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To address the challenge of performance portability and facilitate the implementation of electronic structure solvers, we developed the basic matrix library (BML) and Parallel, Rapid O(N), and Graph-based Recursive Electronic Structure Solver (PROGRESS) library. The BML implements linear algebra operations necessary for electronic structure kernels using a unified user interface for various matrix formats (dense and sparse) and architectures (CPUs and GPUs). Focusing on density functional theory and tight-binding models, PROGRESS implements several solvers for computing the single-particle density matrix and relies on BML. In this paper, we describe the general strategies used for these implementations on various computer architectures, using OpenMP target functionalities on GPUs, in conjunction with third-party libraries to handle performance critical numerical kernels. We demonstrate the portability of this approach and its performance in benchmark problems. [ABSTRACT FROM AUTHOR]

In process industries, cascade control is comprehensively used for disturbance attenuation. This manuscript presents the control of the non-minimum phase (NMP) system with dead time via a series cascade scheme. An improved fractional-filter-based control scheme encompassing inverse and dead time compensators with analytical tuning is proposed. The design hinges on an enhanced Bode's ideal transfer function, which incorporates delay and NMP zero to deal with the system's NMP and dead time. Particle swarm optimization (PSO) is utilized to obtain the optimal assessment of fractional filter-based controller settings by minimizing an objective function. Two benchmark problems are presented to test the efficacy of the recommended controller. The Riemann surface and sensitivity examination are used to realize the stability and robustness of the feedback design. Numerical simulations exhibit the superiority of the suggested controller for closed-loop results. [ABSTRACT FROM AUTHOR]

The aim of a Green Vehicle Routing Problem is to find an optimal route for alternative fuel vehicles to minimize the overall travelling distances while reducing energy consumption and CO2emissions. In this problem each vehicle handles a subset of customers/orders, leaving from and returning to the depot, with respect to maximum distance travelled, while minimizing energy consumptions. We proposed a time window‐based GVRP solution (GVRP‐TW) with exact routing approach. Wherein, each route serves a subset of customers/orders with minimum intermediate refuelling/recharges. To test our method, we conducted experiments using MATLAB software on a set of three reference problem specimens (C‐101, R‐101 and RC‐11). Our approach, evaluated on these benchmark problems, par exceeds in performance in relation to the existing VRP methods (like tabu search, variable neighbourhood search, and GRASP). Moreover, the proposed GVRP‐TW can be further optimized to solve other VRP problems with energy minimisations and less intermediate stops. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

This paper presents a fully multidimensional kernel-based reconstruction scheme for finite volume methods applied to systems of hyperbolic conservation laws, with a particular emphasis on the compressible Euler equations. Nonoscillatory reconstruction is achieved through an adaptive-order weighted essentially nonoscillatory (WENO) method cast into a form suited to multidimensional reconstruction. A kernel-based approach inspired by radial basis functions and Gaussian process modeling, which we call kernel-based finite volume method with WENO, is presented here. This approach allows the creation of a scheme of arbitrary order of accuracy with simply defined multidimensional stencils and substencils. Furthermore, the fully multidimensional nature of the reconstruction allows for a more straightforward extension to higher spatial dimensions and removes the need for complicated boundary conditions on intermediate quantities in modified dimension-by-dimension methods. In addition, a new simple yet effective set of reconstruction variables is introduced, which could be useful in existing schemes with little modification. The proposed scheme is applied to a suite of stringent and informative benchmark problems to demonstrate its efficacy and utility. A highly parallel multi-GPU implementation using Kokkos and the message-passing interface is also provided. [ABSTRACT FROM AUTHOR]

This work solves 3SAT, a classical NP-complete problem, on a CMOS-based Ising hardware chip with all-to-all connectivity. The paper addresses practical issues in going from algorithms to hardware. It considers several degrees of freedom in mapping the 3SAT problem to the chip—using multiple Ising formulations for 3SAT; exploring multiple strategies for decomposing large problems into subproblems that can be accommodated on the Ising chip; and executing a sequence of these subproblems on CMOS hardware to obtain the solution to the larger problem. These are evaluated within a software framework, and the results are used to identify the most promising formulations and decomposition techniques. These best approaches are then mapped to the all-to-all hardware, and the performance of 3SAT is evaluated on the chip. Experimental data shows that the deployed decomposition and mapping strategies impact SAT solution quality: without our methods, the CMOS hardware cannot achieve 3SAT solutions on SATLIB benchmarks. Under the assumption of some hardware improvements, our chip-based 3SAT solver demonstrates a remarkable 250 × acceleration compared to Tabu search in dwave-hybrid on a CPU. [ABSTRACT FROM AUTHOR]

This paper introduces an innovative Particle Swarm Optimization (PSO) Algorithm incorporating Sobol and Halton random number samplings. It evaluates the enhanced PSO's performance against conventional PSO employing Monte Carlo random number samplings. The comparison involves assessing the algorithms across nine benchmark problems and the renowned Travelling Salesman Problem (TSP). The results reveal consistent enhancements achieved by the enhanced PSO utilizing Sobol/Halton samplings across the benchmark problems. Particularly noteworthy are the Sobol-based PSO improvements in iterations and the computational times for the benchmark problems. These findings underscore the efficacy of employing Sobol and Halton random number generation methods to enhance algorithm efficiency. [ABSTRACT FROM AUTHOR]

