Journal of Computational Mathematics and Data Science最新文献_第2页

A neural network approach for solving the Monge–Ampère equation with transport boundary condition 求解带输运边界条件的monge - ampantere方程的神经网络方法

Journal of Computational Mathematics and Data Science

Pub Date : 2025-06-01 DOI: 10.1016/j.jcmds.2025.100119

Roel Hacking , Lisa Kusch , Koondanibha Mitra , Martijn Anthonissen , Wilbert IJzerman

This paper introduces a novel neural network-based approach to solving the Monge–Ampère equation with the transport boundary condition, specifically targeted towards optical design applications. We leverage multilayer perceptron networks to learn approximate solutions by minimizing a loss function that encompasses the equation’s residual, boundary conditions, and convexity constraints. Our main results demonstrate the efficacy of this method, optimized using L-BFGS, through a series of test cases encompassing symmetric and asymmetric circle-to-circle, square-to-circle, and circle-to-flower reflector mapping problems. Comparative analysis with a conventional least-squares finite-difference solver reveals the competitive, and often superior, performance of our neural network approach on the test cases examined here. A comprehensive hyperparameter study further illuminates the impact of factors such as sampling density, network architecture, and optimization algorithm. While promising, further investigation is needed to verify the method’s robustness for more complicated problems and to ensure consistent convergence. Nonetheless, the simplicity and adaptability of this neural network-based approach position it as a compelling alternative to specialized partial differential equation solvers.

本文介绍了一种新的基于神经网络的方法来求解具有传输边界条件的monge - ampantere方程，特别针对光学设计应用。我们利用多层感知器网络，通过最小化包含方程残差、边界条件和凸性约束的损失函数来学习近似解。通过一系列测试用例，包括对称和非对称的圆对圆、方对圆和圆对花反射器映射问题，我们的主要结果证明了该方法的有效性，该方法使用L-BFGS进行了优化。与传统的最小二乘有限差分求解器的比较分析揭示了我们的神经网络方法在这里所检查的测试用例上的竞争性，并且通常是优越的性能。全面的超参数研究进一步阐明了采样密度、网络结构和优化算法等因素的影响。虽然有希望，但需要进一步的研究来验证该方法对更复杂问题的鲁棒性并确保一致收敛。尽管如此，这种基于神经网络的方法的简单性和适应性使其成为专门的偏微分方程求解器的令人信服的替代方案。

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引用次数: 0

Machine learning-driven market value prediction for European football players 机器学习驱动的欧洲足球运动员市场价值预测

Journal of Computational Mathematics and Data Science

Pub Date : 2025-06-01 DOI: 10.1016/j.jcmds.2025.100118

Abdullah Tamim , Md. Wadud Jahan , Md. Rashid Shahriar Chowdhury , Ahammad Hossain , Md. Mizanur Rahman , A.H.M. Rahmatullah Imon

Football is globally recognized as the most widely practiced and watched sport. Precise player value is crucial for clubs seeking to maximize their player acquisition strategy and overall success in football. Conventional player valuation methodologies are mainly dependent on expert judgments and subjective assessments, missing the objectivity and precision provided by data-driven approaches. This study seeks to close this disparity by utilizing machine learning techniques to predict the market valuations of football players. The analysis is conducted using an extensive dataset sourced from the FIFA 22 video game, which was obtained via sofifa.com. The collection includes more than 16,000 players. The Machine Learning (ML) techniques used in this study are Multiple Linear Regression (MLR), Ridge Regression (RR), Support Vector Regression (SVR), and Random Forest Regression (RFR). The machine learning algorithms undergo training using 80% of the samples and are subsequently tested using the remaining 20% of the samples. We evaluate each algorithm’s performance using metrics like Mean Absolute Error (MAE), Mean Squared Error (MSE), Root Mean Squared Error (RMSE), and R-squared (R²) value. Numerical results show that the RFR model demonstrates superior performance by achieving the lowest MAE, MSE, RMSE, and the highest R² value across all samples. The RFR effectively captures non-linear interactions and reliably prevents overfitting. This research finding will enhance the existing knowledge in sports economics by demonstrating how ML can be used to anticipate the market prices of football players with better accuracy. This will provide football teams with valuable insights to make more strategic decisions.

