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Recurrent Neural Networks for Efficient Solutions to Time-Series Forecasting in Complex Mathematical Models

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Recurrent Neural Networks for Efficient Solutions to Time-Se...

Smart Systems for applications in Electrical Sciences (ICSSES), International Conference on

作者： B Uppalaiah Anjum Ara Ahmad A. Annie Lotus Abdul Hameed Al-Shammari Sharmeen Izzat Hassan Dhaaraani R Department of Mathematics Hyderabad Institute of Technology and Management Hyderabad India Department of Statistics Rizvi College of Arts Science & Commerce Mumbai Maharashtra India Department of Mathematics Sona College of Technology Salem India Uruk University Baghdad Iraq Department of Computer Engineering College of Engineering Knowledge University Erbil Iraq Department of AI & DS K. Ramakrishnan College of Engineering Trichy Tamil Nadu India

ISBN: (数字)9798331507671

ISBN: (纸本)9798331507688

Time series Forecasting plays a major role mainly in areas including finance, health, and meteorology. Although, classical forecast methods, including ARIMA models and feedforward neural networks, fail at capturing long-term information and non-linear interactions in temporal systems. This paper explores the application of LSTM networks in improving forecasting accuracy while overcoming the limitations of traditional methods. The contribution of this work is in applying of LSTM models into complex mathematical frameworks capable to work with time-series data with minimal efforts required in feature engineering. A plan of the proposed framework is as follows: LSTM model training on the given time-series data and comparison with ARIMA and feedforward neural networks that leads to the comparison of results based on performance metrics like MAE, RMSE and MAPE. Overall, out of all analysed methods, LSTM model provides the lowest values of mean absolute error equal to 8.12, root mean squared error equal to 10.23 and mean absolute percentage error equal to 5.29 % which proves how good it was in dealing with data which contains relations with a more non-linear nature and experiencing long dependencies. Such results suggest that LSTMs are significantly superior to traditional approaches as a new method of time-series analysis and forecasting for complex systems. It is important to discuss the advantages of LSTM based on the aspect of the capability of being scaled and trainable when it comes to time-series forecasting and its demanding computation resource and training data.

关键词： Training Recurrent neural networks Time series analysis Weather forecasting Training data Mathematical models Data models Feedforward neural networks Forecasting Long short term memory

Radiative heat transfer in MHD copper-based polymer nanofluid over a sphere using larger radius and inter particle spacing of nanoparticles

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Results in engineering 2025年 26卷

作者： Darvesh, Adil Boukhris, Imed Collantes Santisteban, Luis Jaime Al-Buriahi, M.S. Elqahtani, Zainab Mufarreh Akgül, Ali García, Lucerito Katherine Ortiz Hassani, Murad Khan Department of Mathematics and Statistics Hazara University Mansehra21300 Pakistan Department of Physics Faculty of Science King Khalid University P.O. Box 960 Abha Saudi Arabia Department of Mathematics Universidad Nacional Pedro Ruiz Gallo Lambayeque Peru Department of Physics Sakarya University Sakarya Turkey Department of Physics College of science Princess Nourah bint Abdulrahman University P.O. Box 84428 Riyadh11671 Saudi Arabia Department of Electronics and Communication Engineering Saveetha School of Engineering SIMATS Tamilnadu Chennai India Siirt University Art and Science Faculty Department of Mathematics Siirt56100 Turkey Department of Computer Engineering Biruni University Topkapı Istanbul34010 Turkey Near East University Mathematics Research Center Department of Mathematics Near East Boulevard PC: 99138 Nicosia Mersin 10 Turkey Applied Science Research Center. Applied Science Private University Amman Jordan Universidad Nacional Pedro Ruiz Gallo Lambayeque Peru Ghazni University Department of Mathematics Afghanistan

