Linear Benchmark Research Articles

Solving linear elasticity benchmark problems via the overset improved element-free Galerkin-finite element method

A novel approach for the solution of linear elasticity problems is introduced in this communication, which uses a hybrid chimera-type technique based on both finite element and improved element-free Galerkin methods. The proposed overset improved element-free Galerkin-finite element method (Ov-IEFG-FEM) for linear elasticity uses the finite element method (FEM) throughout the entire problem geometry, whereas a fine distribution of overlapping nodes is used to perform higher order approximations via the improved element-free Galerkin (IEFG) technique in regions demanding more computational accuracy. The method relies on keeping the FEM-based results in those regions where low order of approximation is enough to provide the required accuracy, i.e. outside the region where the solution will be enriched via the IEFG technique. The overlapping domains perform an iterative transfer of kinematics information through well-defined immersed boundaries, and a detailed explanation on this regard is also presented in this communication. The Ov-IEFG-FEM is used in a set of increasingly complex linear elasticity problems, and the outcomes demonstrate the suitability and reliability of this technique to solve such problems in an accurate and remarkably simple manner.

Industry return prediction via interpretable deep learning

We apply an interpretable machine learning model, the LassoNet, to forecast and trade U.S. industry portfolio returns. The model combines a regularization mechanism with a neural network architecture. A cooperative game-theoretic algorithm is also applied to interpret our findings. The latter hierarchizes the covariates based on their contribution to the overall model performance. Our findings reveal that the LassoNet outperforms various linear and nonlinear benchmarks concerning out-of-sample forecasting accuracy and provides economically meaningful and profitable predictions. Valuation ratios are the most crucial covariates, followed by individual and cross-industry lagged returns. The constructed industry ETF portfolios attain positive Sharpe ratios and positive and statistically significant alphas, surviving even transaction costs.

Implied volatility is (almost) past-dependent: Linear vs non-linear models

We explore and demonstrate a clear pattern of past-dependence in predicting implied volatility, which extends up to twenty days and is present in both linear and nonlinear models. Empirically, we find that linear models utilizing precedent values up to 20 days explain up to 80% of the variance in the S&P 500 index, while nonlinear models explain 78%. Furthermore, we observe that L2 regularization, as opposed to L1, enhances the performance of linear models and underscores the importance of past-dependence. As a result, a simple linear model with L2 regularization, incorporating precedent values up to the past 20 days, consistently outperforms both linear and nonlinear benchmark models when applied to the S&P 500 index option and SSE 50 ETF option over the past decades. Additionally, we uncover that the impact of all preceding values exists but consistently diminishes over time in all empirical studies involving past-dependence settings. Finally, we demonstrate that these forecasts yield profitable outcomes when implementing a simple long-short portfolio trading strategy. This study primarily investigates the ‘path-dependency’ of implied volatility in financial markets and further confirms that simple models can sometimes surpass complex nonlinear models in predicting volatility.

Nonlinear MHD modeling of soft β limits in W7-AS

An important question for the outlook of stellarator reactors is their robustness against pressure driven modes, and the underlying mechanism behind experimentally observed soft β limits. Towards building a robust answer to these questions, simulation studies are presented using a recently derived reduced nonlinear MHD model. First, the initial model implementation is extended to capture fluid compression by including the influence of parallel flows. Linear benchmarks of a (2, 1) tearing mode in W7-AS geometry, and interchange modes in a finite β, net-zero current carrying stellarator with low magnetic shear are then used to demonstrate the modeling capabilities. Finally, a validation study is conducted on experimental reconstructions of finite β W7-AS discharges. In agreement with past experimental analysis, it is shown that (i) the MHD activity is resistive, (ii) a soft β limit is observed, when the plasma resistivity approaches the estimated experimental value, and (iii) low n MHD activity is observed at intermediate β values, particularly a nonlinearly dominant (2, 1) mode. The MHD activity is mild, explaining the soft β limit, because the plasma volume remains separated into distinct sub-volumes in which field lines are ergodically confined. For the assumed transport parameters, the enhanced perpendicular transport along stochastic magnetic field lines can be overcome with the experimental heating power. The limitations in the current modeling are described, alongside an outlook for characterizing the quasi-steady state operational limit in W7-AS and other devices in more detail in future work.