Direct flexoelectricity is a size-dependent phenomenon, very prominent at smaller scales, that connects the strain gradients and the electric field. The very existence of strain gradients enhances noncentrosymmetry and heightens the interaction between piezoelectricity and flexoelectricity, demanding fully coupled higher-order electromechanical formulations. The numerical instability of the existing finite elements used to model flexoelectricity alone is revealed due to their reliance on the stabilization parameter. Thus, two new finite elements Qu2s2p2l0 (QL0-4) and Qu2s2p2l1 (QL1-16) are proposed for mixed FEM that are numerically robust without any need of such stabilization parameters. Additionally, the existing finite element Qu2s1p2l0 [Q47 in (Deng et al. in J Appl Mech 84:081004, 2017)], is implemented from scratch to replicate known results and benchmark the performance of newly proposed finite elements. To verify the robustness of these elements, various benchmark problems for flexoelectricity in dielectric solids, such as a thick cylinder and truncated pyramid are simulated. The great agreement of the numerical results with the existing ones reflects the foundational nature of the proposed elements. Furthermore, the proposed mixed finite elements were used to successfully analyze cantilever beam and truncated pyramid problems where piezoelectric effects were taken into account for the first time. Current results are intrumental in simulating flexoelectricity and piezoelectricity together to highlight their interactions using newly proposed numerically robust finite elements. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

• Underwater explosion induced cavitation near sacrificial coatings are studied. • RKDG-FE-GFM-IsenCav is developed to study the cavitation effects. • Five benchmark problems are studied. • Effects of geometrical and physical properties of the model are discussed. The load resulting from cavitation collapse is a major threat to structures exposed to underwater explosions. Protective structures for warships, such as sacrificial coatings, which are sandwich structures attached to the wet face of the ship hull. They have energy absorbing cores made of cellular or composite materials that can significantly influence the effects of cavitation. In this study, a physical model consisting of water, an explosion bubble, and a sacrificial coating is established to investigate the effects of cavitation near sacrificial coatings subjected to underwater explosions. A numerical method is developed that couples the Runge-Kutta discontinuous Galerkin method, the finite element method, a Ghost Fluid Method-based numerical technique, and an isentropic one-fluid cavitation model to capture the physical phenomena of shock wave propagation, cavitation inception, expansion and collapse, and explosion bubble expansion and contraction. To ensure the accuracy of the mathematical model, five benchmark problems and a convergence test of the numerical solution are studied. The study comprehensively discusses the influences of core strengths, face sheet thickness, stand-off distances, and structure curvature on the evolution of the cavitation region, pressure profiles near the structure, and structure responses. [ABSTRACT FROM AUTHOR]

Distributed nonconvex optimization underpins key functionalities of numerous distributed systems, ranging from power systems, smart buildings, cooperative robots, vehicle networks to sensor networks. Recently, it has also merged as a promising solution to handle the enormous growth in data and model sizes in deep learning. A fundamental problem in distributed nonconvex optimization is avoiding convergence to saddle points, which significantly degrade optimization accuracy. We find that the process of quantization, which is necessary for all digital communications, can be exploited to enable saddle-point avoidance. More specifically, we propose a stochastic quantization scheme and prove that it can effectively escape saddle points and ensure convergence to a second-order stationary point in distributed nonconvex optimization. With an easily adjustable quantization granularity, the approach allows a user to control the number of bits sent per iteration and, hence, to aggressively reduce the communication overhead. Numerical experimental results using distributed optimization and learning problems on benchmark datasets confirm the effectiveness of the approach. [ABSTRACT FROM AUTHOR]

Metaheuristic techniques are capable of representing optimization frames with their specific theories as well as objective functions owing to their being adjustable and effective in various applications. Through the optimization of deep learning models, metaheuristic algorithms inspired by nature, imitating the behavior of living and non-living beings, have been used for about four decades to solve challenging, complex, and chaotic problems. These algorithms can be categorized as evolution-based, swarm-based, nature-based, human-based, hybrid, or chaos-based. Chaos theory, as a useful approach to understanding neural network optimization, has the basic idea of viewing the neural network optimization as a dynamical system in which the equation schemes are utilized from the space pertaining to learnable parameters, namely optimization trajectory, to itself, which enables the description of the evolution of the system by understanding the training behavior, which is to say the number of iterations over time. The examination of the recent studies reveals the importance of chaos theory, which is sensitive to initial conditions with randomness and dynamical properties that are principally emerging on the complex multimodal landscape. Chaotic optimization, in this regard, accelerates the speed of the algorithm while also enhancing the variety of movement patterns. The significance of hybrid algorithms developed through their applications in different domains concerning real-world phenomena and well-known benchmark problems in the literature is also evident. Metaheuristic optimization algorithms have also been applied to deep learning or deep neural networks (DNNs), a branch of machine learning. In this respect, the basic features of deep learning and DNNs and the extensive use of metaheuristic algorithms are overviewed and explained. Accordingly, the current review aims at providing new insights into the studies that deal with metaheuristic algorithms, hybrid-based metaheuristics, chaos-based metaheuristics as well as deep learning besides presenting recent information on the development of the essence of this branch of science with emerging opportunities, applicability-based optimization aspects and generation of well-informed decisions. [ABSTRACT FROM AUTHOR]

We apply the well-known outer-approximation algorithm (OA) of convex mixed-integer nonlinear optimization to the maximum-entropy sampling problem (MESP), using convex relaxations for MESP from the literature. We discuss possible methodologies to accelerate the convergence of OA, by combining the use of the different relaxations and by selecting additional linearization points using a local-search procedure, disjunctive cuts, a regularization method, and a second-order approximation of the objective of the MESP. We discuss our findings through numerical experiments with a benchmark test problem. [ABSTRACT FROM AUTHOR]