The impact of nanoparticle size and interparticles spacing play a crucial role in fluid theology due to its significance on enhance heat transfer performance, which is crucial in many engineering and industrial processes particularly in thermal management systems. Due to this attention, the proposed study aims to explore the influence of nanoparticle radius and inter-particle spacing on thermal transport in a Copper (Cu) Polymer nanofluid over a sphere with radiative and magnetohydrodynamic (MHD) effects. Physical model incorporates Carreau fluid viscosity model. In addition, with incorporation of exponential heat generation and thermal radiation, the analysis reveals how tuning nanoparticle geometry significantly enhances heat transfer performance, which is critical for advanced thermal management systems. The governing nonlinear partial differential equations (PDEs) are transformed into ordinary differential equations (ODEs) using similarity transformations and solved using the well-known bvp4c computational method. Results of proposed study indicate that larger nanoparticles and wider inter-particle spacing improve thermophysical and rheological behavior of fluid specifically thermal conductivity and fluid viscosity, which enhanced heat transport and intensified the temperature profile. Conversely, velocity profile decreases for smaller particle sizes and spacing but improves with increased nanoparticle dimensions. © 2025 The Author(s)

关键词： Radiant heating

Revealing Actual Viscoelastic Relaxation Times in Capillary Breakup

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arXiv 2025年

作者： Hu, Nan Hwang, Jonghyun Ruangkriengsin, Tachin Stone, Howard A. Department of Mechanical and Aerospace Engineering Princeton University NJ08544 United States Program in Applied and Computational Mathematics Princeton University NJ08544 United States

We use experiments and theory to elucidate the size effect in capillary breakup rheometry, where pre-stretching in the visco-capillary stage causes the apparent relaxation time to be consistently smaller than the actual value. We propose a method accounting for both the experimental size and the finite extensibility of polymers to extract the actual relaxation time. A phase diagram characterizes the expected measurement variability and delineates scaling law conditions. The results refine capillary breakup rheometry for viscoelastic fluids and advance the understanding of breakup dynamics across scales. Copyright © 2025, The Authors. All rights reserved.

关键词： Relaxation time

Taylor dispersion in variable-density, variable-viscosity pulsatile flows

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arXiv 2025年

作者： Rajamanickam, Prabakaran Weiss, Adam D. Department of Mathematics and Statistics University of Strathclyde GlasgowG1 1XQ United Kingdom ATA Engineering Inc. San Diego92128 United States

The phenomenon of Taylor or shear-induced dispersion of a non-passive scalar field in a pulsatile pipe flow is investigated, accounting for the scalar field’s influence on fluid density and transport coefficients. By employing multiple scale analysis, an effective one-dimensional, unsteady mixing problem for the scalar field is obtained, which includes the diffusion coefficient for shear-induced dispersion. The resulting governing equations are applicable to a range of scalar transport problems in pulsatile pipe flows. Copyright © 2025, The Authors. All rights reserved.

关键词： Pulsatile flow

ELFATT: Efficient Linear Fast Attention for Vision Transformers

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arXiv 2025年

作者： Wu, Chong Che, Maolin Xu, Renjie Ran, Zhuoheng Yan, Hong Department of Electrical Engineering Centre for Intelligent Multidimensional Data Analysis City University of Hong Kong Kowloon Hong Kong School of Mathematics and Statistics Guizhou University Guiyang550025 China

The attention mechanism is the key to the success of transformers in different machine learning tasks. However, the quadratic complexity with respect to the sequence length of the vanilla softmax-based attention mechanism becomes the major bottleneck for the application of long sequence tasks, such as vision tasks. Although various efficient linear attention mechanisms have been proposed, they need to sacrifice performance to achieve high efficiency. What’s more, memory-efficient methods, such as FlashAttention-1-3, still have quadratic computation complexity which can be further improved. In this paper, we propose a novel efficient linear fast attention (ELFATT) mechanism to achieve low memory input/output operations, linear computational complexity, and high performance at the same time. ELFATT offers 4-7x speedups over the vanilla softmax-based attention mechanism in high-resolution vision tasks without losing performance. ELFATT is FlashAttention friendly. Using FlashAttention-2 acceleration, ELFATT still offers 2-3x speedups over the vanilla softmax-based attention mechanism on high-resolution vision tasks without losing performance. Even on edge GPUs, ELFATT still offers 1.6x to 2.0x speedups compared to state-of-the-art attention mechanisms in various power modes from 5W to 60W. Furthermore, ELFATT can be used to enhance and accelerate diffusion tasks directly without training. Copyright © 2025, The Authors. All rights reserved.