Nonlinear dynamics of a heaving spar-floater system integrated with inerter pendulum vibration absorber power take-off for wave energy conversion

A power take-off based on the inerter pendulum vibration absorber (called IPVA-PTO) is integrated with a spar-floater system to study its hydrodynamic response suppression and wave energy conversion capabilities in regular waves. The hydrodynamics of the spar-floater system is computed using the boundary element method with linear wave theory. With the wave height and wave frequency as the bifurcation parameters, it is found that the system can undergo two bifurcations: period-doubling bifurcation around the first resonance frequency (spar mode) and secondary Hopf bifurcation around the second resonance frequency (floater mode). The period-doubling bifurcation results in an energy transfer between the spar-floater system and the IPVA-PTO for small electrical damping values. As a result, the IPVA-PTO system simultaneously reduces the maximum response amplitude operator (RAO) of the spar and increases the normalized capture width in comparison with the optimal linear benchmark. Experiments performed on a “dry” single-degree-of-freedom system integrated with the IPVA-PTO where the base excitation is substituted for the wave excitation verify the simultaneous performance enhancement due to the period-doubling bifurcation. The system performance beyond the period-doubling bifurcation is also experimentally investigated. On the other hand, as the wave height approaches and passes the secondary Hopf bifurcation, the pendulum responses transition from primary harmonic responses to quasi-periodic responses to rotations. When the rotations occur, the IPVA-PTO system increases the maximum normalized capture width threefold to fivefold compared with the optimal linear benchmark, yet slightly increases the RAO around the second resonance frequency. Nevertheless, the RAO remains smaller than the global maximum RAO of the optimal linear benchmark. Finally, parametric studies are performed to study the effects of parameters on the bifurcations. It is observed that by varying the electrical damping, the wave height required for achieving the period-doubling bifurcation can be changed significantly, which can be exploited to stabilize the spar.

Management of local finances in crisis conditions on the example of voivodeship governments in 2019-2021

The management of local finances is an intricate process consisting of decisions made by authorized bodies, which, as a result, after taking into account the established goals, both current and strategic, should result in the maximization of socio-economic effects. Indicator analysis is considered one of the important instruments of local government financial management. In the article, based on the data published by the Ministry of Finance, the National Council of Regional Chambers of Accounts and the Central Statistical Office, the financial management of the provincial cross-section of Poland in 2019-2021 was reviewed. The idea of the study was to assess the management of local finances during the crisis caused by the COVID-19 pandemic in synthetic terms, based on the TOPSIS multi-criteria linear ordering method and benchmarking, and to try to identify the factors determining this process. The research was carried out by means of financial analysis of 21 indicators, which were compiled for 16 local government provinces in Poland. The results of the research made it possible to determine the classes of financial condition of the analyzed units. The COVID-19 pandemic caused that in 2020, none of the studied local government provinces ranked in the first class characterizing a very high level of financial condition according to the TOPSIS method, although as many as 9 units were assigned to the second class characterizing a high level of financial condition. Local government provinces in 2019-2021 were characterized by very high development and investment potential, as well as the self-financing rate, they accumulated budget surpluses at the expense of an apparent slowdown in investment activity.

P-Bifurcation Analysis of a Quarter-Car Model With Inerter-Based Pendulum Vibration Absorber: A Wiener Path Integration Approach

Abstract In this theoretical study, a recently developed inerter-based pendulum vibration absorber (IPVA) coupled with energy harvesting capabilities is applied to the quarter car model with class C road conditions (ISO 8608). The impact of varying the pendulum length parameter on power harvesting, ride comfort (sprung mass acceleration), and road handling is investigated. It is discovered that P-bifurcation of the probability density function (PDF), can simultaneously occur with enhanced output power (40% improvements), low sprung mass acceleration (60% improvements), and better road handling (60% improvements) when compared with the linear benchmark system. To predict this bifurcation, a Wiener path integration (WPI) method coupled with curvature checking is developed for the PDF. An efficient bifurcation detection algorithm is developed which leads to the prediction of monomodal, bimodal, and rotation PDF regions in the noise intensity-electrical damping plane. Using Monte Carlo simulations (MCS), the performance metrics were then compared against the optimal linear benchmark for varying driving speed on a class F road while varying the electrical damping so that the system is at or near P-bifurcation. Energy transfer into the electrical domain and power harvested are shown to be up to 43% and 20% higher than for the optimized linear system, respectively. Electrical efficiency considerations show that generator selection is also a factor. Ride comfort and road handling still saw improvements of at least 59%. Finally, the new algorithm effectively reduces an exhaustive MCS for various parameter configurations when qualitative changes in the PDF are linked to performance.

