Numerical Benchmark Research Articles

A Novel Gaussian Process Surrogate Model with Expected Prediction Error for Optimization under Constraints

Optimization, particularly constrained optimization problems (COPs), is fundamental in engineering, influencing various sectors with its critical role in enhancing design efficiency, reducing experimental costs, and shortening testing cycles. This study explores the challenges inherent in COPs, with a focus on developing efficient solution methodologies under stringent constraints. Surrogate models, especially Gaussian Process Regression (GPR), are pivotal in our approach, enabling the approximation of complex systems with reduced computational demand. We evaluate the efficacy of the Efficient Global Optimization (EGO) algorithm, which synergizes GPR with the Expected Improvement (EI) function, and further extend this framework to Constrained Expected Improvement (CEI) and our novel methodology Constrained Expected Prediction Error (CEPE). We demonstrate the effectiveness of these methodologies by numerical benchmark simulations and the real-world application of optimizing a Three-Bar Truss Design. In essence, the innovative CEPE approach promises a potent balance between solution accuracy and computational prowess, offering significant potential in the broader engineering field.

Parallelization of adaptive Bayesian cubature using multimodal optimization algorithms

PurposeBayesian cubature (BC) has emerged to be one of most competitive approach for estimating the multi-dimensional integral especially when the integrand is expensive to evaluate, and alternative acquisition functions, such as the Posterior Variance Contribution (PVC) function, have been developed for adaptive experiment design of the integration points. However, those sequential design strategies also prevent BC from being implemented in a parallel scheme. Therefore, this paper aims at developing a parallelized adaptive BC method to further improve the computational efficiency.Design/methodology/approachBy theoretically examining the multimodal behavior of the PVC function, it is concluded that the multiple local maxima all have important contribution to the integration accuracy as can be selected as design points, providing a practical way for parallelization of the adaptive BC. Inspired by the above finding, four multimodal optimization algorithms, including one newly developed in this work, are then introduced for finding multiple local maxima of the PVC function in one run, and further for parallel implementation of the adaptive BC.FindingsThe superiority of the parallel schemes and the performance of the four multimodal optimization algorithms are then demonstrated and compared with the k-means clustering method by using two numerical benchmarks and two engineering examples.Originality/valueMultimodal behavior of acquisition function for BC is comprehensively investigated. All the local maxima of the acquisition function contribute to adaptive BC accuracy. Parallelization of adaptive BC is realized with four multimodal optimization methods.

Adaptive scaled boundary finite element method for two/three-dimensional structural topology optimization based on dynamic responses

This paper presents an efficient solution for designing the topology of structures that can withstand dynamic loads. The method, called image/stereolithography (STL)-based adaptive scaled boundary finite element (SBFE), is a novel approach to topology optimization (TO) that is particularly effective for designing two/three-dimensional structures. The SBFE-based TO algorithm adopts a bi-evolutionary structural optimization (BESO) approach, which utilizes image/STL-based procedures to automatically adapt meshes and minimize mechanical compliance under varying volume fractions in the time domain. A key advantage of this approach is that it uses images of TO responses, rather than specific error functions, to guide the automatic adaptive mesh schemes. The method also incorporates a quadtree/octree mesh refinement to address the problem of hanging nodes, ensuring fast mesh convergence during the optimization process. Furthermore, a high-order implicit time integration technique provides a close approximation of equivalent static loads, allowing for the accurate mapping of displacement fields under actual dynamic responses at each time step. The effectiveness of this method is demonstrated through a variety of numerical examples and benchmarks.

Asymptotic quasisymmetric high-beta three-dimensional magnetohydrodynamic equilibria near axisymmetry

Quasisymmetry (QS), a hidden symmetry of the magnetic field strength, is known to support nested flux surfaces and provide superior particle confinement in stellarators. In this work, we study the ideal magnetohydrodynamic (MHD) equilibrium and stability of high-beta plasma in a large-aspect-ratio stellarator. In particular, we show that the lowest-order description of a near-axisymmetric equilibrium vastly simplifies the problem of three-dimensional quasisymmetric MHD equilibria, which can be reduced to a standard elliptic Grad–Shafranov equation for the flux function. We show that any large-aspect-ratio tokamak, deformed periodically in the vertical direction, is a stellarator with approximate volumetric QS. We discuss exact analytical solutions and numerical benchmarks. Finally, we discuss the ideal ballooning and interchange stability of some of our equilibrium configurations.

