Typical Benchmark Problems Research Articles

Image classification with symbolic hints using limited resources.

Typical machine learning classification benchmark problems often ignore the full input data structures present in real-world classification problems. Here we aim to represent additional information as "hints" for classification. We show that under a specific realistic conditional independence assumption, the hint information can be included by late fusion. In two experiments involving image classification with hints taking the form of text metadata, we demonstrate the feasibility and performance of the fusion scheme. We fuse the output of pre-trained image classifiers with the output of pre-trained text models. We show that calibration of the pre-trained models is crucial for the performance of the fused model. We compare the performance of the fusion scheme with a mid-level fusion scheme based on support vector machines and find that these two methods tend to perform quite similarly, albeit the late fusion scheme has only negligible computational costs.

Theoretical and Empirical Analysis of Cost-Function Merging for Implicit Hitting Set WCSP Solving

The Implicit Hitting Set (HS) approach has shown very effective for MaxSAT solving. However, only preliminary promising results have been obtained for the very similar Weighted CSP framework. In this paper we contribute towards both a better theoretical understanding of the HS approach and a more effective HS-based solvers for WCSP. First, we bound the minimum number of iterations of HS thanks to what we call distinguished cores. Then, we show a source of inefficiency by introducing two simple problems where HS is unfeasible. Next, we propose two reformulation methods that merge cost-functions to overcome the problem. We provide a theoretical analysis that quantifies the magnitude of the improvement of each method with respect to the number of iterations of the algorithm. In particular, we show that the reformulations can bring an exponential number of iterations down to a constant number in our working examples. Finally, we complement our theoretical analysis with two sets of experiments. First, we show that our results are aligned with real executions. Second, and most importantly, we conduct experiments on typical benchmark problems and show that cost-function merging may be heuristically applied and it may accelerate HS algorithms by several orders of magnitude. In some cases, it even outperforms state-of-the-art solvers.

Brownian motion based multi-objective particle swarm optimization methodology and application in binary classification

The particle swam optimization (PSO) method has been widely applied in evolutionary computation and related industrial areas. However, the optimization performance of traditional PSO is usually influenced by particle updating displacement and velocity, which is randomly distributed and makes the solution solving process inefficient. To deal with this challenge, a Brownian particle motion and Euler-Maruyama (EM) methodology-based model is proposed to improve the performance of the multi-objective PSO. The EM based PSO principles and algorithm framework are introduced by theoretical analysis and mathematical modeling, and then the optimization performance of four comparing PSO models is tested, while the feasibility of the new PSO4 is verified by typical benchmark problems. Afterwards, the characterizations of the EM based PSO method are investigated from the perspective of particle motion mechanism analysis, binary classification application and various optimization performance comparison. The result manifests that the new PSO4 features higher accuracy and less running time among 24 related optimization methods for 4 typical standard datasets of Ionosphere, Breast, Diabetes and Wine. Finally, the multi-objective optimization and classification application potential of the Brownian motion and EM based PSO4 is demonstrated, and the future work regarding the new PSO model is discussed.

A Population-Based Search Approach to Solve Continuous Distributed Constraint Optimization Problems

Distributed Constraint Optimization Problems (DCOPs) are an efficient framework widely used in multi-agent collaborative modeling. The traditional DCOP framework assumes that variables are discrete and constraint utilities are represented in tabular forms. However, the variables are continuous and constraint utilities are in functional forms in many practical applications. To overcome this limitation, researchers have proposed Continuous DCOPs (C-DCOPs), which can model DCOPs with continuous variables. However, most of the existing C-DCOP algorithms rely on gradient information for optimization, which means that they are unable to solve the situation where the utility function is a non-differentiable function. Although the Particle Swarm-Based C-DCOP (PCD) and Particle Swarm with Local Decision-Based C-DCOP (PCD-LD) algorithms can solve the situation with non-differentiable utility functions, they need to implement Breadth First Search (BFS) pseudo-trees for message passing. Unfortunately, employing the BFS pseudo-tree results in expensive computational overheads and agent privacy leakage, as messages are aggregated to the root node of the BFS pseudo-tree. Therefore, this paper aims to propose a fully distributed C-DCOP algorithm to solve the utility function form problem and avoid the disadvantages caused by the BFS pseudo-tree. Inspired by the population-based algorithms, we propose a fully decentralized local search algorithm, named Population-based Local Search Algorithm (PLSA), for solving C-DCOPs with three-fold advantages: (i) PLSA adopts a heuristic method to guide the local search to achieve a fast search for high-quality solutions; (ii) in contrast to the conventional C-DCOP algorithm, PLSA can solve utility functions of any form; and (iii) compared to PCD and PCD-LD, PLSA avoids complex message passing to achieve efficient computation and agent privacy protection. In addition, we implement an extended version of PLSA, named Population-based Global Search Algorithm (PGSA), and empirically show that our algorithms outperform the state-of-the-art C-DCOP algorithms on three types of benchmark problems.