关键词： Machine vision

A numerical treatment through Bayesian regularization neural network for the chickenpox disease model

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Computers in Biology and Medicine 2025年 187卷 109807-109807页

作者： Sabir, Zulqurnain Mehmood, Muhammad Athar Umar, Muhammad Salahshour, Soheil Altun, Yener Arbi, Adnène Ali, Mohamed R. Department of Mathematics and Statistics Hazara University Mansehra Pakistan Department of Mathematics University of Gujrat Pakistan Faculty of Engineering and Natural Sciences Istanbul Okan University Istanbul Turkey Faculty of Engineering and Natural Sciences Bahcesehir University Istanbul Turkey Faculty of Economics and Administrative Sciences Department of Business Administration Yuzuncu Yil University Van Turkey EPT University of Carthage Carthage Tunisia Faculty of Engineering Benha National University Obour Campus Egypt Basic Engineering Science Department Benha Faculty of Engineering Benha University Benha Egypt

Objectives: The current research investigations designates the numerical solutions of the chickenpox disease model by applying a proficient optimization framework based on the artificial neural network. The mathematical form of the chickenpox disease model is divided into different categories of individuals, susceptible, vaccinated, infected, exposed, recovered, and infected with/without complications. Method: The construction of neural network is performed by using the single hidden layer and the optimization of Bayesian regularization. A dataset is assembled using the explicit Runge-Kutta technique for reducing the mean square error using the training 76 %, while 12 %, 12 % for validation and testing. The whole stochastic procedure is based on logistic sigmoid fitness function, single hidden layer structure with thirty neurons, along with the optimization capability of Bayesian regularization. Finding: The designed procedure's correctness and reliability is observed by results matching, negligible absolute error around 10−04 to 10−06, regression, error histogram, and state transmission. Moreover, the best performance values based on the mean square error are performed as 10−09 to 10−11. Novelty: The current neural network framework using the construction of a single hidden layer and the optimization of Bayesian regularization is applied first time to solve the chickenpox disease model. © 2025 Elsevier Ltd

关键词： Neural network models

On modeling and forecasting the stock risk using a new statistical distribution and time series models

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Alexandria engineering Journal 2025年 122卷 65-76页

作者： Yan, Lelin Zhou, Weihong Odhah, Omalsad Hamood Widyan, Adel M. Khalifa, Hamiden Abd El-Wahed Alqahtani, Haifa College of Information Science and Engineering Qilu Normal University Jinan 250013 Shandong China Master of Social Work Party School of Hunan Provincial Committee of C.P.C Hunan Changsha 410006 China Department of Mathematical Sciences College of Science Princess Nourah bint Abdulrahman University P.O. Box 84428 Riyadh11671 Saudi Arabia Department of Mathematics College of Science Qassim University Buraydah51452 Saudi Arabia Department of Statistics and Business Analytics United Arab Emirates University Al Ain Abu Dhabi15551 United Arab Emirates