The small strain shear modulus is an important characteristic of geomaterials that can be measured experimentally using piezoelectric sensors (bender elements). However, most conventional signal interpretation techniques are based on the visual observation of the output signal and therefore inherently subjective. Objective techniques also exist, like the cross-correlation of the input and output signals, but they lack physical insight, as they rely on the (incorrect) assumption that input and output signals are similar. This paper presents GeoHyTE, the first objective and physically consistent toolbox for the automatic processing of the output signal of bender element sensors. GeoHyTE updates a finite element model of the experiment, iteratively searching for the small strain shear modulus that maximises the correlation between the experimental and numerical output signals. The method is objective, as the results do not depend on the experience of the user, and physically consistent, as the wave propagation process is modelled in full and signals of the same nature (output) are correlated. Moreover, GeoHyTE is nearly insensitive to grossly erroneous input by the user, both in terms of the starting point of the iterative maximisation process and refinement of the finite element model. The results obtained with GeoHyTE are validated against benchmark measurements reported in the literature and experimental data obtained by the authors. A detailed statistical analysis of the results obtained with GeoHyTE and conventional interpretation techniques is also presented. [ABSTRACT FROM AUTHOR]

We study the dynamics of a class of mechanical systems subjected to non-holonomic constraints by employing a method termed "modified vakonomic method" (MVM), and developed by Llibre, Ramírez and Sadovskaia in 2014. In particular, we test the MVM for the "rolling coin" problem and a variant of the "non-holonomic skate" problem. For our purposes, we divide our work in two parts. For the first one, our point of departure is a paper published in this journal by Lemos in 2022, in which, for the "rolling coin" problem, Kozlov's vakonomic method is shown to lead to inconsistencies with the so-called Lagrange–D'Alembert traditional non-holonomic method (TNHM). In this case, we prove that, if the MVM is used, the equivalence with the TNHM can be restored, and the two methods can be reconciled. In the second part, we formulate a thought experiment consisting of an electrically charged "non-holonomic skate" interacting with a magnetic field, and we examine its dynamics by means of the MVM. In this case, we point out the differences with the predictions of the TNHM, and we propose a reformulation of the MVM capable of retrieving the results obtained with the TNHM. Moreover, we give some insight into the main computational aspects related to the MVM for non-holonomic constraints linear in the generalized velocities. [ABSTRACT FROM AUTHOR]

The accuracy of real-time hybrid simulation (RTHS) is greatly influenced by the inevitable time delay and amplitude error due to the control plant dynamics. Several tracking controllers have been implemented to improve the overall performance, and among them, model predictive control (MPC) loses its prediction advantage due to the characteristic of real-time command calculation of RTHS. In this study, an improved tracking controller based on MPC controller combined with a polynomial-based forward reference prediction (MPC-RP) is proposed according to the principle of providing future data insight. First, the proposed controller is described, and the basic implementation procedure is presented. Then, validation tests were carried out to evaluate the tracking performance of the proposed controller based on the virtual RTHS benchmark problem. The results show that the MPC-RP controller has an effective delay compensation performance and a good amplitude error regulation capacity. It is also demonstrated that the MPC-RP controller has a great robust performance concerning control plant uncertainties, which ensures highly improved accuracy of RTHS. [ABSTRACT FROM AUTHOR]

Performance of a new incompressible smoothed particle hydrodynamics (I-SPH) model for simulating free surface flows using Lagrangian description of motion is numerically evaluated. In the SPH method, kernel or weight functions are used for approximation of a function and its spatial derivatives based on the theory of integral interpolants exhibiting poor accuracy. In this study, the pressure field is obtained by solving a pressure Poisson equation that is derived from a two-step prediction–correction approach applied for temporal discretization of the governing equations of fluid flows and enforcement of incompressibility. A newly developed gradient model in the context of the mesh-less moving particle semi-implicit (MPS) method is applied to improve the standard gradient and Laplacian models of I-SPH method in the proposed approach. The higher accuracy of the modified SPH scheme, which is a kernel gradient-free model, in comparison with the standard I-SPH method is validated trough solving the classic benchmark problems including the dam break flow, solitary wave propagation, standing wave motion, liquid sloshing and water drop stretching. [ABSTRACT FROM AUTHOR]

Existing deep learning techniques for image fusion either learn image mapping (LIM) directly, which renders them ineffective at preserving details due to the equal consideration to each pixel, or learn detail mapping (LDM), which only attains a limited level of performance because only details are used for reasoning. The recent lossless invertible network (INN) has demonstrated its detail-preserving ability. However, the direct applicability of INN to the image fusion task is limited by the volume-preserving constraint. Additionally, there is the lack of a consistent detail-preserving image fusion framework to produce satisfactory outcomes. To this aim, we propose a general paradigm for image fusion based on a novel conditional INN (named DCINN). The DCINN paradigm has three core components: a decomposing module that converts image mapping to detail mapping; an auxiliary network (ANet) that extracts auxiliary features directly from source images; and a conditional INN (CINN) that learns the detail mapping based on auxiliary features. The novel design benefits from the advantages of INN, LIM, and LDM approaches while avoiding their disadvantages. Particularly, using INN to LDM can easily meet the volume-preserving constraint while still preserving details. Moreover, since auxiliary features serve as conditional features, the ANet allows for the use of more than just details for reasoning without compromising detail mapping. Extensive experiments on three benchmark fusion problems, i.e., pansharpening, hyperspectral and multispectral image fusion, and infrared and visible image fusion, demonstrate the superiority of our approach compared with recent state-of-the-art methods. The code is available at https://github.com/wwhappylife/DCINN [ABSTRACT FROM AUTHOR]

For expensive problems, as the number of objectives and the number of decision variables increase, the number of non-dominated solutions in the population increases dramatically, and the population does not have enough convergence pressure to converge to the true pareto frontier. A Kriging-assisted Multi-stage Evolutionary Algorithm (K-MSEA) is proposed to enhance the exploratory capacity of populations in expensive many-objective optimization problems. A multi-stage strategy is used in K-MSEA. Mating selection and environmental selection of populations are divided into three stages based on convergence and diversity indices. Targeted selection of individuals should be conducted at each stage of population development. The population independently chooses the appropriate stage in accordance with the current demands of convergence and diversity. Differential evolutionary algorithm is used to improve the search ability of the population. To guide the population in the correct direction, K-MSEA employs an elite retention strategy in environmental selection. The population utilizes individual renewal, where underperforming parents are replaced by better-performing offspring. The surrogate model is then updated with the uncertainty information supplied by the Kriging model. Finally, K-MSEA is benchmarked against five other algorithms in experiments on two benchmark problems and two realistic expensive problems. Mathematical analysis demonstrates that K-MSEA is more competitive than others. [ABSTRACT FROM AUTHOR]