Linear cross-entropy benchmarking with Clifford circuits

Linear cross-entropy benchmarking with Clifford circuits

TwoFold: Highly accurate structure and affinity prediction for protein-ligand complexes from sequences

We describe our development of ab initio protein-ligand binding pose prediction models based on transformers and binding affinity prediction models based on the neural tangent kernel (NTK). Folding both protein and ligand, the TwoFold models achieve efficient and quality predictions matching state-of-the-art implementations while additionally reconstructing protein structures. Solving NTK models points to a new use case for highly optimized linear solver benchmarking codes on HPC.

The simplified MITC4+ shell element and its performance in linear and nonlinear analysis

The recently developed improved MITC4+ shell element exhibits excellent convergence behavior in both bending- and membrane-dominated shell problems. Compared to the widely recognized MITC4 shell element, the membrane and in-plane shear locking were significantly alleviated. However, it is difficult to implement the assumed membrane strain field because of its complexity. In this study, a simplified MITC4+ shell element is developed. A simpler assumed membrane strain field that facilitates the extension to nonlinear formulations is proposed. To reduce the sensitivity of the element performance to mesh distortion, a geometry-dependent Gauss integration scheme is employed. The proposed element passes the patch, zero-energy mode, and isotropy tests. The performance of the simplified MITC4+ shell element is demonstrated using various linear and nonlinear benchmark problems.

Nonlinear Energy Transfer of a Spar-Floater System Using the Inerter Pendulum Vibration Absorber

Abstract The inerter pendulum vibration absorber (IPVA) is integrated between a spar and an annulus floater using a ball-screw mechanism to study its wave energy conversion potential. Hydrodynamic stiffness, added mass, and radiation damping effects on the spar-floater system are characterized using the boundary element method. It is found that a 1:2 internal resonance via a period-doubling bifurcation in the system is responsible for nonlinear energy transfer between the spar-floater system and the pendulum vibration absorber. This nonlinear energy transfer occurs when the primary harmonic solution of the system becomes unstable due to the 1:2 internal resonance phenomenon. The focus of this paper is to analyze this 1:2 internal resonance phenomenon near the first natural frequency of the system. The IPVA system when integrated with the spar-floater system is shown to outperform a linear coupling between the spar and the floater both in terms of the response amplitude operator (RAO) of the spar and one measure of the energy conversion potential of the system. Finally, experiments are performed on the IPVA system integrated with single-degree-of-freedom system (without any hydrodynamic effects) to observe the 1:2 internal resonance phenomenon and the nonlinear energy transfer between the primary mass and the pendulum vibration absorber. It is shown experimentally that the IPVA system outperforms a linear benchmark in terms of vibration suppression due to the energy transfer phenomenon.

Fast immersed boundary method based on weighted quadrature

Combining sum factorization, weighted quadrature, and row-based assembly enables efficient higher-order computations for tensor product splines. We aim to transfer these concepts to immersed boundary methods, which perform simulations on a regular background mesh cut by a boundary representation that defines the domain of interest. Therefore, we present a novel concept to divide the support of cut basis functions to obtain regular parts suited for sum factorization. These regions require special discontinuous weighted quadrature rules, while Gauss-like quadrature rules integrate the remaining support. Two linear elasticity benchmark problems confirm the derived estimate for the computational costs of the different integration routines and their combination. Although the presence of cut elements reduces the speed-up, its contribution to the overall computation time declines with h-refinement.

Kirchhoff–Love shell representation and analysis using triangle configuration B-splines

This paper presents the application of triangle configuration B-splines (TCB-splines) for representing and analyzing the Kirchhoff–Love shell in the context of isogeometric analysis (IGA). TCB-splines offer flexibility in modeling complex geometries with C1 continuity, making them naturally fit into the Kirchhoff–Love shell formulation with complex geometries. We first propose a linear least-squares-based framework to reparametrize the mid-surface of a thin shell, which consists of multiple (trimmed) NURBS patches and is topologically equivalent to an open disk with a finite number of holes, into a single TCB-surface defined over a carefully computed parametric domain. We then utilize TCB-splines for geometric representation and solution approximation in shell analysis. We verify the accuracy and robustness of our method by applying it to linear and nonlinear benchmark shell problems. The applicability of the proposed approach to shell analysis is further exemplified by performing geometrically nonlinear Kirchhoff–Love shell simulations of a pipe junction and a front bumper represented by a single patch of TCB-splines.