Young’s modulus and damping of partially sintered potassium sodium niobate (KNN) ceramics and its temperature dependence determined via the impulse excitation technique (IET)

Potassium sodium niobate (KNN) is suitable for the preparation of lead-free piezoelectric ceramics, and thus the elastic properties and damping behavior should be reliably known for practical applications. In this work we compare partially sintered KNN ceramics prepared by uniaxial and conventional sintering from three different KNN powders and show that the impulse excitation technique (IET) is perfectly suited to determine Young’s modulus at room temperature as well as the temperature dependence of Young’s modulus and damping (heating-cooling cycles with maximum temperature 800 °C). Room temperature values of the effective Young’s modulus of partially sintered KNN ceramics are below the predictions for convex pores and above a recently published numerical benchmark relation for concave pores. The phase transition temperatures determined by the IET are 160–190 °C for the low-temperature orthorhombic-tetragonal / tetragonal-orthorhombic transition and 388–412 °C for the high-temperature tetragonal-cubic / cubic-tetragonal transition, with hysteresis 12–25 K.

Multicomponent droplet evaporation in a geometric volume-of-fluid framework

This work proposes an innovative model for multicomponent phase change in interface-resolved simulations. The two-phase system is described by a geometric Volume-Of-Fluid (VOF) approach, and considers multiple components in non-isothermal environments, relaxing the hypothesis of pure liquid droplets usually studied in the literature. The model includes the Stefan flow and implements the following solutions for the complications that arise when studying liquid mixtures: i) a coupled approach for solving the interface jump conditions; ii) a proper strategy to obtain a liquid velocity for the advection of the volume fraction field, also applicable to static droplets with strong density ratio; iii) and a geometric approach to discretize the scalar fields transport equations. This model was implemented in the open-source code Basilisk, and it was tested on a number of benchmark phase change problems, such as the fixed flux evaporation, the Stefan problem, Epstein Plesset, and the Scriven problem. These test cases demonstrate the convergence of the numerical methods to the analytical solutions. More complex configurations, such as multicomponent isothermal and non-isothermal droplets are compared using numerical benchmark solutions obtained assuming spherical symmetry. The code, as well as the simulation setups, are released on the Basilisk website, making it the first model and open-source implementation of multicomponent phase change in a VOF framework.

SciEval: A Multi-Level Large Language Model Evaluation Benchmark for Scientific Research

Recently, there has been growing interest in using Large Language Models (LLMs) for scientific research. Numerous benchmarks have been proposed to evaluate the ability of LLMs for scientific research. However, current benchmarks are mostly based on pre-collected objective questions. This design suffers from data leakage problem and lacks the evaluation of subjective Q/A ability. In this paper, we propose SciEval, a comprehensive and multi-disciplinary evaluation benchmark to address these issues. Based on Bloom's taxonomy, SciEval covers four dimensions to systematically evaluate scientific research ability. In particular, we design a "dynamic" subset based on scientific principles to prevent evaluation from potential data leakage. Both objective and subjective questions are included in SciEval. These characteristics make SciEval a more effective benchmark for scientific research ability evaluation of LLMs. Comprehensive experiments on most advanced LLMs show that, although GPT-4 achieves SOTA performance compared to other LLMs, there is still substantial room for improvement, especially for dynamic questions. The codes and data are publicly available on https://github.com/OpenDFM/SciEval.

Nonlinear reduction using the extended group finite element method

In this paper, we develop a nonlinear reduction framework based on our recently introduced extended group finite element method. By interpolating nonlinearities onto approximation spaces defined with the help of finite elements, the extended group finite element formulation achieves a noticeable reduction in the computational overhead associated with nonlinear finite element problems. However, the problem’s size still leads to long solution times in most applications. Aiming to make real-time and/or many-query applications viable, we consider model order reduction and complexity reduction techniques to reduce the problem size and efficiently handle the reduced nonlinear terms, respectively. For proof of concept, we focus on the proper orthogonal decomposition and discrete empirical interpolation methods. While similar approaches based on the group finite element method only focus on semilinear problems, our proposed framework is also compatible with quasilinear problems. Compared to existing methods, our reduced models prove to be superior in many different aspects as demonstrated in three numerical benchmark problems.

