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hyperparameter optimization of orthogonal functions in the numerical solution of differential equations

MATHEMATICAL METHODS IN THE APPLIED SCIENCES 2025年第1期48卷 605-625页

作者： Aghaei, Alireza Afzal Parand, Kourosh Shahid Beheshti Univ Fac Math Sci Dept Comp & Data Sci Tehran Iran Shahid Beheshti Univ Inst Cognit & Brain Sci Dept Cognit Modeling Tehran Iran

Numerical methods for solving differential equations often rely on the expansion of the approximate solution using basis functions. The choice of an appropriate basis function plays a crucial role in enhancing the accuracy of the solution. In this study, our aim is to develop algorithms that can identify an optimal basis function for any given differential equation. To achieve this, we explore fractional rational Jacobi functions as a versatile basis, incorporating hyperparameters related to rational mappings, Jacobi polynomial parameters, and fractional components. Our research develops hyperparameter optimization algorithms, including parallel grid search, parallel random search, Bayesian optimization, and parallel genetic algorithms. To evaluate the impact of each hyperparameter on the accuracy of the solution, we analyze two benchmark problems on a semi-infinite domain: Volterra's population model and Kidder's equation. We achieve improved convergence and accuracy by judiciously constraining the ranges of the hyperparameters through a combination of random search and genetic algorithms. Notably, our findings demonstrate that the genetic algorithm consistently outperforms other approaches, yielding superior hyperparameter values that significantly enhance the quality of the solution, surpassing state-of-the-art results.

关键词： hyperparameter optimization Jacobi polynomials machine learning nonlinear differential equations

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hyperparameter optimization in Generative Adversarial Networks (GANs) Using Gaussian AHP

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IEEE ACCESS 2025年 13卷 770-788页

作者： Rodrigues, Thiago Serafim Pinheiro, Placido Rogerio Univ Fortaleza Grad Program Appl Informat BR-60811905 Fortaleza Brazil

This study explores optimizing hyperparameters in Generative Adversarial Networks (GANs) using the Gaussian Analytical Hierarchy Process (Gaussian AHP). By integrating machine learning techniques and multi-criteria decision methods, the aim is to enhance the performance and efficiency of GAN models. It trains GAN models using the Fashion MNIST dataset. It applies Gaussian AHP to optimize hyperparameters based on multiple performance criteria, such as the quality of generated images, training stability, and training time. Iterative experiments validate the methodology by automatically adjusting hyperparameters based on the obtained scores, thereby maximizing the model's efficiency and quality. Results indicate significant improvements in image generation quality and computational efficiency. The study highlights the effectiveness of combining Gaussian AHP with GANs for systematic hyperparameter optimization, providing insights into achieving higher performance in image generation tasks. Future research could extend this approach to other neural network architectures and diverse datasets, further demonstrating the versatility of this optimization technique. This method's potential applications extend across various domains, including data augmentation and anomaly detection, indicating its broad applicability and impact.

关键词： Training hyperparameter optimization Generative adversarial networks optimization Computational modeling Bayes methods Scalability Analytic hierarchy process Load modeling Iterative methods hyperparameter optimization gaussian analytical hierarchy process multicriteria decision-making machine learning

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hyperparameter optimization of apple leaf dataset for the disease recognition based on the YOLOv8

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JOURNAL OF AGRICULTURE AND FOOD RESEARCH 2025年 21卷

作者： Lee, Yong-Suk Patil, Maheshkumar Prakash Kim, Jeong Gyu Seo, Yong Bae Ahn, Dong-Hyun Kim, Gun-Do Pukyong Natl Univ Inst Food Sci Dept Food Sci & Technol Busan 48513 South Korea Pukyong Natl Univ Ind Univ Cooperat Fdn Busan 48513 South Korea Pukyong Natl Univ Dept Microbiol Busan 48513 South Korea