Nodal expansion method based reduced-order model for control rod movement

Control rod movement is one of the main considerations for nuclear reactor safety analysis, whose accuracy simulation requires a significant amount of computing time. In this paper, combined with the proper orthogonal method (POD) and least square method (LSM), a novel reduced-order method based on the nodal expansion method (RO-NEM) is proposed to reduce the consumption of computational resources. Based on the snapshots obtained from NEM, the reduced-order model constructed by RO-NEM can predict the neutron flux distribution at the unknown state efficiently. Results from typical benchmark problem demonstrate that the proposed RO-NEM can accurately and efficiently obtain neutron distribution. Global POD (GPOD) and local POD (LPOD) methods for selecting snapshots to generate POD basis are compared in this work. Results show that LPOD has better calculation accuracy and efficiency than GPOD. This work provides new perspectives and directions for improving the efficiency of numerical calculations in nuclear reactor engineering.

MPM vs. CEL: Numerical modelling of penetration processes

MPM vs. CEL: Numerical modelling of penetration processes

On the Uncertainty Analysis of the Data-Enabled Physics-Informed Neural Network for Solving Neutron Diffusion Eigenvalue Problem

We performed uncertainty analysis and further numerical studies on the data-enabled physics-informed neural network (DEPINN). The purpose of DEPINN is to accurately and efficiently use a small amount of prior data to solve the neutron diffusion eigenvalue equations based on the physics-informed neural network. However, in practical engineering experiments, these prior data are acquired through different kinds of sensors, which are inevitably polluted by noise. Numerical results of three typical benchmark problems show that the classical DEPINN is not so robust with respect to noise. To improve the noise robustness, we propose an interval loss function to deal with the noisy prior data term; the weight of the noisy prior data term is also set to be noise dependent. Numerical results show that the proposed framework effectively enhances the robustness of DEPINN and improves the efficiency of utilizing the noisy prior data and thus promotes the engineering application of DEPINN.

GPU implementation of the discrete unified gas kinetic scheme for low-speed isothermal flows

In this paper, two GPU parallel algorithms are proposed for the discrete unified gas kinetic scheme (DUGKS) for simulating low-speed isothermal flows. Algorithm-I uses a two-level fine-grain technique for the parallelization of physical spatial space, while Algorithm-II adopts this technique for both physical spatial and particle velocity spaces. To evaluate the performance of the proposed algorithms, several typical benchmark problems are simulated, including the two-dimensional (2D) and three-dimensional (3D) lid-driven cavity flows, the micro channel and cavity flows. Numerical results show that our GPU algorithms can achieve satisfactory computational efficiency. For Algorithm-I, the speedup can reach 250 and 338 on a Tesla V100 GPU card for the 2D and 3D continuum cavity flows, respectively, and a hundredfold acceleration can be obtained for the rarefied cases. While for Algorithm-II, a speedup of about 70 can be attained for rarefied cases. However, it is not applied to continuum problems that only require a small number of velocity points. Moreover, comparisons between the two GPU algorithms are also conducted for the rarefied flows with various grid meshes and velocity directions. The results show that Algorithm-I performs better when physical mesh size is large, while Algorithm-II can provide higher efficiency for a coarser mesh with medium number of discrete velocities. Special attention is also paid to comparisons between Algorithm-I and MPI parallelization with 128 CPU cores based on physical space discretization approach, and it is found that Algorithm-I has a clear advantage on V100 GPU when dealing with sparse physical grids in both continuum and rarefied cases.

