, for strictly increasing sampling (the sampling point set is strictly increasing), the condition is that the equal arc length interval of the sensors should be less than frac{1}{2Omega }. The Omega is the maximum frequency of the detected object. For the latter, if the sampling frequency is more than twice the sampling frequency required, the reconstruction error (RRMSE and MRE) is less than 5%. If the sampling frequency is more than 2.5 times, the reconstruction error is less than 3%. The simulation and the application test are carried out, and the results show that a sensor array with equal arc length interval can reconstruct the detected object with high accuracy.

A sharp discrepancy bound for jittered sampling

For m , d ∈ N m, d \in {\mathbb N} , a jittered (or stratified) sampling point set P P having N = m d N = m^d points in [ 0 , 1 ) d [0,1)^d is constructed by partitioning the unit cube [ 0 , 1 ) d [0,1)^d into m d m^d axis-aligned cubes of equal size and then placing one point independently and uniformly at random in each cube. We show that there are constants c > 0 c > 0 and C C such that for all d d and all m ≥ d m \ge d the expected non-normalized star discrepancy of a jittered sampling point set satisfies \[ c d m d − 1 2 1 + log ⁡ ( m d ) ≤ E D ∗ ( P ) ≤ C d m d − 1 2 1 + log ⁡ ( m d ) . c \,dm^{\frac {d-1}{2}} \sqrt {1 + \log (\tfrac md)} \le {\mathbb E} D^*(P) \le C\, dm^{\frac {d-1}{2}} \sqrt {1 + \log (\tfrac md)}. \] This discrepancy is thus smaller by a factor of Θ ( ( 1 + log ⁡ ( m / d ) m / d ) 1 / 2 ) \Theta \big (\big (\frac {1+\log (m/d)}{m/d}\big )^{1/2}\big ) than the one of a uniformly distributed random point set (Monte Carlo point set) of cardinality m d m^d . This result improves both the upper and the lower bound for the discrepancy of jittered sampling given by Pausinger and Steinerberger [J. Complexity 33 (2016), pp. 199–216]. It also removes the asymptotic requirement that m m is sufficiently large compared to d d .

Prediction of curing process for thermosetting prepreg compression molding process based on machine learning

AbstractIn the curing process of thermosetting prepreg compression molding (PCM), the distribution of the temperature field and the curing degree field have an important influence on the performance of composites. Therefore, the establishment of method to accurately predict the temperature difference and the degree of cure (DoC) difference during the curing process is significance for improving the performance of composites. In this paper, three kinds of machine learning models are studied: back propagation (BP) neural network, genetic algorithm‐back propagation (GA‐BP) neural network, radial basis function (RBF) neural network, then predictive models based on finite element method (FEM) and machine learning models are proposed. In the double‐dwell curing curve, six typical parameters are selected as inputs; the maximum value of temperature, the maximum value of temperature overshoot, the maximum DoC difference, the curing time, these four parameters during the curing process are selected as outputs, then the rapid predictive model is established. Within the value range of the process parameters, the Latin hypercube sampling (LHS) method is used to select 100 sets of sample points, and after training on three predictive models, comparison, and verification are carried out. The results show that the predictive effect of the RBF model is the best. In these three models, the RBF model is more suitable for the performance prediction of composites PCM. In this article, the research provides the basis for the performance prediction of composites and the multiobjective optimization of the curing process.

Stochastic Analysis on the Resonance of Railway Trains Moving over a Series of Simply Supported Bridges

Resonance problems encountered in vehicle-bridge interaction (VBI) have attracted widespread concern over the past decades. Due to system random characteristics, the prediction of resonant speeds and responses will become more complicated. To this end, this study presents stochastic analysis on the resonance of railway trains moving over a series of simply supported bridges with consideration of the randomness of system parameters. A train-slab track-bridge (TSB) vertically coupled dynamics model is established following the basic principle of vehicle-track-coupled dynamics. The railway train is composed of multiple vehicles, and each of them is built by seven rigid parts assigned with a total of 10 degrees of freedom. The rail, track slab, and bridge are considered as Euler–Bernoulli beams, and the vibration equations of which are established by the modal superposition method (MSM). Except for the nonlinear wheel-rail interaction based on the Hertz contact theory, the other coupling relations between each subsystem are assumed to be linear elastic. The number theory method is employed to obtain the representative sample point sets of the random parameters, and the flow trajectories of probabilities for the TSB dynamics system are captured by a probability density evolution method (PDEM). Numerical results indicate that the maximum bridge and vehicle responses are mainly dominated by the primary train-induced resonant speed; the last vehicle of a train will be more seriously excited when the bridges are set in resonance by the train; the resonant speeds and responses are rather sensitive to the system randomness, and the possible maximum amplitudes predicted by the PDEM are significantly underestimated by the traditional deterministic method; optimized parameters of the TSB system are preliminary obtained based on the representative point sets and imposed screening conditions.

Exploring Geostatistical Modeling and VisualizationTechniques of Uncertainties for Categorical Spatial Data

This article presents and analyzes the indicator geostatistical modeling and some visualization techniques of uncertainty models for categorical spatial attributes. A set of sample points of some categorical attribute is used as input information. The indicator approach requires a transformation of sample points on fields of indicator samples according to the classes of interest. Experimental and theoretical semivariograms of the indicator fields are defined representing the spatial variation of the indicator information. The indicator fields, along with their semivariograms, are used to determine the uncertainty model, the conditioned probability distribution function, of the attribute at any location inside the geographic region delimited by the samples. The probability functions are considered for producing prediction and probability maps based on the maximum class probability criterion. These maps can be visualized using different techniques. In this work, it is considered individual visualization of the predicted and probability maps and a combination of them. The predicted maps can also be visualized with or without constraints related to the uncertainty probabilities. The combined visualizations are based on three-dimensional (3D) planar projection and on the Red-Green-Blue to Intensity-Hue-Saturation (RGB-IHS) fusion transformation techniques. The methodology of this article is illustrated by a case study with real data, a sample set of soil textures observed in an experimental farm located in the region of São Carlos city in São Paulo State, Brazil. The resulting maps of this case study are presented and the advantages and the drawbacks of the visualization options are analyzed and discussed.

Node Generation for RBF-FD Methods by QR Factorization

Polyharmonic spline (PHS) radial basis functions (RBFs) have been used in conjunction with polynomials to create RBF finite-difference (RBF-FD) methods. In 2D, these methods are usually implemented with Cartesian nodes, hexagonal nodes, or most commonly, quasi-uniformly distributed nodes generated through fast algorithms. We explore novel strategies for computing the placement of sampling points for RBF-FD methods in both 1D and 2D while investigating the benefits of using these points. The optimality of sampling points is determined by a novel piecewise-defined Lebesgue constant. Points are then sampled by modifying a simple, robust, column-pivoting QR algorithm previously implemented to find sets of near-optimal sampling points for polynomial approximation. Using the newly computed sampling points for these methods preserves accuracy while reducing computational costs by mitigating stencil size restrictions for RBF-FD methods. The novel algorithm can also be used to select boundary points to be used in conjunction with fast algorithms that provide quasi-uniformly distributed nodes.