Neural network (NN) potentials are a natural choice for coarse-grained (CG) models. Their many-body capacity allows highly accurate approximations of the potential of mean force, promising CG simulations of unprecedented accuracy. CG NN potentials trained bottom-up via force matching (FM), however, suffer from finite data effects: They rely on prior potentials for physically sound predictions outside the training data domain, and the corresponding free energy surface is sensitive to errors in the transition regions. The standard alternative to FM for classical potentials is relative entropy (RE) minimization, which has not yet been applied to NN potentials. In this work, we demonstrate, for benchmark problems of liquid water and alanine dipeptide, that RE training is more data efficient, due to accessing the CG distribution during training, resulting in improved free energy surfaces and reduced sensitivity to prior potentials. In addition, RE learns to correct time integration errors, allowing larger time steps in CG molecular dynamics simulation, while maintaining accuracy. Thus, our findings support the use of training objectives beyond FM, as a promising direction for improving CG NN potential's accuracy and reliability. [ABSTRACT FROM AUTHOR]

This article presents an effective and simple approximation scheme to analytically approximate solution behavior of a multi‐dimensional reaction–diffusion Brusselator system. This system has applications in cooperative processes of chemical kinetics and biochemical reaction processes. The proposed residual power series method is based on multiple power series expansion and residual error function formulation. The convergence properties and error bounds of the proposed scheme are theoretically established and numerically verified. Two benchmark problems in two‐ and three‐dimensional space are considered to validate the efficiency and accuracy of the proposed scheme. The obtained results verified reliability, accuracy, and simplicity of the proposed scheme against the available results in literature. [ABSTRACT FROM AUTHOR]

In this study, a deep learning-based approach is used to address inverse problems involving the inversion of a magnetic field and the identification of the relevant source, given the field data within a specific subdomain. Three different techniques are proposed: the first one is characterized by the use of a conditional variational autoencoder (CVAE) and a convolutional neural network (CNN); the second one employs the CVAE (its decoder, more specifically) and a fully connected deep artificial neural network; while the third one (mainly used as a comparison) uses a CNN directly operating on the available data without the use of the CVAE. These methods are applied to the magnetostatic problem outlined in the TEAM 35 benchmark problem, and a comparative analysis between them is conducted. [ABSTRACT FROM AUTHOR]

For the simultaneous optimization of many conflicting objectives, the capability of optimization algorithms must be increased. In this research, a non-dominated sorting (NDS) and crowding distance (CD)-based multi-objective variant of an advanced moth flame optimization (MFO) has been offered. Firstly, a mathematical quasi-reflection-based learning (QRL) strategy and weight strategy (WS) have been added to the classical MFO to alleviate the drawbacks of MFO. Next, this advanced MFO has been extended into multi-objective variant, namely MOQRMFO, with the help of NDS and CD approaches for well-distributed Pareto optimal front. The efficiency of the suggested MOQRMFO algorithm is tested in three phases. In the first phase, five ZDT multi-objective optimization problems (MOOPs) were considered under four performance metrics, namely general distance (GD), inverted general distance (IGD), spacing (S) and spread metric (Δ ) and then compared it with competitive multi-objective optimization algorithms. Secondly, six problems from the DTLZ test suite are considered under the above performance metrics to examine the effectiveness of the suggested MOQRMFO algorithm. The MOQRMFO algorithm's capacity to solve real-world problems has been evaluated by considering four multi-objective real-world engineering design issues in the third phase using several performance metrics. The experimental outcomes show that the MOQRMFO is a better candidate algorithm achieving more than 95% superior results for multi-objective benchmarks and real-life problems in contrast to several other algorithms. [ABSTRACT FROM AUTHOR]

Discovering mathematical equations that govern physical and biological systems from observed data is a fundamental challenge in scientific research. We present a new physics-informed framework for parameter estimation and missing physics identification (gray-box) in the field of Systems Biology. The proposed framework—named AI-Aristotle—combines the eXtreme Theory of Functional Connections (X-TFC) domain-decomposition and Physics-Informed Neural Networks (PINNs) with symbolic regression (SR) techniques for parameter discovery and gray-box identification. We test the accuracy, speed, flexibility, and robustness of AI-Aristotle based on two benchmark problems in Systems Biology: a pharmacokinetics drug absorption model and an ultradian endocrine model for glucose-insulin interactions. We compare the two machine learning methods (X-TFC and PINNs), and moreover, we employ two different symbolic regression techniques to cross-verify our results. To test the performance of AI-Aristotle, we use sparse synthetic data perturbed by uniformly distributed noise. More broadly, our work provides insights into the accuracy, cost, scalability, and robustness of integrating neural networks with symbolic regressors, offering a comprehensive guide for researchers tackling gray-box identification challenges in complex dynamical systems in biomedicine and beyond. Author summary: Our study addresses the fundamental challenge of uncovering mathematical rules governing physical and biological systems from real-world data. We introduce a novel framework, AI-Aristotle, designed for parameter estimation and identifying hidden physics (gray-box) in Systems Biology. AI-Aristotle combines the powerful eXtreme Theory of Functional Connections (X-TFC), Physics-Informed Neural Networks (PINNs), and symbolic regression (SR) techniques to discover parameters and uncover hidden relationships. Our work offers guidance to researchers addressing gray-box identification challenges in complex dynamic systems, including applications in biomedicine and beyond. [ABSTRACT FROM AUTHOR]