The digital economy is an important path to boosting common prosperity

Abstract Promoting progress in the digital development of social wealth is the key strategy to promote wealth transformation. The increase has been increasing at present. Increase GDP of national wealth strategy to our country to promote wealth transformation The increase of wealth is increasing at present. This paper proposes recommendations for other regional differences to promote continuous updating of development concepts, innovation-driven development, and optimization of industrial structure to provide a good environment for the digital economy to promote the increase of wealth in increasing construction. With this as the key theory from 2012 to 2019, here we designed an economic measurement model that uses simple linear regression, benchmark test, correlation test, and intermediary effect test to conduct empirical research, measure the current situation, and develop existing grade classification and economic development level, and empirically analyzes the impact of development grade phenomenon on the commonwealth. The results show that different regions have different conditions. At the same time, grade performance contributes to the development of good results economy, with the greatest impact on the West and the least impact on the Center. In general, a subdivision of social hierarchy, the level of the high-quality economy has been improving, parameter problems in different regions roughly describe a stable, rising direction, average values of the national, eastern and central, and western regions in 2007 are 31.11, 37.53 and 27.40, rising to 42.65, 50.11 and 38.34 in 2019, respectively. Thus, the digital economy provides effective and feasible new development ideas and changes in key economic issues and is a key force driving China’s economic growth and an important path to boost common prosperity.

Patch-wise quadrature of trimmed surfaces in Isogeometric Analysis

This work presents an efficient quadrature rule for shell analysis fully integrated in CAD by means of Isogeometric Analysis (IGA). General CAD-models may consist of trimmed parts such as holes, intersections, cut-offs etc. Therefore, IGA should be able to deal with these models in order to fulfil its promise of closing the gap between design and analysis. Trimming operations violate the tensor-product structure of the used Non-Uniform Rational B-spline (NURBS) basis functions and of typical quadrature rules. Existing efficient patch-wise quadrature rules consider actual knot vectors and are determined in 1D. They are extended to further dimensions by means of a tensor-product. Therefore, they are not directly applicable to trimmed structures. The herein proposed method extends patch-wise quadrature rules to trimmed surfaces. Thereby, the number of quadrature points can be significantly reduced. Geometrically linear and non-linear benchmarks of plane, plate and shell structures are investigated. The results are compared to a standard trimming procedure and a good performance is observed.

Safety Verification of Nonlinear Systems with Bayesian Neural Network Controllers

Bayesian neural networks (BNNs) retain NN structures with a probability distribution placed over their weights. With the introduced uncertainties and redundancies, BNNs are proper choices of robust controllers for safety-critical control systems. This paper considers the problem of verifying the safety of nonlinear closed-loop systems with BNN controllers over unbounded-time horizon. In essence, we compute a safe weight set such that as long as the BNN controller is always applied with weights sampled from the safe weight set, the controlled system is guaranteed to be safe. We propose a novel two-phase method for the safe weight set computation. First, we construct a reference safe control set that constraints the control inputs, through polynomial approximation to the BNN controller followed by polynomial-optimization-based barrier certificate generation. Then, the computation of safe weight set is reduced to a range inclusion problem of the BNN on the system domain w.r.t. the safe control set, which can be solved incrementally and the set of safe weights can be extracted. Compared with the existing method based on invariant learning and mixed-integer linear programming, we could compute safe weight sets with larger radii on a series of linear benchmarks. Moreover, experiments on a series of widely used nonlinear control tasks show that our method can synthesize large safe weight sets with probability measure as high as 95% even for a large-scale system of dimension 7.

Omitted Budget Constraint Bias and Implications for Competitive Pricing

Standard choice-based conjoint models often ignore or insufficiently approximate consumers’ budget constraints, despite the prominent role of budget constraints in economic theory. The authors offer a theoretically motivated improvement to the choice-based conjoint model that is especially appropriate for high-ticket durable goods and develop a Bayesian method for the inference of unobserved budget constraints. The proposed method leverages respondents’ stated budget constraints that suffer from measurement error and respondents’ financial demographic variables as additional information to reduce the dependency on functional form assumptions in the estimation. The authors show that accounting for budget constraints substantially increases model fit and the accuracy of competitive pricing in an industry-grade discrete-choice experiment on consumer preferences for high-end laptops. The proposed model performs better than the canonical linear price benchmark model, which is not flexible enough to approximate budget constraints. In theory, more flexible utility specifications, such as the nonlinear dummy price model, can approximate consumers’ budget constraints. However, they perform poorly when only finite data are available. The authors conclude that applied researchers in industry and academia will benefit from having a better tool for estimating budgets in high-ticket categories.

