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Journal articles on the topic 'Tanh Function'

Author: Grafiati

Published: 5 June 2025

Last updated: 2 August 2025

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1

Belete, Biazen Bezabeh, and Debasu Mengistu Abrham. "The effects of multiple layers feed-forward neural network transfer function in digital based ethiopian soil classification and moisture prediction." International Journal of Electrical and Computer Engineering (IJECE) 10, no. 4 (2020): 4073–79. https://doi.org/10.11591/ijece.v10i4.pp4073-4079.

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In the area of machine learning performance analysis is the major task in order to get a better performance both in training and testing model. In addition, performance analysis of machine learning techniques helps to identify how the machine is performing on the given input and also to find any improvements needed to make on the learning model. Feed-forward neural network (FFNN) has different area of applications, but the epoch convergences of the network differs from the usage of transfer function. In this study, to build the model for classification and moisture prediction of soil, rectifie

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2

CHEN, YONG, BIAO LI, and HONGQING ZHANG. "GENERALIZED RICCATI EQUATION EXPANSION METHOD AND ITS APPLICATION TO THE (2+1)-DIMENSIONAL BOUSSINESQ EQUATION." International Journal of Modern Physics C 14, no. 04 (2003): 471–82. http://dx.doi.org/10.1142/s0129183103004668.

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Based on the computerized symbolic system Maple and a Riccati equation, a new Riccati equation expansion method for constructing nontraveling wave and coefficient functions' soliton-like solutions is presented by a new general ansätz. The proposed method is more powerful than most of the existing tanh methods, the extended tanh-function method, the modified extended tanh-function method, and generalized hyperbolic-function method. By using the method, we not only successfully recovered the previously known formal solutions but could also construct new and more general formal solutions for some

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3

Gözükızıl, Ömer Faruk, Şamil Akçağıl, and Tuğba Aydemir. "Unification of all hyperbolic tangent function methods." Open Physics 14, no. 1 (2016): 524–41. http://dx.doi.org/10.1515/phys-2016-0051.

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AbstractOver the last twenty years, several “different” hyperbolic tangent function methods have been proposed to search solutions for nonlinear partial differential equations (NPDEs). The most common of these methods were the tanh-function method, the extended tanh-function method, the modified extended tanh-function method, and the complex tanh-function method. Besides the excellent sides of these methods, weaknesses and deficiencies of each method were encountered. The authors realized that they did not actually give “very different and comprehensive results”, and some of them are even unne

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Wafaa M. Taha, Abbas H. Kadhim, Raad A. Hameed, and M. S. M. Noorani. "New modified tanh-function method for nonlinear evolution equations." Tikrit Journal of Pure Science 21, no. 6 (2023): 187–91. http://dx.doi.org/10.25130/tjps.v21i6.1100.

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The aim of this paper is to calculate the Traveling waves solutions by using a new technique which is called modified tanh-function method, which are successfully performed to get analytical solutions for Korteweg-deVries (KdV)–Burgers’ equation and (2+1)-dimensional Calogero–Bogoyavlenskii–Schiff (CBS) equation. As a result, when the equation parameters are taken as special values, some new solitary wave solution are obtained. Moreover we find in this work that the modified tanh-function method give some new results which are easier and faster to compute by the help of a symbolic computation

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5

Wang, Xiaodong, Jianping Wu, Yazi Wang, and Can Chen. "Extended Tanh-Function Method and Its Applications in Nonlocal Complex mKdV Equations." Mathematics 10, no. 18 (2022): 3250. http://dx.doi.org/10.3390/math10183250.

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In order to construct the multiple traveling wave solutions of the nonlocal modified Korteweg de Vires (mKdV) equation, the modified tanh-function approach for local soliton equations is extended to a nonlocal complex mKdV equation. The central idea of this method is to use the solution of the Riccati equation to replace the tanh function in the tanh function (THF) method. As an application, we investigate a new traveling wave solution for the nonlocal complex mKdV equation of Ablowitz and Musslimani. Moreover, some exciting diagrams show the underlying dynamics of some given solutions.