足球是全球公认的最广泛练习和观看的运动。精确的球员价值对于寻求最大化球员获取策略和足球整体成功的俱乐部至关重要。传统的玩家评估方法主要依赖于专家判断和主观评估，缺少数据驱动方法所提供的客观性和精确性。这项研究试图通过利用机器学习技术来预测足球运动员的市场估值来缩小这种差距。该分析使用了来自FIFA 22视频游戏的广泛数据集，该数据集是通过soffifa.com获得的。收藏了超过16000名球员。本研究中使用的机器学习（ML）技术是多元线性回归（MLR）、岭回归（RR）、支持向量回归（SVR）和随机森林回归（RFR）。机器学习算法使用80%的样本进行训练，随后使用剩余20%的样本进行测试。我们使用平均绝对误差（MAE）、均方误差（MSE）、均方根误差（RMSE）和r平方（R2）值等指标来评估每种算法的性能。数值结果表明，RFR模型通过在所有样本中实现最低的MAE、MSE、RMSE和最高的R2值，显示出优越的性能。RFR有效捕获非线性相互作用，可靠地防止过拟合。这一研究发现将通过展示如何使用ML来更好地预测足球运动员的市场价格，从而增强体育经济学的现有知识。这将为足球队提供有价值的见解，以做出更多的战略决策。

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引用次数: 0

An improved descent hybrid gradient-based projection algorithm for nonlinear equations and signal recovery problems 一种改进的基于下降混合梯度的投影算法用于非线性方程和信号恢复问题

Journal of Computational Mathematics and Data Science

Pub Date : 2025-05-20 DOI: 10.1016/j.jcmds.2025.100117

M. Koorapetse, P. Kaelo, T. Diphofu, S. Lekoko, T. Yane, B. Modise, C.R. Sam

Derivative-free projection methods for solving nonlinear monotone equations have recently gained favor with researchers. Based on a hybrid conjugate gradient algorithm and the projection techniques, in this work, we present a descent derivative-free projection method for finding solutions to large-scale nonlinear monotone equations. The proposed method satisfies the descent condition and, under some suitable assumptions, its global convergence is established. The presented method’s efficacy is demonstrated through numerical experiments. Results show that, compared to other methods with similar structure, the method performs better. The method is further applied to an application in signal recovery, and it is proving to be efficient.

求解非线性单调方程的无导数投影方法近年来得到了研究人员的青睐。本文基于混合共轭梯度算法和投影技术，提出了一种求解大规模非线性单调方程的无下降导数投影方法。该方法满足下降条件，并在适当的假设条件下证明了其全局收敛性。通过数值实验验证了该方法的有效性。结果表明，与其他结构相似的方法相比，该方法具有更好的性能。将该方法进一步应用于信号恢复，证明了该方法的有效性。

引用次数: 0

Universal approximation property of ODENet and ResNet with a single activation function 单一激活函数下ODENet和ResNet的普遍逼近性质

Journal of Computational Mathematics and Data Science

Pub Date : 2025-05-15 DOI: 10.1016/j.jcmds.2025.100116

Masato Kimura , Kazunori Matsui , Yosuke Mizuno

We study a universal approximation property of ODENet and ResNet. The ODENet is a map from an initial value to the final value of an ODE system in a finite interval. It is considered a mathematical model of a ResNet-type deep learning system. We consider dynamical systems with vector fields given by a single composition of the activation function and an affine mapping, which is the most common choice of the ODENet or ResNet vector field in actual machine learning systems. We demonstrate that both ODENets and ResNets with the restricted vector field of a single composition of the activation function and an affine mapping can uniformly approximate ODENets within the broader class that utilize a general vector field.