Parameter-robust preconditioners for Biot’s model

This work presents an overview of the most relevant results obtained by the authors regarding the numerical solution of the Biot’s consolidation problem by preconditioning techniques. The emphasis here is on the design of parameter-robust preconditioners for the efficient solution of the algebraic system of equations resulting after proper discretization of such poroelastic problems. The classical two- and three-field formulations of the problem are considered, and block preconditioners are presented for some of the discretization schemes that have been proposed by the authors for these formulations. These discretizations have been proved to be well-posed with respect to the physical and discretization parameters, what provides a framework to develop preconditioners that are robust with respect to such parameters as well. In particular, we construct both norm-equivalent (block diagonal) and field-of-value-equivalent (block triangular) preconditioners, which are proved to be parameter-robust. The theoretical results on this parameter-robustness are demonstrated by considering typical benchmark problems in the literature for Biot’s model.

An Efficient Improved Harris Hawks Optimizer and Its Application to Form Deviation-Zone Evaluation.

Evaluation of the deviation zone based on discrete measured points is crucial for quality control in manufacturing and metrology. However, deviation-zone evaluation is a highly nonlinear problem that is difficult to solve using traditional numerical optimization methods. Swarm intelligence has many advantages in solving this problem: it produces gradient-free, high-quality solutions and is characterized by its ease of implementation. Therefore, this study applies an improved Harris hawks algorithm (HHO) to tackle the problem. The average fitness is applied to replace the random operator in the exploration phase to solve the problem of conflicting exploration strategies due to randomness. In addition, the salp swarm algorithm (SSA) with a nonlinear inertia weight is embedded into the HHO, such that the superior explorative ability of SSA can fill the gap in the exploration of HHO. Finally, the optimal solution is greedily selected between SSA-based individuals and HHO-based individuals. The effectiveness of the proposed improved HHO optimizer is checked through a comparison with other swarm intelligence methods in typical benchmark problems. Moreover, the experimental results of form deviation-zone evaluation on primitive geometries show that the improved method can accurately solve various form deviations, providing an effective general solution for primitive geometries in the manufacturing and metrology fields.

Reduced-order with least square-finite difference method for neutron transport equation

Consumption of computing resource in neutron transport solving has been gradually emphasized, especially for large-scale engineering calculation. To simulate the neutron transport processes efficiently, based on theory of proper orthogonal decomposition (POD), a novel reduced-order model called reduced-order with least square-finite difference method (RO-LSFDM) is proposed in this work, which is constructed by combining with the finite difference method (FDM) and least square method (LSM). Compared with the widely used reduced basis-finite element method, the proposed RO-LSFDM is much easier to execute and computing resource saving. Results of some typical benchmark problems prove that the RO-LSFDM can obtain accurate neutron distribution with high efficiency in mono-group, multi-group, source-driven and eigenvalue problems. Compared with classical discrete-ordinate method, the proposed method can reach thousands of times speedup ratio. This work can provide a new perspectives and directions on the research of improving the efficiency of numerical calculations in nuclear reactor engineering.

Full Bayesian identification of linear dynamic systems using stable kernels

System identification learns mathematical models of dynamic systems starting from input-output data. Despite its long history, such research area is still extremely active. New challenges are posed by identification of complex physical processes given by the interconnection of dynamic systems. Examples arise in biology and industry, e.g., in the study of brain dynamics or sensor networks. In the last years, regularized kernel-based identification, with inspiration from machine learning, has emerged as an interesting alternative to the classical approach commonly adopted in the literature. In the linear setting, it uses the class of stable kernels to include fundamental features of physical dynamical systems, e.g., smooth exponential decay of impulse responses. Such class includes also unknown continuous parameters, called hyperparameters, which play a similar role as the model discrete order in controlling complexity. In this paper, we develop a linear system identification procedure by casting stable kernels in a full Bayesian framework. Our models incorporate hyperparameters uncertainty and consist of a mixture of dynamic systems over a continuum spectrum of dimensions. They are obtained by overcoming drawbacks related to classical Markov chain Monte Carlo schemes that, when applied to stable kernels, are proved to become nearly reducible (i.e., unable to reconstruct posteriors of interest in reasonable time). Numerical experiments show that full Bayes frequently outperforms the state-of-the-art results on typical benchmark problems. Two real applications related to brain dynamics (neural activity) and sensor networks are also included.