Continual technological advances associated with the recent automation revolution have tremendously increased the impact of computer technology in the industry. Software development and testing are time-consuming processes, and the current market faces a lack of specialized experts. Introducing automation to this field could, therefore, improve software engineers' common workflow and decrease the time to market. Even though many code-generating algorithms have been proposed in textual-based programming languages, to the best of the authors' knowledge, none of the studies deals with the implementation of such algorithms in graphical programming environments, especially LabVIEW. Due to this fact, the main goal of this study is to conduct a proof-of-concept for a requirement-based automated code-developing system within the graphical programming environment LabVIEW. The proposed framework was evaluated on four basic benchmark problems, encompassing a string model, a numeric model, a boolean model and a mixed-type problem model, which covers fundamental programming scenarios. In all tested cases, the algorithm demonstrated an ability to create satisfying functional and errorless solutions that met all user-defined requirements. Even though the generated programs were burdened with redundant objects and were much more complex compared to programmer-developed codes, this fact has no effect on the code's execution speed or accuracy. Based on the achieved results, we can conclude that this pilot study not only proved the feasibility and viability of the proposed concept, but also showed promising results in solving linear and binary programming tasks. Furthermore, the results revealed that with further research, this poorly explored field could become a powerful tool not only for application developers but also for non-programmers and low-skilled users. [ABSTRACT FROM AUTHOR]

Background: 5-Methylcytosine (5mC) plays a very important role in gene stability, transcription, and development. Therefore, accurate identification of the 5mC site is of key importance in genetic and pathological studies. However, traditional experimental methods for identifying 5mC sites are time-consuming and costly, so there is an urgent need to develop computational methods to automatically detect and identify these 5mC sites. Results: Deep learning methods have shown great potential in the field of 5mC sites, so we developed a deep learning combinatorial model called i5mC-DCGA. The model innovatively uses the Convolutional Block Attention Module (CBAM) to improve the Dense Convolutional Network (DenseNet), which is improved to extract advanced local feature information. Subsequently, we combined a Bidirectional Gated Recurrent Unit (BiGRU) and a Self-Attention mechanism to extract global feature information. Our model can learn feature representations of abstract and complex from simple sequence coding, while having the ability to solve the sample imbalance problem in benchmark datasets. The experimental results show that the i5mC-DCGA model achieves 97.02%, 96.52%, 96.58% and 85.58% in sensitivity (Sn), specificity (Sp), accuracy (Acc) and matthews correlation coefficient (MCC), respectively. Conclusions: The i5mC-DCGA model outperforms other existing prediction tools in predicting 5mC sites, and it is currently the most representative promoter 5mC site prediction tool. The benchmark dataset and source code for the i5mC-DCGA model can be found in https://github.com/leirufeng/i5mC-DCGA. [ABSTRACT FROM AUTHOR]

This article aims to determine the time-dependent heat coefficient together with the temperature solution for a type of semi-linear time-fractional inverse source problem by applying a method based on the finite difference scheme and Tikhonov regularization. An unconditionally stable implicit finite difference scheme is used as a direct (forward) solver. While by the MATLAB routine lsqnonlin from the optimization toolbox, the inverse problem is reformulated as nonlinear least square minimization and solved efficiently. Since the problem is generally incorrect or illposed that means any error inclusion in the input data will produce a large error in the output data. Therefore, the Tikhonov regularization technique is applied to obtain stable and accurate results. Finally, to demonstrate the accuracy and effectiveness of our scheme, two benchmark test problems have been considered, and its good working with different noise levels. [ABSTRACT FROM AUTHOR]

This paper concerns numerical solution of the diffusion equation with strong anisotropy on meshes not aligned with the anisotropic vector field. In order to resolve the numerical pollution for simulations on a non-anisotropy-aligned mesh and reduce the associated high computational cost we propose an effective preconditioner, extending our previous work [D. Green et al., Comput. Phys. Commun., 9 (2022), 108333]. Similar to the anisotropy-aligned mesh case, we apply the auxiliary space preconditioning framework to design a preconditioner where a continuous finite element space is used as the auxiliary space for the discontinuous finite element space. The key component is an effective line smoother that can mitigate the high-frequency errors perpendicular to the magnetic field. We design a graph-based approach to find such a line smoother that is approximately perpendicular to the vector fields when the mesh does not align with the anisotropy. Numerical experiments for several benchmark problems are presented, demonstrating the effectiveness and robustness of the proposed preconditioner when applied to Krylov iterative methods. [ABSTRACT FROM AUTHOR]

In this paper, the mathematical model of Vehicle Routing Problem with Time Windows (VRPTW) is established based on the directed graph, and a 3-stage multi-modal multi-objective differential evolution algorithm (3S-MMDEA) is proposed. In the first stage, in order to expand the range of individuals to be selected, a generalized opposition-based learning (GOBL) strategy is used to generate a reverse population. In the second stage, a search strategy of reachable distribution area is proposed, which divides the population with the selected individual as the center point to improve the convergence of the solution set. In the third stage, an improved individual variation strategy is proposed to legalize the mutant individuals, so that the individual after variation still falls within the range of the population, further improving the diversity of individuals to ensure the diversity of the solution set. Based on the synergy of the above three stages of strategies, the diversity of individuals is ensured, so as to improve the diversity of solution sets, and multiple equivalent optimal paths are obtained to meet the planning needs of different decision-makers. Finally, the performance of the proposed method is evaluated on the standard benchmark datasets of the problem. The experimental results show that the proposed 3S-MMDEA can improve the efficiency of logistics distribution and obtain multiple equivalent optimal paths. The method achieves good performance, superior to the most advanced VRPTW solution methods, and has great potential in practical projects. [ABSTRACT FROM AUTHOR]