我们研究了ODENet和ResNet的普遍近似性质。ODENet是ODE系统在有限区间内从初始值到最终值的映射。它被认为是resnet型深度学习系统的数学模型。我们考虑具有由激活函数和仿射映射的单一组合给出的矢量场的动态系统，这是实际机器学习系统中ODENet或ResNet矢量场的最常见选择。我们证明了ODENets和ResNets都具有激活函数和仿射映射的单一组合的受限向量场，可以在使用一般向量场的更广泛的类中一致地近似ODENets。

引用次数: 0

Crafting a Player Impact Metric through analysis of football match event data 通过分析足球比赛事件数据制作球员影响指标

Journal of Computational Mathematics and Data Science

Pub Date : 2025-05-12 DOI: 10.1016/j.jcmds.2025.100115

Mohamed Elsharkawi, Raja Hashim Ali, Talha Ali Khan

The evaluation of football players remains a challenging task due to the limitations of existing rating models as well as the diverse nature of in-game actions and their varying impact on outcome of the matches, which often emphasize offensive actions while overlooking key defensive and strategic contributions. While some player impact metrics exist for football, their effectiveness, complete in-depth analysis, and relationship with match outcomes (win, loss, draw) has not been studied well. In this study, we have developed a Player Impact Metric (PIM) that provides a more comprehensive and data-driven assessment of player performance by incorporating match event data, Expected Goals (xG), Expected Threat (xT), and defensive contributions. The PIM framework assigns weighted scores to player actions using ordinal logistic regression based on their influence on match outcomes. The model evaluates player contributions using event-level data, integrating both offensive and defensive actions. The dataset is sourced from WhoScored, with structured data processing in PostgreSQL and analytical modeling techniques applied to derive impact scores. The PIM was tested against WhoScored Ratings, revealing notable differences in player rankings, particularly for defensive players. Our findings show that PIM provides a more balanced assessment, capturing critical non-scoring contributions that traditional rating systems tend to undervalue. We have introduced PIM as an advanced evaluation metric for football analytics, offering a data-driven, context-aware, and holistic approach to player performance assessment in this study. We show that the PIM can serve as a valuable tool for coaches, analysts, and scouts, enabling more accurate talent identification and match analysis.

由于现有评级模型的局限性，以及游戏中行动的多样性及其对比赛结果的不同影响，足球运动员的评估仍然是一项具有挑战性的任务，这些模型往往强调进攻行动，而忽略了关键的防守和战略贡献。虽然足球中存在一些球员影响指标，但它们的有效性、完整的深度分析以及与比赛结果（赢、输、平）的关系还没有得到很好的研究。在这项研究中，我们开发了一个球员影响指标（PIM），通过结合比赛数据，预期进球（xG），预期威胁（xT）和防守贡献，提供了一个更全面和数据驱动的球员表现评估。PIM框架根据玩家行为对比赛结果的影响，使用有序逻辑回归为玩家行为分配加权分数。该模型使用事件级数据评估玩家的贡献，整合了进攻和防守行动。数据集来自whoscoscore，采用PostgreSQL结构化数据处理和分析建模技术来获得影响评分。PIM与whoscoscore评分进行了测试，揭示了球员排名的显著差异，尤其是防守球员。我们的研究结果表明，PIM提供了一个更平衡的评估，捕获了传统评级系统往往低估的关键非评分贡献。在本研究中，我们将PIM作为足球分析的高级评估指标，为球员表现评估提供了一种数据驱动、情境感知和整体的方法。我们表明PIM可以作为教练、分析师和球探的宝贵工具，实现更准确的人才识别和比赛分析。

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引用次数: 0

Exploring singularities in data with the graph Laplacian: An explicit approach 利用图拉普拉奇探索数据中的奇点：一种明确的方法

Journal of Computational Mathematics and Data Science

Pub Date : 2025-03-01 DOI: 10.1016/j.jcmds.2025.100113

Martin Andersson, Benny Avelin

We develop theory and methods that use the graph Laplacian to analyze the geometry of the underlying manifolds of datasets. Our theory provides theoretical guarantees and explicit bounds on the functional forms of the graph Laplacian when it acts on functions defined close to singularities of the underlying manifold. We use these explicit bounds to develop tests for singularities and propose methods that can be used to estimate geometric properties of singularities in the datasets.