Apple leaf diseases have a major influence on apple productivity and quality, demanding a precise and efficient recognition system. Using the YOLOv8 family of object detection models, we created a disease recognition model for the apple leaf dataset in this study. The developed model was fine-tuned extensively by hyperparameter optimization to identify the best variant for practical deployment. Firstly, fine-tuning with different YOLOv8 series was conducted on an apple leaf dataset including various types of images. Among them, the YOLOv8s demonstrated the best balance with a fitness of 0.97171, a precision of 0.97082, a recall of 0.96837, a mAP@0.5 of 0.98016, and an image processing speed of 1.58 ms. Further hyperparameter optimization was conducted using the One-Factor-At-a-Time (OFAT) and Random Search (RS) methods. In this case, the optimal settings determined as per the OFAT method were a batch size of 48, a learning rate of 0.01, a weight decay of 0.0005, a momentum of 0.963, and 200 epochs. These settings were adopted as the baseline for RS. RS then searched for 50 additional configurations;the best configuration, C34 (batch size of 48, learning rate of 0.0137, momentum of 0.9433, and weight decay of 0.0009), achieved a fitness score of 0.97688, a precision of 0.97797, a recall of 0.97295, and a mAP@0.5 of 0.98257. The correlation analysis showed that learning rate and momentum significantly impacted the performance of the models. Overall, the C34 model demonstrates high accuracy, rapid processing speed, and robustness suitable for training real-time, large-scale apple leaf disease recognition.

关键词： Apple leaf disease YOLOv8 hyperparameter optimization One-factor-at-a-time Random search

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Penalty hyperparameter optimization with diversity measure for nonnegative low-rank approximation

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APPLIED NUMERICAL MATHEMATICS 2025年 208卷 189-204页

作者： Del Buono, Nicoletta Esposito, Flavia Selicato, Laura Zdunek, Rafal Univ Bari Aldo Moro Dept Math Via Orabona 4 I-70125 Bari Italy Natl Res Council IRSA CNR Water Res Inst Vle Francesco Blasio 5 I-70132 Bari Italy Wroclaw Univ Sci & Technol Fac Elect Photon & Microsyst 27 Wybrzeze Wyspianskiego St PL-50370 Wroclaw Poland

Learning tasks are often based on penalized optimization problems in which a sparse solution is desired. This can lead to more interpretative results by identifying a smaller subset of important features or components and reducing the dimensionality of the data representation, as well. In this study, we propose a new method to solve a constrained Frobenius norm-based nonnegative low- rank approximation, and the tuning of the associated penalty hyperparameter, simultaneously. The penalty term added is a particular diversity measure that is more effective for sparseness purposes than other classical norm-based penalties (i.e., 81 or 8 2,1 norms). As it is well known, setting the hyperparameters of an algorithm is not an easy task. Our work drew on developing an optimization method and the corresponding algorithm that simultaneously solves the sparsity-constrained nonnegative approximation problem and optimizes its associated penalty hyperparameters. We test the proposed method by numerical experiments and show its promising results on several synthetic and real datasets.

关键词： hyperparameter optimization Penalty coefficient Sparseness Low-rank approximation

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MetaGen: A framework for metaheuristic development and hyperparameter optimization in machine and deep learning

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NEUROCOMPUTING 2025年 637卷

作者： Gutierrez-aviles, David Jimenez-navarro, Manuel Jesus Torres, Jose Francisco Martinez-Alvarez, Francisco Univ Seville Dept Comp Sci ES-41012 Seville Spain Pablo de Olavide Univ Data Sci & Big Data Lab ES-41013 Seville Spain

hyperparameter optimization is a pivotal step in enhancing model performance within machine learning. Traditionally, this challenge is addressed through metaheuristics, which efficiently explore large search spaces to uncover optimal solutions. However, implementing these techniques can be complex without adequate development tools, which is the primary focus of this paper. Hence, we introduce MetaGen, a novel Python package designed to provide a comprehensive framework for developing and evaluating metaheuristic algorithms. MetaGen follows best practices in Python design, ensuring minimalistic code implementation, intuitive comprehension, and full flexibility in solution representation. The package defines two distinct user roles: Developers, responsible for algorithm implementation for hyperparameter optimization, and Solvers, who leverage pre-implemented metaheuristics to address optimization problems. Beyond algorithm implementation, MetaGen facilitates benchmarking through built-in test functions, ensuring standardized performance comparisons. It also provides automated reporting and visualization tools to analyze optimization progress and outcomes effectively. Furthermore, its modular design allows distribution and integration into existing machine learning workflows. Several illustrative use cases are presented to demonstrate its adaptability and efficacy. The package, along with code, a user manual, and supplementary materials, is available at: https://***/Data-Science-Big-Data-Research-Lab/MetaGen.