The complex variable finite element method (ZFEM) is a numerical technique which aims to find the partial derivatives of the independent variables with respect to variation in dependent parameters declared in the physics. This is done by combining the complex Taylor series expansion within the weak formulation of the governing equation in a coupled system of linear equations forming a complex valued block matrix given by the Cauchy–Riemann matrix representation. In this work, two‐dimensional linear first‐order elements have been implemented in ZFEM to predict the design derivatives of the mechanical displacement field and the voltage potential field for a layered piezoelectric system in a steady‐state study with Dirichlet boundary condition applied at the top and bottom edges of the geometry. This approach allows the standard FEM solution to quantify the sensitivity of the mechanical displacement and voltage potential fields with respect to small variations in the material properties through the information obtained from the computation of the derivatives. The domain is formed by a layered body with PZT‐4 and PZT‐5 stacked together. For result verification, the numerical solution obtained with ZFEM was compared to results from a commercial FEM package and the solution from the imaginary part was compared to the exact solution of a well‐known benchmark problem. Comparison of the results showed good agreement for both the real and imaginary parts of the solution and the largest sensitivities were found in PZT‐5 specifically in C13, C33, and ε33. [ABSTRACT FROM AUTHOR]

Kinetic theory provides modeling of open quantum systems subject to Markovian noise via the Wigner–Fokker–Planck equation, which is an alternate of the Lindblad master equation setting, having the advantage of great physical intuition as it is the quantum equivalent of the classical phase space description. We perform a numerical inspection of the Wehrl entropy for the benchmark problem of a harmonic potential, since the existence of a steady state and its analytical formula have been proven theoretically in this case. When there is friction in the noise terms, no theoretical results on the monotonicity of absolute entropy are available. We provide numerical results of the time evolution of the entropy in the case with friction using a stochastic (Euler–Maruyama-based Monte Carlo) numerical solver. For all the chosen initial conditions studied (all of them Gaussian states), up to the inherent numerical error of the method, one cannot disregard the possibility of monotonic behavior even in the case under study, where the noise includes friction terms. [ABSTRACT FROM AUTHOR]

Sequential decision-making under multiple objective functions includes the problem of exhaustively searching for a Pareto-optimal policy and the problem of selecting a policy from the resulting set of Pareto-optimal policies based on the decision maker's preferences. This paper focuses on the latter problem. In order to select a policy that reflects the decision maker's preferences, it is necessary to order these policies, which is problematic because the decision-maker's preferences are generally tacit knowledge. Furthermore, it is difficult to order them quantitatively. For this reason, conventional methods have mainly been used to elicit preferences through dialogue with decision-makers and through one-to-one comparisons. In contrast, this paper proposes a method based on inverse reinforcement learning to estimate the weight of each objective from the decision-making sequence. The estimated weights can be used to quantitatively evaluate the Pareto-optimal policies from the viewpoints of the decision-makers preferences. We applied the proposed method to the multi-objective reinforcement learning benchmark problem and verified its effectiveness as an elicitation method of weights for each objective function. [ABSTRACT FROM AUTHOR]

Large-scale benchmark datasets are crucial in advancing research within the computer science communities. They enable the development of more sophisticated AI models and serve as "golden" benchmarks for evaluating their performance. Thus, ensuring the quality of these datasets is of utmost importance for academic research and the progress of AI systems. For the emerging vision-language tasks, some datasets have been created and frequently used, such as Flickr30k, COCO, and NoCaps, which typically contain a large number of images paired with their ground-truth textual descriptions. In this paper, an automatic method is proposed to assess the quality of large-scale benchmark datasets designed for vision-language tasks. In particular, a new cross-modal matching model is developed, which is capable of automatically scoring the textual descriptions of visual images. Subsequently, this model is employed to evaluate the quality of vision-language datasets by automatically assigning a score to each 'ground-truth' description for every image picture. With a good agreement between manual and automated scoring results on the datasets, our findings reveal significant disparities in the quality of the ground-truth descriptions included in the benchmark datasets. Even more surprising, it is evident that a small portion of the descriptions are unsuitable for serving as reliable ground-truth references. These discoveries emphasize the need for careful utilization of these publicly accessible benchmark databases. [ABSTRACT FROM AUTHOR]

Many real-world optimization problems, particularly engineering ones, involve constraints that make finding a feasible solution challenging. Numerous researchers have investigated this challenge for constrained single- and multi-objective optimization problems. In particular, this work extends the boundary update (BU) method proposed by Gandomi and Deb (Comput. Methods Appl. Mech. Eng. 363:112917, 2020) for the constrained optimization problem. BU is an implicit constraint handling technique that aims to cut the infeasible search space over iterations to find the feasible region faster. In doing so, the search space is twisted, which can make the optimization problem more challenging. In response, two switching mechanisms are implemented that transform the landscape along with the variables to the original problem when the feasible region is found. To achieve this objective, two thresholds, representing distinct switching methods, are taken into account. In the first approach, the optimization process transitions to a state without utilizing the BU approach when constraint violations reach zero. In the second method, the optimization process shifts to a BU method-free optimization phase when there is no further change observed in the objective space. To validate, benchmarks and engineering problems are considered to be solved with well-known evolutionary single- and multi-objective optimization algorithms. Herein, the proposed method is benchmarked using with and without BU approaches over the whole search process. The results show that the proposed method can significantly boost the solutions in both convergence speed and finding better solutions for constrained optimization problems. [ABSTRACT FROM AUTHOR]