A data-enabled physics-informed neural network with comprehensive numerical study on solving neutron diffusion eigenvalue problems

We put forward a data-enabled physics-informed neural network (DEPINN) with comprehensive numerical study for solving industrial scale neutron diffusion eigenvalue problems (NDEPs). In order to achieve an engineering acceptable accuracy for complex engineering problems, a very small amount of prior data from physical experiments are suggested to be used, to improve the accuracy and efficiency of training. We design an adaptive optimization procedure with Adam and LBFGS to accelerate the convergence in the training stage. We discuss the effect of different physical parameters, sampling techniques, loss function allocation and the generalization performance of the proposed DEPINN model for solving complex eigenvalue problems. The feasibility of proposed DEPINN model is verified on three typical benchmark problems, from simple geometry to complex geometry, and from mono-energetic equation to two-group equations. Numerous numerical results show that DEPINN can efficiently solve NDEPs with an appropriate optimization procedure. The proposed DEPINN can be generalized for other input parameter settings once its structure been trained. This work confirms the possibility of DEPINN for practical engineering applications in nuclear reactor physics.

SPANet: Generalized permutationless set assignment for particle physics using symmetry preserving attention

The creation of unstable heavy particles at the Large Hadron Collider is the most direct way to address some of the deepest open questions in physics. Collisions typically produce variable-size sets of observed particles which have inherent ambiguities complicating the assignment of observed particles to the decay products of the heavy particles. Current strategies for tackling these challenges in the physics community ignore the physical symmetries of the decay products and consider all possible assignment permutations and do not scale to complex configurations. Attention based deep learning methods for sequence modelling have achieved state-of-the-art performance in natural language processing, but they lack built-in mechanisms to deal with the unique symmetries found in physical set-assignment problems. We introduce a novel method for constructing symmetry-preserving attention networks which reflect the problem's natural invariances to efficiently find assignments without evaluating all permutations. This general approach is applicable to arbitrarily complex configurations and significantly outperforms current methods, improving reconstruction efficiency between 19% - 35% on typical benchmark problems while decreasing inference time by two to five orders of magnitude on the most complex events, making many important and previously intractable cases tractable. A full code repository containing a general library, the specific configuration used, and a complete dataset release, are available at https://github.com/Alexanders101/SPANet

Performance of the radial point interpolation method (RPIM) with implicit time integration scheme for transient wave propagation dynamics

The radial point interpolation method (RPIM) is combined with the appropriate implicit time integration technique for transient wave propagation analysis in this work. The dispersion error issue of the numerical results is investigated detailedly by performing the dispersion analysis. It is found that the RPIM with sufficiently large support domains of quadrature points is able to yield almost no spatial dispersion errors which are much lower than those from the traditional finite element (FE) approach with the identical node distributions, hence we can monotonically improve the computation accuracy of the numerical results by using the decreasing time steps, namely the present method shows the important and attractive monotonic convergence property for transient wave analysis. This property makes the present method clearly superior to the standard FE approach in transient wave analysis and much more accurate solutions can be achieved. Several typical benchmark problems of transient wave propagations are studied to assess the robust and superior performance of the present method over the conventional FE for transient wave analysis.

High-order compact difference schemes on wide computational stencils with a spectral-like accuracy

In this paper, we propose a generalized framework for the derivation of compact difference schemes for the approximation of an arbitrary order derivative. We formulate a methodology for calculating the approximation coefficients involving a large number of mesh points leading to very high-order formulas, e.g., 20th or 30th order. The main emphasis is on the first and second order derivative occurring in the Navier-Stokes equations governing fluid flow problems. Contrary to most studies on compact schemes in which the computational stencils employed in the discretization are narrow and consist of only a few mesh points K, in the presented paper we consider wide stencils that in practice are limited only by the overall number of the nodes in a computational grid. We analyze the features of such wide stencil based schemes in physical and spectral space. It is shown that the solutions obtained applying the schemes of the same order but involving different number of the mesh points characterize significantly different accuracy. This is presented by direct comparisons of the analytically derived formula for the leading terms of the truncation errors as well as in practical simulations. The test cases include a second order ordinary differential equation with variable coefficients, 1D Burgers equation and three typical benchmark problems used in Computational Fluid Dynamics (CFD), i.e., inviscid vortex advection, convected Taylor-Green vortices and a double jet flow. The obtained results are compared with available analytical solutions and the solutions obtained with the help of a pseudo-spectral method. We found that very high-order compact schemes reach the spectral accuracy characterized by the error decrease proportional to O(hK). In some cases, they show even higher accuracy, and moreover, reaching the limit of the machine precision they are substantially more resistant to the round-off errors.