关键词： Metaheuristics hyperparameter optimization Machine learning Deep learning Python

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A Novel hyperparameter optimization Approach for Supervised Classification: Phase Prediction of Multi-Principal Element Alloys

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COGNITIVE COMPUTATION 2025年第1期17卷 1-14页

作者： Fatimi, Syed Hassan Wang, Zidong Chang, Isaac T. H. Liu, Weibo Liu, Xiaohui Brunel Univ London Dept Comp Sci Uxbridge UB8 3PH Middlesex England Brunel Univ London Brunel Ctr Adv Solidificat Technol BCAST Uxbridge UB8 3PH Middlesex England

In this paper, a hyperparameter optimization approach is proposed for the phase prediction of multi-principal element alloys (MPEAs) through the introduction of two novel hyperparameters: outlier detection and feature subset selection. To gain a deeper understanding of the connection between alloy phases and their elemental properties, an artificial neural network is employed, with hyperparameter optimization performed using a genetic algorithm to select the optimum hyperparameters. The two novel hyperparameters, outlier detection and feature subset selection, are introduced within the optimization framework, along with new crossover and mutation operators for handling single and multi-valued genes simultaneously. Ablation studies are conducted, illustrating an improvement in prediction accuracy with the inclusion of these new hyperparameters. A comparison with five existing algorithms in multi-class classification is made, demonstrating an improvement in the performance of phase prediction, thereby providing a better perception of the alloy phase space for high-throughput MPEA design.

关键词： hyperparameter optimization Outlier detection Feature selection Artificial neural networks Genetic algorithm Multi-principal element alloys

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Least Squares Support Vector Machines With Variable Selection and hyperparameter optimization for Complex Structures Reliability Assessment

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QUALITY AND RELIABILITY ENGINEERING INTERNATIONAL 2025年第0期 1461-1470页

作者： Dong, Xiaowei Zhang, Hao Li, Zhenao Zhu, Chunyan Yi, Shujuan Chen, Changhai Heilongjiang Bayi Agr Univ Sch Engn Daqing Heilongjiang Peoples R China Minist Agr & Rural Affairs Inspect & Test Ctr Agr Prod & Processed Prod Qual Daqing Heilongjiang Peoples R China Heilongjiang Bayi Agr Univ Coll Elect & Informat Daqing Heilongjiang Peoples R China Harbin Acad Agr Sci Harbin Heilongjiang Peoples R China

For effectively estimating the reliability of complex structures, a least squares support vector machine with variable selection and hyperparameter optimization (SVMSO, short for) is proposed based on local linear embedding with Pearson coefficient and location density with particle swarm optimization (LDPSO) algorithm. In this proposed method, the local linear embedding with Pearson coefficient is used to select the variables that have a strong correlation with output responses, which are embedded in relatively low-dimensional space to avoid the negative influence of high-dimensional input parameters. The optimal hyperparameters of least squares support vector machines (LSSVM) are obtained by applying the LDPSO to improve the accuracy of LSSVM affected by the hyperparameters. Taking civil aircraft turbine blisk as a study case, the effectiveness and applicability of SVMSO are verified in aspects of modeling quality and simulation characteristics, by comparing direct simulation, support vector machine, and LSSVM. The case results and conclusions represent that the proposed method has good precision and efficiency under a high-dimensional data scale, and is suitable for reliability analysis of complex structures.

关键词： hyperparameter optimization least squares support vector machines reliability analysis turbine blisk variable selection

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Sound absorption performance prediction of multi-dimensional Helmholtz resonators based on deep learning and hyperparameter optimization

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PHYSICA SCRIPTA 2025年第2期100卷 026013-026013页

作者： Liu, Yan Hang, Yin Li, Qiutong Shanghai Res Inst Mat Co Ltd Acoust Metamat Lab Shanghai 200437 Peoples R China Shanghai Res Inst Mat Ltd Shanghai Key Lab Engn Mat Applicat & Evaluat Shanghai 200437 Peoples R China Shanghai Polytech Univ Sch Energy & Mat Shanghai 201209 Peoples R China