Tasmanian devil optimization (TDO) algorithm represents one of the most recent optimization algorithms that were introduced based on the nature behavior of Tasmanian devil behavior. However, as a recent optimizer, its performance may provide inadequate balance among the exploitation and exploration abilities, especially when dealing with the multimodal and high-dimensional natures of optimization tasks. To overcome this shortage, a novel variant of the TDO, called improved Tasmanian devil optimization (ITDO), is introduced in this paper. In ITDO, two competitive strategies are embedded into TDO to enrich the scope of the searching capability with the aim of improving the diversification and identification of the algorithm. The effectiveness of the ITDO algorithm is examined by validating its performance on CEC 2020 benchmark functions with different landscape natures. The recorded results proved that the ITDO is very competitive with other counterparts. After ITDO exhibited a sufficient performance, then, it was applied to estimate the parameters of the 1 kVA, 230/230 V, single-phase transformer. Some assessment metrics along with convergence analysis are conducted to affirm the performance of the proposed algorithm. The recorded results confirm the competitive performance of the proposed method in comparison with the other optimization methods for the benchmark functions and can identify the accurate parameters for the single-phase transformer as the estimated parameters by ITDO are highly coincident with the experimental parameters. [ABSTRACT FROM AUTHOR]

How can we quantify uncertainty if our favorite computational tool--be it a numerical, statistical, or machine learning approach, or just any computer model--provides singlevalued output only? In this article, we introduce the Easy Uncertainty Quantification (EasyUQ) technique, which transforms real-valued model output into calibrated statistical distributions, based solely on training data of model output--outcome pairs, without any need to access model input. In its basic form, EasyUQ is a special case of the recently introduced isotonic distributional regression (IDR) technique that leverages the pool-adjacent-violators algorithm for nonparametric isotonic regression. EasyUQ yields discrete predictive distributions that are calibrated and optimal in finite samples, subject to stochastic monotonicity. The workflow is fully automated, without any need for tuning. The Smooth EasyUQ approach supplements IDR with kernel smoothing, to yield continuous predictive distributions that preserve key properties of the basic form, including both stochastic monotonicity with respect to the original model output and asymptotic consistency. For the selection of kernel parameters, we introduce multiple one-fit grid search, a computationally much less demanding approximation to leave-one-out cross-validation. We use simulation examples and forecast data from weather prediction to illustrate the techniques. In a study of benchmark problems from machine learning, we show how EasyUQ and Smooth EasyUQ can be integrated into the workflow of neural network learning and hyperparameter tuning, and we find EasyUQ to be competitive with conformal prediction as well as more elaborate input-based approaches. [ABSTRACT FROM AUTHOR]

In chemical industries, multiphase flows in a bubble column reactor are frequently observed. The nonlinearity associated with bubble hydrodynamics, such as bubble–bubble and bubble–liquid interactions, gives rise to complex spatiotemporal patterns with increased gas or liquid velocities, which are extremely difficult to model and predict. In the current study, we propose a new, computationally efficient recurrence-based approach involving the angular separation between suitably defined state vectors and implement it on the experimental multiphase flow variables. The experimental dataset that consists of image frames obtained using a high-speed imaging system is generated by varying air and water flow rates in a bubble column reactor setup. The recurrence plots using the new approach are compared with those derived from conventional recurrence, considering standard benchmark problems. Further, using the recurrence plots and recurrence quantification from the new recurrence methodology, we discover a transition from a high recurrence state to a complex regime with very low recurrence for an increase in airflow rate. Determinism exhibits a rise for the decrease in airflow rate. A sharp decline in determinism and laminarity, signifying the quick shift to complex dynamics, is more prominent for spatial recurrence than temporal recurrence, indicating that the rise in airflow rate significantly impacts the spatial location of bubbles. We identify three regimes that appeared as distinct clusters in the determinism–laminarity plane. The bubbly regime, characterized by high values of determinism and laminarity, is separated by an intermediate regime from the slug flow regime, which has low determinism and laminarity. [ABSTRACT FROM AUTHOR]

This paper presents the Multiscale Medalist Learning Algorithm (MMLA) as a novel heuristic approach for complex engineering optimization problems. By extending the Medalist Learning Algorithm, MMLA offers enhanced solution efficiency. The algorithm divides the learning process into successive periods with reduced search spaces, enabling focused search efforts in promising areas. Within each period, predefined learning stages are implemented. Top performers, known as medalists, engage in self-improvement operations through neighborhood searches, while common learners either learn from medalists or adapt based on the current state using neighborhood fluctuation. The MMLA balances exploration and exploitation capabilities through a natural growth curve that determines the learning efficiency. The MMLA's effectiveness and robustness are illustrated through the solution of a two-dimensional benchmark optimization problem and the successful resolution of ten well-known engineering design optimization problems. Comparative analysis demonstrates that the MMLA consistently outperforms other algorithms, providing competitive solutions with strict feasibility and minimal variation. [ABSTRACT FROM AUTHOR]

A multigrid coupling approach of the extended isogeometric–meshfree (XIMF) method and bond-based peridynamics (PD) is developed for static and dynamic fracture problems. The coupling approach exploits the advantages of the XIMF method and PD, including the computational efficiency of the XIMF method and the generality of the PD in dealing with fracture problems. To couple the two methods, a problem domain is divided into the peridynamic and isogeometric–meshfree subdomains. The former subdomain aims to model both the crack-tip and potential cracking zone and is discretized by fine peridynamic points, while the latter corresponds to the remaining zone and is discretized by coarse isogeometric–meshfree meshes. The two subdomains are connected with the interface meshes, at which the ghost peridynamic particles are embedded and the displacement constraints are enforced. In this way, fracture patterns can be captured without requiring the crack-tip enrichment functions which are complicated in three dimensions while obtaining the comparable efficiency of the XIMF method. Furthermore, an adaptive switching strategy is proposed to convert the isogeometric–meshfree meshes into peridynamic particles. Finally, several representative benchmark problems including the two-dimensional static crack propagation in a double cantilever beam and dynamic crack branching, and the three-dimensional mixed-mode fracture in a skew-notched structure are attempted to validate the proposed approach. [ABSTRACT FROM AUTHOR]