Generalized Empirical Interpolation Method With H1 Regularization: Application to Nuclear Reactor Physics

The generalized empirical interpolation method (GEIM) can be used to estimate the physical field by combining observation data acquired from the physical system itself and a reduced model of the underlying physical system. In presence of observation noise, the estimation error of the GEIM is blurred even diverged. We propose to address this issue by imposing a smooth constraint, namely, to constrain the H1 semi-norm of the reconstructed field of the reduced model. The efficiency of the approach, which we will call the H1 regularization GEIM (R-GEIM), is illustrated by numerical experiments of a typical IAEA benchmark problem in nuclear reactor physics. A theoretical analysis of the proposed R-GEIM will be presented in future works.

Continuous Finite Element Subgrid Basis Functions for Discontinuous Galerkin Schemes on Unstructured Polygonal Voronoi Meshes

We propose a new high order accurate nodal discontinuous Galerkin (DG) method for the solution of nonlinear hyperbolic systems of partial differential equations (PDE) on unstructured polygonal Voronoi meshes. Rather than using classical polynomials of degree N inside each element, in our new approach the discrete solution is represented by piecewise continuous polynomials of degree N within each Voronoi element, using a continuous finite element basis defined on a subgrid inside each polygon. We call the resulting subgrid basis an agglomerated finite element (AFE) basis for the DG method on general polygons, since it is obtained by the agglomeration of the finite element basis functions associated with the subgrid triangles. The basis functions on each sub-triangle are defined, as usual, on a universal reference element, hence allowing to compute universal mass, flux and stiffness matrices for the subgrid triangles once and for all in a pre-processing stage for the reference element only. Consequently, the construction of an efficient quadrature-free algorithm is possible, despite the unstructured nature of the computational grid. High order of accuracy in time is achieved thanks to the ADER approach, making use of an element-local space-time Galerkin finite element predictor. The novel schemes are carefully validated against a set of typical benchmark problems for the compressible Euler and Navier-Stokes equations. The numerical results have been checked with reference solutions available in literature and also systematically compared, in terms of computational efficiency and accuracy, with those obtained by the corresponding modal DG version of the scheme.

An efficient three-dimensional non-hydrostatic model for undular bores in open channels

A three-dimensional (3D) non-hydrostatic model is presented to simulate open-channel free-surface flows involving undular bores. The 3D unsteady mass conservation and momentum equations are solved using an explicit projection method in a nonstandard staggered grid. The grid system is built from a two-dimensional horizontal structured grid by adding horizontal layers. The model is validated using four typical benchmark problems, including undular bore development, an undular bore generated by a sudden discharge, and two test cases involving undular hydraulic jumps. The proposed model results are compared with experimental data and results from other models. Overall, the agreement between the proposed model results and experimental data is generally good, demonstrating the capability of the model to resolve undular bores. In addition, the non-hydrostatic pressure field under the undular free surface is revealed, and the efficiency of the proposed model is presented. It is shown that the proposed model behaves better than a volume of fluid model in terms of efficiency, because the proposed model can use fewer computational grid cells to resolve undular bores in open channels.

Differential Evolution with Shadowed and General Type-2 Fuzzy Systems for Dynamic Parameter Adaptation in Optimal Design of Fuzzy Controllers

This work is mainly focused on improving the differential evolution algorithm with the utilization of shadowed and general type 2 fuzzy systems to dynamically adapt one of the parameters of the evolutionary method. Previously, we have worked with both kinds of fuzzy systems in different types of benchmark problems and it has been found that the use of fuzzy logic in combination with the differential evolution algorithm gives good results. In some of the studies, it is clearly shown that, when compared to other algorithms, our methodology turns out to be statistically better. In this case, the mutation parameter is dynamically moved during the evolution process by using shadowed and general type-2 fuzzy systems. The main contribution of this work is the ability to determine, through experimentation in a benchmark control problem, which of the two kinds of the used fuzzy systems has better results when combined with the differential evolution algorithm. This is because there are no similar works to our proposal in which shadowed and general type 2 fuzzy systems are used and compared. Moreover, to validate the performance of both fuzzy systems, a noise level is used in the controller, which simulates the disturbances that may exist in the real world and is thus able to validate statistically if there are significant differences between shadowed and general type 2 fuzzy systems.