我们发展的理论和方法，使用图拉普拉斯来分析数据集的底层流形的几何。我们的理论提供了图拉普拉斯函数的函数形式的理论保证和明确的界，当它作用于定义在底层流形的奇点附近的函数时。我们使用这些显式界限来开发奇点的测试，并提出可用于估计数据集中奇点几何性质的方法。

引用次数: 0

Penalizing Low-Rank Matrix Factorization: From theoretical connections to practical applications 惩罚低秩矩阵分解：从理论联系到实际应用

Journal of Computational Mathematics and Data Science

Pub Date : 2025-02-22 DOI: 10.1016/j.jcmds.2025.100111

Nicoletta Del Buono , Flavia Esposito , Laura Selicato

Low-rank (LR) factorization techniques aim to represent data in a low-dimensional space by identifying fundamental sources. Standard LR approaches often require additional constraints to account for real-world complexity, resulting in penalized low-rank matrix factorizations. These techniques incorporate penalties or regularization terms to improve robustness and adaptability to practical constraints, bridging theoretical research with real-world applications.

This paper explores a nonnegative constrained low-rank decomposition technique, namely, Nonnegative Matrix Factorization (NMF), and its constrained variants as powerful tools for analyzing nonnegative data. We cover theoretical foundations and practical implementations, review algorithms for standard NMF, and address challenges in setting hyperparameters for penalized variants. We emphasize applications in omics data analysis with a model that incorporates biological constraints to extract meaningful insights, and highlight applications in environmental data analysis.

低秩（LR）分解技术旨在通过识别基本来源来表示低维空间中的数据。标准LR方法通常需要额外的约束来考虑现实世界的复杂性，从而导致惩罚的低秩矩阵分解。这些技术包含惩罚或正则化术语，以提高鲁棒性和对实际约束的适应性，将理论研究与实际应用联系起来。本文探讨了一种非负约束低秩分解技术，即非负矩阵分解（NMF）及其约束变体作为分析非负数据的有力工具。我们涵盖了理论基础和实际实现，回顾了标准NMF的算法，并解决了为惩罚变量设置超参数的挑战。我们强调在组学数据分析中的应用，该模型包含生物约束以提取有意义的见解，并强调在环境数据分析中的应用。

引用次数: 0

Directional node strength entropy centrality: Ranking influential nodes in complex networks 定向节点强度熵中心性：复杂网络中影响节点排序

Journal of Computational Mathematics and Data Science

Pub Date : 2025-02-18 DOI: 10.1016/j.jcmds.2025.100112

Giridhar Maji

Identifying influential spreaders within a network is an important research area. Existing centrality metrics have limitations of either performing well on certain networks, but being computationally demanding, or having lower resolution in ranking. Also, most of the earlier studies ignore the directional and weighted aspect of a(n) relationship/edge that we exploit in the present study. In the real world, the relationships and influences between entities are often not symmetric. For example, a charismatic individual may have a significant impact on a common citizen, while the reverse may not be true. We propose a new approach called Directional Node Strength Entropy (DNSE), a topology-based method to identify critical nodes in an undirected network that can maximize spreading influence. An important neighbor exerts more influence on a node than it exerts back to that neighbor if its own importance is less than the neighbor. Our premise is that the strengths of network edges (connections) are directional and this strength depends on the importance of the starting node. We assign potential weights to the edges and use the degree of a node as a proxy for its importance. Directional node entropy across the neighborhood is used to rank the nodes. We conducted an extensive evaluation on real-world networks from various domains. We compared the proposed DNSE method against similar topology-based methods using Kendall’s rank correlation, ranking uniqueness, ccdf, and spreading influence, utilizing the SIR model as the benchmark. Results show that the proposed DNSE demonstrates superior or at-par performance compared to the state-of-the-art.