The value of probability distributions in reflecting practical events, especially in financial risk, is significant. The flexible Weibull extension distribution, recognized as a significant modification of the Weibull distribution, serves as a foundational distribution in our study. Thus, we present a new distribution known as the sine cosine flexible Weibull extension (SCFWE) distribution. We conduct a detailed study of the mathematical properties associated with the SCFWE distribution. We also detail the methodology for parameter estimation and present simulation studies that explore various combinations of parameter values. Furthermore, we analyze a practical data set that highlights the volatility of the financial market, thereby demonstrating the relevance of the SCFWE distribution within the financial sector. Furthermore, we use the traditional time series models such as the autoregressive (AR), autoregressive integrated moving average (ARIMA), and random walk for forecasting the stock volatility. Our findings show that ARIMA is the most accurate model having the lowest root mean squared error and mean absolute error, the AR performed poorly with the highest errors, while, the random walk showed moderate performance, but ARIMA emerged as the most reliable model for precise predictions. © 2025 The Authors

关键词： Flexible Weibull extension Sine function Cosine function Volatility Financial risk Time series models Statistical analysis Data set

ORIENTIFOLDS FOR F-THEORY ON K3 SURFACES

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arXiv 2025年

作者： Doran, Charles Malmendier, Andreas Méndez-Diez, Stefan Rosenberg, Jonathan Department of Mathematical and Statistical Sciences University of Alberta EdmontonABT6G 2G1 Canada Mathematics Program Bard College P.O. Box 5000 AnnandaleNY12504-5000 United States Mathematics and Statistics Department Utah State University LoganUT84322-3900 United States Department of Mathematics University of Maryland College ParkMD20742-4015 United States

We study F-theory orientifolds, starting with products of two elliptic curves, but focusing mostly on a family of K3 surfaces, lattice polarized by the rank-17 lattice h8i ☉ 2D8(−1), generalizing the family (to which it degenerates) of Kummer surfaces of products of two non-isogenous elliptic curves. After a thorough study of the complex geometry of this family and its elliptic fibrations, we proceed to study real structures on the K3 surfaces in the family which are equivariant with respect to an elliptic fibration. We also study the physics of the associated F-theory orientifolds with a particular focus on the impact of the real structure on the charge spectrum. We also study how these orientifolds degenerate to the case of isotrivial Kummer surface *** Codes 14J27 (Primary) 14J28, 14J81, 11F55, 19L47, 19L50, 81T30 (Secondary) Copyright © 2025, The Authors. All rights reserved.

关键词： Algebra

Evaluating efficiency in water and sewerage services: An integrated DEA approach with DOE and PCA

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Science of the Total Environment 2025年 959卷 178288页

作者： Pishini, Khodarahm Abdolazimi, Omid Shishebori, Davood Rezaee, Mustafa Jahangoshai Sepehrifar, Mohammad Department of Industrial Engineering Yazd University Yazd Iran Department of Industrial and Systems Engineering Mississippi State University Mississippi StateMS United States University of Quebec Montreal Canada Department of Industrial Engineering Urmia University of Technology Urmia Iran Department of Mathematics and Statistics Mississippi State University Mississippi StateMS United States

Evaluating the performance of service organizations like Water and Sewerage companies is essential for optimal operations, high-quality service, and cost efficiency. This paper introduces a model using data envelopment analysis (DEA) to assess the efficiency of operational units within such companies. The selection of key performance indicators is complicated by the numerous inputs and outputs, each affecting systems and activities differently. To enhance DEA model performance due to the imbalance between the number of inputs/outputs and the number of units under evaluation, this research integrates design of experiments (DOE) and principal component analysis (PCA) for variable screening and data reduction, creating new linear combinations with minimal information loss. These methods represent a new direction in handling numerous variables in DEA models. Addressing unit heterogeneity by removing environmental factors from inputs reduces research errors. A case study showed that some units can achieve high efficiency with fewer inputs and more valuable outputs. The findings offered managerial insights for informed decision-making and strategic planning, optimizing resources in line with the company's mission and vision. This methodology ultimately improves service reliability, customer satisfaction, and environmental sustainability. The graphical abstract has been simplified to enhance readability and focus on the primary methodological advances. It emphasizes the integration of PCA for dimensionality reduction, DOE for variable scereening, and DEA for efficiency evaluation. © 2024 The Authors

关键词： Customer satisfaction