Comparison of quantum advantage experiments using random circuit sampling

Random circuit sampling, the task of sampling bit strings from a random unitary operator, has been implemented to demonstrate quantum advantage on the Sycamore quantum processor with 53 qubits and on the Zuchongzhi quantum processor with 56 and 61 qubits. Recently, it was claimed that classical computers using tensor network simulation could catch on to current noisy quantum processors for random circuit sampling. While the linear cross-entropy benchmark fidelity was used to certify all these claims, it may not capture statistical properties of outputs in detail. Here, we compare the bit strings sampled from classical computers using tensor network simulation by Pan et al. [F. Pan, K. Chen, and P. Zhang, Phys. Rev. Lett. 129, 090502 (2022)] and by Kalachev et al. [G. Kalachev, P. Panteleev, P. Zhou, and M.-H. Yung, arXiv:2112.15083] with the bit strings from the Sycamore quantum processor. It is shown that all of Kalachev et al.'s samples passed the NIST random number tests. The heat maps of bit strings show that Pan et al.'s and Kalachev et al.'s samples are quite different from the Sycamore or Zuchongzhi samples. The analysis with the Marchenko-Pastur distribution and the Wasssertein distances demonstrates that Kalachev et al.'s samples are statistically closer to the Sycamore samples than Pan et al.'s while the three datasets have similar values for the linear cross-entropy fidelity. Our finding implies that further study is needed to certify or beat the claims of quantum advantage using random circuit sampling.

ULD-Net: 3D unsupervised learning by dense similarity learning with equivariant-crop.

Although many recent deep learning methods have achieved good performance in point cloud analysis, most of them are built upon the heavy cost of manual labeling. Unsupervised representation learning methods have attracted increasing attention due to their high label efficiency. How to learn more useful representations from unlabeled 3D point clouds is still a challenging problem. Addressing this problem, we propose a novel unsupervised learning approach for point cloud analysis, named ULD-Net, consisting of an equivariant-crop (equiv-crop) module to achieve dense similarity learning. We propose dense similarity learning that maximizes consistency across two randomly transformed global-local views at both the instance level and the point level. To build feature correspondence between global and local views, an equiv-crop is proposed to transform features from the global scope to the local scope. Unlike previous methods that require complicated designs, such as negative pairs and momentum encoders, our ULD-Net benefits from the simple Siamese network that relies solely on stop-gradient operation preventing the network from collapsing. We also utilize the feature separability constraint for more representative embeddings. Experimental results show that our ULD-Net achieves the best results of context-based unsupervised methods and comparable performances to supervised models in shape classification and segmentation tasks. On the linear support vector machine classification benchmark, our ULD-Net surpasses the best context-based method spatiotemporal self-supervised representation learning (STRL) by 1.1% overall accuracy. On tasks with fine-tuning, our ULD-Net outperforms STRL under fully supervised and semisupervised settings, in particular, 0.1% accuracy gain on the ModelNet40 classification benchmark, and 0.6% medium intersection of union gain on the ShapeNet part segmentation benchmark.

Self-adaptive physics-informed neural networks

Physics-Informed Neural Networks (PINNs) have emerged recently as a promising application of deep neural networks to the numerical solution of nonlinear partial differential equations (PDEs). However, it has been recognized that adaptive procedures are needed to force the neural network to fit accurately the stubborn spots in the solution of “stiff” PDEs. In this paper, we propose a fundamentally new way to train PINNs adaptively, where the adaptation weights are fully trainable and applied to each training point individually, so the neural network learns autonomously which regions of the solution are difficult and is forced to focus on them. The self-adaptation weights specify a soft multiplicative soft attention mask, which is reminiscent of similar mechanisms used in computer vision. The basic idea behind these SA-PINNs is to make the weights increase as the corresponding losses increase, which is accomplished by training the network to simultaneously minimize the losses and maximize the weights. In addition, we show how to build a continuous map of self-adaptive weights using Gaussian Process regression, which allows the use of stochastic gradient descent in problems where conventional gradient descent is not enough to produce accurate solutions. Finally, we derive the Neural Tangent Kernel matrix for SA-PINNs and use it to obtain a heuristic understanding of the effect of the self-adaptive weights on the dynamics of training in the limiting case of infinitely-wide PINNs, which suggests that SA-PINNs work by producing a smooth equalization of the eigenvalues of the NTK matrix corresponding to the different loss terms. In numerical experiments with several linear and nonlinear benchmark problems, the SA-PINN outperformed other state-of-the-art PINN algorithm in L2 error, while using a smaller number of training epochs.