Amalgamating Multi-Task Models with Heterogeneous Architectures

Multi-task learning (MTL) is essential for real-world applications that handle multiple tasks simultaneously, such as selfdriving cars. MTL methods improve the performance of all tasks by utilizing information across tasks to learn a robust shared representation. However, acquiring sufficient labeled data tends to be extremely expensive, especially when having to support many tasks. Recently, Knowledge Amalgamation (KA) has emerged as an effective strategy for addressing the lack of labels by instead learning directly from pretrained models (teachers). KA learns one unified multi-task student that masters all tasks across all teachers. Existing KA for MTL works are limited to teachers with identical architectures, and thus propose layer-to-layer based approaches. Unfortunately, in practice, teachers may have heterogeneous architectures; their layers may not be aligned and their dimensionalities or scales may be incompatible. Amalgamating multi-task teachers with heterogeneous architectures remains an open problem. For this, we design Versatile Common Feature Consolidator (VENUS), the first solution to this problem. VENUS fuses knowledge from the shared representations of each teacher into one unified generalized representation for all tasks. Specifically, we design the Feature Consolidator network that leverages an array of teacher-specific trainable adaptors. These adaptors enable the student to learn from multiple teachers, even if they have incompatible learned representations. We demonstrate that VENUS outperforms five alternative methods on numerous benchmark datasets across a broad spectrum of experiments.

Surrogate-assisted differential evolution using manifold learning-based sampling for high- dimensional expensive constrained optimization problems

To address the challenges of high-dimensional constrained optimization problems with expensive simulation models, a Surrogate-Assisted Differential Evolution using Manifold Learning-based Sampling (SADE-MLS) is proposed. In SADE-MLS, differential evolution operators are executed to generate numerous high-dimensional candidate points. To alleviate the curse of dimensionality, a Manifold Learning-based Sampling (MLS) mechanism is developed to explore the high-dimensional design space effectively. In MLS, the intrinsic dimensionality of the candidate points is determined by a maximum likelihood estimator. Then, the candidate points are mapped into a low-dimensional space using the dimensionality reduction technique, which can avoid significant information loss during dimensionality reduction. Thus, Kriging surrogates are constructed in the low-dimensional space to predict the responses of the mapped candidate points. The candidate points with high constrained expected improvement values are selected for global exploration. Moreover, the local search process assisted by radial basis function and differential evolution is performed to exploit the design space efficiently. Several numerical benchmarks are tested to compare SADE-MLS with other algorithms. Finally, SADE-MLS is successfully applied to a solid rocket motor multidisciplinary optimization problem and a re-entry vehicle aerodynamic optimization problem, with the total impulse and lift to drag ratio being increased by 32.7% and 35.5%, respectively. The optimization results demonstrate the practicality and effectiveness of the proposed method in real engineering practices.

An OpenFOAM multi-region solver for tritium transport modeling in fusion systems

The transport, permeation and retention of tritium inside nuclear fusion reactors is a topic of great interest due to the scarcity of the isotope, its ease of diffusion through materials and its radioactivity. An accurate balance of tritium is needed in all the fuel cycle, and each loss term needs to be evaluated in detail. In this context, reliable and flexible tools to evaluate tritium permeation and retention are a necessity for the development of fusion technologies. This work presents the OpenFOAM PermeAtion Solver for Tritium Analysis Foam (pastaFoam) solver and two custom boundary conditions, along with a series of verification and validation cases. The solver inherits all capabilities of the base solver, chtMultiRegionFoam, and is capable to simulate hydrogen transport in coupled fluid–solid systems in the presence of hydrogen traps, under diffusion limited regime or accounting for surface effects. All features are tested against analytical solutions and results are compared with other tritium transport codes. Agreement with experimental data is aligned with results of numerical benchmarks from literature.

A method to estimate the rectangular orthotropic plate elastic constants using least-squares and Chladni patterns

A method to retrieve the elastic constants of rectangular wooden plates is presented, relying on the measurement of a set of eigenfrequencies and the identification of the corresponding mode shapes, and belonging to the more general category of non-destructive inverse parameter estimation methods. Compared to previous work, the current method is effective with any choice of boundary conditions. Furthermore, the error function is linear in the elastic constants, which may be computed easily via a matrix inversion. This framework lends itself naturally to a physical interpretation of the results in terms of linear combinations of eigenmodes, yielding new sets of modes and associated combined mode shapes in which the elastic constants are completely uncoupled. Several numerical benchmark tests and experimental cases are treated in detail, highlighting the reliability of the proposed methodology in cases of interest in acoustics and musical acoustics.