The inflation of hyperelastic thin shells is a highly nonlinear problem that arises in multiple important engineering applications. It is characterised by severe kinematic and constitutive nonlinearities and is subject to various forms of instabilities. To accurately simulate this challenging problem, we present an isogeometric approach to compute the inflation and associated large deformation of hyperelastic thin shells following the Kirchhoff–Love hypothesis. Both the geometry and the deformation field are discretized using Catmull–Clark subdivision bases which provide the required C 1 -continuous finite element approximation. To follow the complex nonlinear response exhibited by hyperelastic thin shells, inflation is simulated incrementally, and each incremental step is solved using the Newton–Raphson method enriched with arc-length control. An eigenvalue analysis of the linear system after each incremental step assesses the possibility of bifurcation to a lower energy mode upon loss of stability. The proposed method is first validated using benchmark problems and then applied to engineering applications, where the ability to simulate large deformation and associated complex instabilities is clearly demonstrated. [ABSTRACT FROM AUTHOR]

Numerical analysis of complex problems invariably requires the use of inputs from experimental methods like photoelasticity to validate the boundary conditions as well as the numerical modelling. In this era where the engineering community follows open-source culture to solve numerical problems, this brief note brings out a procedure to plot the photoelastic contours from FE results. The methodology is verified using a benchmark problem of a disk under diametral compression with experimental results and applied to a plate with an edge crack problem. [ABSTRACT FROM AUTHOR]

Background: Monte Carlo (MC) simulations are considered the gold‐standard for accuracy in radiotherapy dose calculation; so far however, no commercial treatment planning system (TPS) provides a fast MC for supporting clinical practice in carbon ion therapy. Purpose: To extend and validate the in‐house developed fast MC dose engine MonteRay for carbon ion therapy, including physical and biological dose calculation. Methods: MonteRay is a CPU MC dose calculation engine written in C++ that is capable of simulating therapeutic proton, helium and carbon ion beams. In this work, development steps taken to include carbon ions in MonteRay are presented. Dose distributions computed with MonteRay are evaluated using a comprehensive validation dataset, including various measurements (pristine Bragg peaks, spread out Bragg peaks in water and behind an anthropomorphic phantom) and simulations of a patient plan. The latter includes both physical and biological dose comparisons. Runtimes of MonteRay were evaluated against those of FLUKA MC on a standard benchmark problem. Results: Dosimetric comparisons between MonteRay and measurements demonstrated good agreement. In terms of pristine Bragg peaks, mean errors between simulated and measured integral depth dose distributions were between −2.3% and +2.7%. Comparing SOBPs at 5, 12.5 and 20 cm depth, mean absolute relative dose differences were 0.9%, 0.7% and 1.6% respectively. Comparison against measurements behind an anthropomorphic head phantom revealed mean absolute dose differences of 1.2%±1.1%$1.2\% \pm 1.1\;\%$ with global 3%/3 mm 3D‐γ passing rates of 99.3%, comparable to those previously reached with FLUKA (98.9%). Comparisons against dose predictions computed with the clinical treatment planning tool RayStation 11B for a meningioma patient plan revealed excellent local 1%/1 mm 3D‐γ passing rates of 98% for physical and 94% for biological dose. In terms of runtime, MonteRay achieved speedups against reference FLUKA simulations ranging from 14× to 72×, depending on the beam's energy and the step size chosen. Conclusions: Validations against clinical dosimetric measurements in homogeneous and heterogeneous scenarios and clinical TPS calculations have proven the validity of the physical models implemented in MonteRay. To conclude, MonteRay is viable as a fast secondary MC engine for supporting clinical practice in proton, helium and carbon ion radiotherapy. [ABSTRACT FROM AUTHOR]

In this paper, a new crack surface energy for the simulation of ductile fracture is proposed, which is based on the Allen–Cahn theory of diffuse interfaces. In contrast to existing fracture approaches, here, the crack surface energy density is a double-well potential based on a new interpretation of the crack surface. That is, the energy associated with the whole diffuse region between the fully cracked and intact regions is interpreted as crack surface energy. This kind of formulation, on the one hand, results in the balance of micromechanical forces and on the other hand, is a priori thermodynamically consistent. Furthermore, the proposed formulation is based on a gamma-convergent interface energy and it is in agreement with the classical solution of Irwin (Appl Mech Trans ASME E24:351–369, 1957). It is shown that in contrast to existing models, crack irreversibility is automatically fulfilled and no further constraints related to neither local nor global irreversibility are needed. To also account for potential plastic shear band localization, the approach is extended by a micromorphic plasticity model. By analyzing two different classical numerical benchmark problems, the proposed formulation is shown to enable mesh-independent results which are in agreement with the results of competing approaches. [ABSTRACT FROM AUTHOR]

Real-world applications often involve "uncertain" objectives, i.e., where optimisation algorithms observe objective values as a random variables with positive variance. In the past decade, several rigorous analysis results for evolutionary algorithms (EAs) on discrete problems show that EAs can cope with low-level uncertainties, i.e. when the variance of the uncertain objective value is small, and sometimes even benefit from uncertainty. Previous work showed that a large population combined with a non-elitist selection mechanism is a promising approach to handle high levels of uncertainty. However, the population size and the mutation rate can dramatically impact the performance of non-elitist EAs, and the optimal choices of these parameters depend on the level of uncertainty in the objective function. The performance and the required parameter settings for non-elitist EAs in some common objective-uncertainty scenarios are still unknown. We analyse the runtime of non-elitist EAs on two classical benchmark problems OneMax and LeadingOnes in in the one-bit, the bitwise, the Gaussian, and the symmetric noise models, and the dynamic binary value problem (DynBV). Our analyses are more extensive and precise than previous analyses of non-elitist EAs. In several settings, we prove that the non-elitist EAs outperform the current state-of-the-art results. Furthermore, we provide more precise guidance on how to choose the mutation rate, the selective pressure, and the population size as a function of the level of uncertainty. [ABSTRACT FROM AUTHOR]