The problem of low-frequency noise is becoming increasingly severe and measuring the sound absorption performance of acoustic metamaterials (AMs) using accurate absorption coefficients is of great interest in low-frequency noise control engineering. Conventional calculation methods such as Finite Element Method (FEM) simulations and the theoretical analysis methods (TAM) have specific limitations. Deep learning (DL) models provide new perspectives for studying AMs acoustic performance. However, the prediction performance of DL models is highly dependent on the proper tuning of hyperparameters. As far as is known, existing literature has not systematically explored the impact of hyperparameter tuning on DL models in the context of acoustic performance studies. The present paper designed a multi-dimensional Helmholtz resonator (MDHR) consisting of a 4 x 4-type continuous parallel arrangement, while a dataset was established via FEM. Furthermore, a deep neural network (HPO-DNNs) model based on hyperparameter optimization (HPO) was proposed to predict the acoustic performance of the MDHR. Random search (RS), Bayesian optimization (BO), Simulated annealing (SA), and genetic algorithm (GA) were introduced to optimize the hyperparameters (learning rate, weight decay, optimizer, and batch size) of the DNNs. The mean square error (MSE), coefficient of determination (R2) of the testing dataset and the optimization time were used as the evaluation metrics, GA was selected for further study based on the comparison results (MSE = 0.00177, R2 = 0.98151) of the optimization efficiency and predictive precision of DNNs from the four HPO algorithms. Finally, the prediction performance of the GA-DNNs model was evaluated in single-, multi-, and broadband conditions in practical applications, demonstrating high precision and stability and providing a new approach for acoustics performance studies.

关键词： helmholtz resonator deep learning hyperparameter optimization

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An improved decision tree model through hyperparameter optimization using a modified gray wolf optimization for diabetes classification

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COMPUTER METHODS IN BIOMECHANICS AND BIOMEDICAL ENGINEERING 2025年 1-17页

作者： Sam'an, Muhammad Farikhin, Muhammad Munsarif, Muhammad Univ Muhammadiyah Semarang Dept Informat Semarang Indonesia Univ Muhammadiyah Malaysia Fac Business Management & Informat Technol Semarang Malaysia Univ Diponegoro Dept Math Semarang Indonesia

Diabetes is a chronic condition that affects blood sugar levels and vital organs in the body. Early detection is crucial given the increasing global prevalence of diabetes and the grave risk of complications if not properly managed. Thus, a good prediction system is necessary. Although the Decision Tree (DT) is commonly used for classification, it is less effective with large datasets. We propose hyperparameter optimization of the DT using the Grey Wolf optimization (GWO), which has exploration and both exploitation capabilities. However, the limited search space of GWO may hinder practical exploration and exploitation, leading to premature optimization. To address this, we propose a modified GWO (MGWO) by adding the Levy distribution function to enhance the movements of alpha, beta, and delta wolves. We also provide GA (Genetic Algorithm) as a comparative algorithm. The fitness value of MGWO is 0.8498, surpassing GWO (0.8373) and GA (0.8492). Evaluation results indicate that MGWO and GA yield similar and superior accuracy compared to GWO. The proposed method outperforms existing ones. Further research is needed to evaluate the impact of varying the number of wolves on optimization performance and classification accuracy.

关键词： Diabetes decision tree hyperparameter optimization grey wolf optimization classification

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Improving the robustness of tree-based prediction model of oil/water relative permeability through hyperparameter optimization and re-ensemble algorithm

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FUEL 2025年 385卷

作者： Wu, Dongwei Xue, Xinhua Zhou, Lei Sichuan Univ Coll Architecture & Environm State Key Lab Intelligent Construct & Hlth Operat Chengdu 610065 Peoples R China Sichuan Univ Coll Water Resource & Hydropower Chengdu 610065 Peoples R China

In petroleum engineering, accurate prediction of the oil and water relative permeability is vital for increasing production rates, reducing extraction costs, etc. This study utilizes tree-based models to build prediction models of oil/water permeability at different temperatures. To further improve the performance of the prediction model, a two-step combining hyperparameter optimization and re-ensemble algorithms is adopted. Five metrics (i.e. R-square (R2), Mean Absolute Error (MAE), Root Mean Square Error (RMSE), Root Mean Squared Logarithmic Error ( RMSLE ) and Logarithmic Discrepancy Ratio (LDR)) are adopted for model performance evaluation. Results indicate the two-step model significantly improves the performance of the model;the mean values of MAE decrease 38.67% and 72.48% for oil and water prediction, respectively. The mean values of RMSE decrease 41.05% and 77.77% for oil and water prediction respectively. This study provides a convenient and economical method to predict oil/water relative permeability rapidly.

关键词： Permeability prediction Oil-water two phases Tree-based model hyperparameter optimization Re-ensemble algorithm SHapley additive exPlanations (SHAP)

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