Fast and accurate transcranial ultrasound simulation using the asymptotic model of the Civa Healthcare platform

To ensure its efficacy and safety, transcranial ultrasound therapy treatment planning requires accurate pressure field simulations and phase law corrections. Despite their long computation time and high memory usage, full numerical methods are often used since they are considered more accurate than semi-analytical methods. This work will present the so-called “pencil method“, a fast asymptotic model embedded in the CIVA HealthCare simulation platform. It allows computation in harmonic and impulse mode and the consideration of complex configurations, including solid obstacles, considering, at each interface, refractions and reflections with or without mode conversion of the acoustic field. This model was successfully compared to a recent collaborative work by Aubry et al. that presented a set of numerical benchmarks for transcranial propagation, to allow comparisons between various modeling tools. It was used to investigate the influence of parametric variation of skull material properties on the quality of acoustic focusing through the human skull. Its ability to predict the thermal rise at the intracranial target was validated against experimental data obtained ex-vivo through human skulls. Finally, works in progress will be shared about its connection to the open-source Kranion software developed at the FUS Foundation to facilitate comparison between clinical and simulated data.

Short-Term Probabilistic Wind Speed Predictions Integrating Multivariate Linear Regression and Generative Adversarial Network Methods

The precise forecasting of wind speeds is critical to lessen the harmful impacts of wind fluctuations on power networks and aid in merging wind energy into the grid system. However, prior research has predominantly focused on point forecasts, often overlooking the uncertainties inherent in the prediction accuracy. For this research, we suggest a new approach for forecasting wind speed intervals (PI). Specifically, the actual wind speed series are initially procured, and the complete ensemble empirical mode decomposition coupled with adaptive noise (CEEMDAN) method decomposes the actual wind speed series into constituent numerous mode functions. Furthermore, a generative adversarial network (GAN) is utilized to achieve the wind speed PI in conjunction with the multivariate linear regression method. To confirm the effectiveness of the suggested model, four datasets are selected. The validation results suggest that this suggested model attains a superior PI accuracy compared with those of numerous benchmark techniques. In the context of PI of dataset 4, the PINAW values show improvements of 68.06% and 32.35% over the CEEMDAN-CNN and VMD-GRU values in single-step forecasting, respectively. In conclusion, the proposed model excels over the counterpart models by exhibiting diminished a PINAW and CWC, while maintaining a similar PICP.

Trustworthy multi-view clustering via alternating generative adversarial representation learning and fusion

Multi-view clustering (MVC) has attached extensive attention as it provides an effective approach to deal with the unlabeled data in real-world applications. To enjoy the strong feature extraction capacity of deep learning, traditional shallow MVC methods are further extended to deep version. Though achieve superiorities in many fields, most existing deep MVC models are still limited by their lacking assurance of the trustworthiness and robustness. This drawback also leads to the possible poor clustering performance. To tackle this drawback, we propose an alternating generative adversarial learning strategy based network, termed as Alternating Generative Adversarial Representation Learning (AGARL) network for multi-view clustering, aiming to drive different views to fall into the same semantic space for the further alignment and information fusion. Various from the traditional generative adversarial learning strategy, the proposed alternating adversarial representation learning strategy successes in further aligning the distributions of the view-specific representations and exploring the cross-view consistency credited by its setting each view as the reference alternately. Then a consensus representative latent representation can be learned through an attention-like sub-network for all views. Finally, a self-supervised clustering module is employed in the proposed network to guide the learning of cluster assignment. In addition, comprehensive experiments on numerous benchmark MVC datasets have been performed to demonstrate the effectiveness of the proposed network compared to other state-of-the-art methods.

The boundary element method for acoustic transmission with nonconforming grids

Acoustic wave propagation through a homogeneous material embedded in an unbounded medium can be formulated as a boundary integral equation and accurately solved with the boundary element method. The computational efficiency deteriorates at high frequencies due to the increase in mesh size with a fixed number of elements per wavelength and also at high material contrasts due to the ill-conditioning of the linear system. This study presents the design of boundary element methods feasible for nonconforming surface meshes at the material interface. The nonconforming algorithm allows for independent grid generation, improves flexibility, and reduces the degrees of freedom. It works for different boundary integral formulations for Helmholtz transmission problems, operator preconditioning, and coupling with finite element solvers. The extensive numerical benchmarks at canonical configurations and an acoustic foam model confirm the significant improvements in computational efficiency when employing the nonconforming grid coupling in the boundary element method.