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Xuan, Heng-Nong, and Biao Lia. "Symbolic Computation and Construction of Soliton-like Solutions of some Nonlinear Evolution Equations." Zeitschrift für Naturforschung A 58, no. 2-3 (2003): 167–75. http://dx.doi.org/10.1515/zna-2003-2-315.

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Based on the computerized symbolic computation system Maple and a Riccati equation, a new generalized Riccati equation expansion method for constructing non-travelling waves and coefficient functions’ soliton-like solutions of nonlinear evolution equations (NEEs) is presented by a general ansatz. Compared with most of the existing tanh methods, namely the extended tanh-function method, the modified extended tanh-function method and the generalized hyperbolic-function method, the proposed method is more powerful. By use of the method one can not only successfully recover the previously known fo

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Tarigan, Yuni Franciska br, Teddy Surya Gunawan, and B. Herawan Hayadi. "Combination Of SqueezeNet And Multilayer Backpropagation Algorithm In Hanacaraka Script Recognition." International Conference on Information Science and Technology Innovation (ICoSTEC) 2, no. 1 (2023): 163–70. http://dx.doi.org/10.35842/icostec.v2i1.56.

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Javanese script is one of Indonesia's cultural heritages that are increasingly rarely used today. The difficulty of recognizing the shapes of letters, let alone writing them, is the main obstacle in using the Hanacaraka script. This research offers an alternative to Hanacaraka script recognition using a combination of image feature extraction and machine learning, where we utilize a pre-trained SquzeeNet model and Multilayer Backpropagation algorithm. Of the 18 models built using ReLu, Sigmoid, and Tanh activation functions, we found that the Tanh activation function, using the combination of

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Pardede, Doughlas, Ichsan Firmansyah, Meli Handayani, Meisarah Riandini, and Rika Rosnelly. "COMPARISON OF MULTILAYER PERCEPTRON’S ACTIVATION AND OP-TIMIZATION FUNCTIONS IN CLASSIFICATION OF COVID-19 PATIENTS." JURTEKSI (Jurnal Teknologi dan Sistem Informasi) 8, no. 3 (2022): 271–78. http://dx.doi.org/10.33330/jurteksi.v8i3.1482.

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Abstract: Patient’s symptoms could be used as features in Covid-19 classification. Using multi layer perceptron, the classification uses data set that contains patient’s diagnosis which has Covid-19 symptoms dan processes the data set to see if the patient is Covid-19 positive or not. This paper compare four activation function such as identity, logistic, ReLu and tanh and combined them with optimizer such as L-BFGS-B, SGD and Adam. Using 5-fold and 10-fold cross validation technique to get the accuracy, F1, precision and recall values, the result that we get is that logistic function with L-B

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9

Yang, Zonghang, and Benny Y. C. Hon. "An Improved Modified Extended tanh-Function Method." Zeitschrift für Naturforschung A 61, no. 3-4 (2006): 103–15. http://dx.doi.org/10.1515/zna-2006-3-401.

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In this paper we further improve the modified extended tanh-function method to obtain new exact solutions for nonlinear partial differential equations. Numerical applications of the proposed method are verified by solving the improved Boussinesq equation and the system of variant Boussinesq equations. The new exact solutions for these equations include Jacobi elliptic doubly periodic type,Weierstrass elliptic doubly periodic type, triangular type and solitary wave solutions

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10

Fisher, Brian, and Adem Kılıçman. "On the Composition and Neutrix Composition of the Delta Function with the Hyperbolic Tangent and Its Inverse Functions." Journal of Applied Mathematics 2011 (2011): 1–13. http://dx.doi.org/10.1155/2011/846736.

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LetFbe a distribution inD'and letfbe a locally summable function. The compositionF(f(x))ofFandfis said to exist and be equal to the distributionh(x)if the limit of the sequence{Fn(f(x))}is equal toh(x), whereFn(x)=F(x)*δn(x)forn=1,2,…and{δn(x)}is a certain regular sequence converging to the Dirac delta function. It is proved that the neutrix compositionδ(rs-1)((tanhx+)1/r)exists andδ(rs-1)((tanhx+)1/r)=∑k=0s-1∑i=0Kk((-1)kcs-2i-1,k(rs)!/2sk!)δ(k)(x)forr,s=1,2,…, whereKkis the integer part of(s-k-1)/2and the constantscj,kare defined by the expansion(tanh-1x)k={∑i=0∞(x2i+1/(2i+1))}k=∑j=k∞cj,kxj,

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Bagul, Yogesh J., and Christophe Chesneau. "Sigmoid functions for the smooth approximation to the absolute value function." Moroccan Journal of Pure and Applied Analysis 7, no. 1 (2021): 12–19. http://dx.doi.org/10.2478/mjpaa-2021-0002.