识别网络中有影响力的传播者是一个重要的研究领域。现有的中心性指标存在局限性，要么在某些网络上表现良好，但计算要求很高，要么在排名中分辨率较低。此外，大多数早期的研究忽略了我们在本研究中利用的(n)关系/边缘的方向和加权方面。在现实世界中，实体之间的关系和影响往往不是对称的。例如，一个有魅力的人可能会对一个普通公民产生重大影响，而反之则可能不成立。我们提出了一种称为定向节点强度熵（DNSE）的新方法，这是一种基于拓扑的方法，用于识别无向网络中可以最大化传播影响的关键节点。一个重要的邻居对一个节点施加的影响大于当它自己的重要性小于该邻居时它对该邻居施加的影响。我们的前提是网络边（连接）的强度是有方向性的，这种强度取决于起始节点的重要性。我们为边缘分配潜在的权重，并使用节点的程度作为其重要性的代理。通过邻域的定向节点熵对节点进行排序。我们对来自不同领域的真实网络进行了广泛的评估。我们将提出的DNSE方法与类似的基于拓扑的方法进行了比较，使用Kendall的秩相关、排序唯一性、ccdf和传播影响，并以SIR模型为基准。结果表明，与最先进的DNSE相比，所提出的DNSE表现出优越或同等的性能。

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引用次数: 0

Data-driven ambiguous cognitive map for complex decision-making in supply chain management 数据驱动的供应链复杂决策模糊认知图

Journal of Computational Mathematics and Data Science

Pub Date : 2025-02-13 DOI: 10.1016/j.jcmds.2025.100110

Pritpal Singh

Fuzzy cognitive maps (FCMs) have the potential to model complex systems, but they face challenges in uncertainty, complexity, and dynamic conditions. This study tackles three main issues: modeling and quantifying uncertainty in relationships and weights with imprecise inputs, managing the complexity as the number of activation levels and causal relationships increases, and determining appropriate weights and thresholds in uncertain contexts. By using ambiguous set theory, the research introduces the ambiguous cognitive map (ACM) to improve the traditional FCM and address these problems. This theory allows for the representation of states with four membership values: true, false, partially true, and partially false, which provides a more refined approach to managing uncertainty. Mathematical formulas are employed by ACM to calculate weights based on these membership values instead of randomly selecting. The introduction of rank allows for the identification of the most influential state by its highest rank in priority decisions. The application of ACM in decision-making scenarios related to the supply chain system demonstrates its efficiency in systematically prioritizing and resolving complex decisions. The ACM effectively identifies key variables and provides actionable rankings to support decision-making in the supply chain system. The results demonstrate that ACM offers a systematic approach to resolving complex decisions under uncertainty.

Impact Statement ACMs replace the conventional random assignment of relationship weights with a mathematical formulation based on the four membership values, enhancing the accuracy and reliability of the modeled system. The study also introduces a rank-based decision-making process, where the most influential state is determined by the highest rank derived from the membership values. The proposed ACM framework not only addresses the limitations of traditional FCMs but also opens new avenues for artificial intelligence (AI)-driven analysis of complex, uncertain systems.