Multi-objective constrained robust design of a metamaterial vibration isolator with a limited budget

Many real-world engineering design optimisation problems encounter input uncertainties, which may introduce undesired fluctuations in design performance or even make the design solution infeasible. Robust design optimisation (RDO) is widely studied due to its ability to deal with uncertainties. RDO methods require many evaluations generally, which is prohibitive when relying on expensive simulations. Surrogate-assisted optimisation can help to reduce the number of simulation calls. An improved constrained multi-objective efficient robust global optimisation method (CMO-ERGO) is proposed in this work, which combines the robust expected improvement of ERGO with the probability of feasibility. CMO-ERGO improves the ERGO framework and quantifies the robustness of the objective and the constraint functions using an analytical uncertainty quantification based on the Kriging surrogate. The proposed method is tested on three numerical benchmark functions and applied to the robust design of a metamaterial vibration isolator with a honeycomb structure to explore its performance in solving engineering applications. The robustness of optimal solutions is demonstrated using the Monte Carlo Method. Moreover, comparisons between CMO-ERGO and several existing RDO methods illustrate the effectiveness and efficiency of CMO-ERGO.

Active and passive controls of magnetized Buongiorno Reiner–Phillipoff nanofluid

This attempt demonstrates the nature of mass and heat transportation in non-Newtonian Reiner–Philippoff liquid flow over moving surface by considering zero and nonzero normal mass flux conditions and transverse magnetic field. Thermophoresis and Brownian movement is accounted due to the Buongiorno model of nanofluid. The expressions of flow are reframed through appropriate variables into pairs of self-similar expressions. Further, these self-similar expressions are executed numerically through the Shooting procedure (Runge–Kutta 4th order). Numerical benchmarks and graphical illustrations are prepared to visualize the role of influential constraints on interesting quantities. It is observed that Lorentz force is beneficial in obtaining effective velocity and heat transfer. Improvement in thermophoresis factor enriches temperature field in case of active control while reverse nature is observed in passive control situation.

Two new single/multi-objective multi-strategy algorithms for the parametric estimation of dual band-notched ultra wideband antennas

This article introduces a novel single objective and a multi-objective multi-hybrid naked mole-rat (moIGDN) algorithm optimization techniques for solving numerical benchmarks and electromagnetic engineering problems. The hybridization was introduced to overcome the basic naked mole-rat algorithm’s (NMRA’s) local optima stagnation and poor exploration problems. The global exploration search equations of INFO, gazelle optimization algorithm (GOA), and dwarf mongoose optimization algorithm (DMO) have been added into the NMRA’s worker phase. Additionally, five mutation operators have been introduced for parametric enhancements and adaptations. For single-objective performance evaluation, three benchmark datasets namely classical benchmark, CEC 2014, CEC 2017, and CEC 2022 have been analysed. A comparison with JADE, SaDE, CMA-ES, success history based DE (SHADE), fractional-order calculus-based FPA (FA-FPO), LSHADE-SPACMA, NL-SHADE-LBC, evolutionary algorithms with eigen crossover (EA4eig), S-LSHADE-DP, L-SHADE-RSP-MID, EBOwithCMAR, LSHADE-EpSin among others. Apart from that, the proposed moIGDN algorithm was utilized to optimize the design of two electromagnetic multi-objective printed monopole antennas categorized as basic ultra-wideband (B-UWB) and dual band-notched ultra-wideband (DBN-UWB) antennas. Simulations have been performed by using the EM-MATLAB optimization interface with two objective functions: trying to minimize pass-band signal reflection and maximizing antenna gain, by mapping solutions to the Pareto-front boundary in the objective space. The best obtained antenna structure had an impedance bandwidth of 2.92–11.96 GHz (fractional bandwidth of 122%), efficient band-rejection characteristics for the WI-MAX (3.3 GHz–3.7 GHz) and WLAN (5.15 GHz–5.85 GHz) bands, and a compact geometry. Based on simulation results, moIGDN is found to be effective and can be utilized to solve complex wireless communication and advanced engineering optimization problems.

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.