模糊认知图（fcm）具有模拟复杂系统的潜力，但在不确定性、复杂性和动态条件下面临挑战。本研究解决了三个主要问题：不精确输入的关系和权重的不确定性建模和量化，随着激活水平和因果关系数量的增加而管理复杂性，以及在不确定环境中确定适当的权重和阈值。本研究利用模糊集合理论，引入模糊认知图（ACM）来改进传统的FCM，解决这些问题。该理论允许用四个成员值表示状态：真、假、部分真和部分假，这为管理不确定性提供了更精细的方法。ACM采用数学公式来计算基于这些隶属度值的权重，而不是随机选择。排名的引入允许根据其在优先决策中的最高排名来确定最具影响力的国家。ACM在与供应链系统相关的决策场景中的应用证明了它在系统地确定优先级和解决复杂决策方面的效率。ACM有效地识别关键变量，并提供可操作的排名，以支持供应链系统中的决策。结果表明，ACM提供了一种系统的方法来解决不确定性下的复杂决策。影响陈述模型用基于四个隶属度值的数学公式取代了传统的随机分配关系权重的方法，提高了建模系统的准确性和可靠性。该研究还引入了基于排名的决策过程，其中最具影响力的国家由成员值得出的最高排名确定。提出的ACM框架不仅解决了传统fcm的局限性，而且为人工智能（AI）驱动的复杂、不确定系统的分析开辟了新的途径。

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引用次数: 0

Modified least squares ratio estimator for autocorrelated data: Estimation and prediction 自相关数据的修正最小二乘比值估计：估计与预测

Journal of Computational Mathematics and Data Science

Pub Date : 2025-02-07 DOI: 10.1016/j.jcmds.2025.100109

Satyanarayana Poojari, Sachin Acharya, Varun Kumar S.G., Vinitha Serrao

Autocorrelated errors in regression models make ordinary least squares (OLS) estimators inefficient, potentially leading to the misinterpretation of test procedures. Generalized least squares (GLS) estimation is a more efficient approach than OLS in the presence of autocorrelated errors. The GLS estimators based on Cochrane–Orcutt (COR) and Hildreth–Lu (HU) methods are the most commonly used to estimate unknown model parameters. This study investigates the impact of autocorrelation on parameter estimation and prediction in regression models and introduces a novel approach to address the challenge possessed by autocorrelated errors. In this paper, two modified GLS estimators based on the least square ratio method are proposed namely the Least Square Ratio-Cochrane–Orcutt Estimator (LSRE-COR) estimator and the Least Square Ratio-Hildreth–Lu (LSRE-HU) estimator. A Monte Carlo simulation study is carried out to compare the performance of the proposed estimators with OLS, COR, HU, maximum likelihood estimator (MLE), and least square ratio estimator (LSRE) based on total mean square error (TMSE) and root mean square error (RMSE). The results show that the proposed LSRE-HU and LSRE-COR consistently outperform all other estimators across various levels of autocorrelation and numbers of regressors for moderately large samples. The effectiveness of these methods is illustrated through real-life applications.

回归模型中的自相关误差使普通最小二乘（OLS）估计器效率低下，潜在地导致对测试过程的误解。在存在自相关误差的情况下，广义最小二乘（GLS）估计比OLS估计更有效。基于Cochrane-Orcutt （COR）和Hildreth-Lu （HU）方法的GLS估计器是最常用的未知模型参数估计方法。本文研究了自相关对回归模型参数估计和预测的影响，并引入了一种新的方法来解决自相关误差所带来的挑战。本文提出了基于最小二乘比值法的两个改进的GLS估计量，即最小二乘比值- cochrane - orcut估计量（LSRE-COR）和最小二乘比值- hildreth - lu估计量（LSRE-HU）。通过蒙特卡罗仿真研究，比较了基于总均方误差（TMSE）和均方根误差（RMSE）的估计器与OLS、COR、HU、最大似然估计器（MLE）和最小二乘比值估计器（LSRE）的性能。结果表明，对于中等规模的样本，所提出的LSRE-HU和LSRE-COR在各种自相关水平和回归量数量上始终优于所有其他估计器。通过实际应用说明了这些方法的有效性。

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引用次数: 0