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AbstractWe present smooth approximations to the absolute value function |x| using sigmoid functions. In particular, x erf(x/μ) is proved to be a better smooth approximation for |x| than x tanh(x/μ) and \sqrt {{x^2} + \mu } with respect to accuracy. To accomplish our goal we also provide sharp hyperbolic bounds for the error function.

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Ratnawati, Fajar, Apri Siswanto, Jaroji, Akmar Effendy, and Agus Tedyyana. "Optimizing Pigeon-Inspired Algorithm to Enhance Intrusion Detection System Performance Internet of Things Environments." JOIV : International Journal on Informatics Visualization 7, no. 4 (2023): 2215. http://dx.doi.org/10.62527/joiv.7.4.1724.

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Intrusion Detection Systems (IDS) are crucial in maintaining network security and safeguarding sensitive information against external and internal threats. This study proposes a novel approach by utilizing a Pigeon-Inspired Algorithm optimized with the Hyperbolic Tangent Function (Tanh) function to enhance the performance of IDS in threat detection specifically tailored for Internet of Things (IoT) environments. We aim to create a more robust solution for optimizing intrusion detection systems by integrating the efficient and effective Tanh function into the Pigeon-Inspired Algorithm. The prop

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13

Peleshchak, Ivan, and Diana Koshtura. "Evaluation of Classification Accuracy Using Feedforward Neural Network for Dynamic Objects." Vìsnik Nacìonalʹnogo unìversitetu "Lʹvìvsʹka polìtehnìka". Serìâ Ìnformacìjnì sistemi ta merežì 15 (July 15, 2024): 260–72. http://dx.doi.org/10.23939/sisn2024.15.260.

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This paper investigates the impact of the number of hidden layers, the number of neurons in these layers, and the types of activation functions on the accuracy of classifying projectiles of six types (A – (artillery); A/M – (artillery/missile); A/R – (armor-piercing); A/RC – (armor-piercing- incendiary); M – (missile); R – (armor-piercing shells)) using a multi-layer neural network, evaluated by a confusion matrix. Specifically, confusion matrices were constructed to assess the accuracy of classifying projectiles of six types (A – (artillery); A/M – (artillery/missile); A/R – (armor-piercing),

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Rossomando, Francisco G., Emanuel Serrano, Carlos M. Soria, and Gustavo Scaglia. "Neural Dynamics Variations Observer Designed for Robot Manipulator Control Using a Novel Saturated Control Technique." Mathematical Problems in Engineering 2020 (May 21, 2020): 1–14. http://dx.doi.org/10.1155/2020/3240210.

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This work presents a novel controller for the dynamics of robots using a dynamic variations observer. The proposed controller uses a saturated control law based on sintg−1. function instead of tanh.. Besides, this function is an alternative to the use of tanh. in saturation control, since it reaches its maximum value more gradually than the hyperbolic tangent function. Using this characteristic, the transition between states is smoother, with similar accuracy to tanh.. The controller is designed using a saturated SMC (sliding mode controller) and a dynamic variations observer based on GRNN (ge

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15

Zhuo-Sheng, Lü, and Zhang Hong-Qing. "On a New Modified Extended Tanh-Function Method." Communications in Theoretical Physics 39, no. 4 (2003): 405–8. http://dx.doi.org/10.1088/0253-6102/39/4/405.

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Bai, Cheng-Lin, and Hong Zhao. "Generalized extended tanh-function method and its application." Chaos, Solitons & Fractals 27, no. 4 (2006): 1026–35. http://dx.doi.org/10.1016/j.chaos.2005.04.069.

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17

Akter, Shahrin, and Mohammad Rafiqul Haider. "mTanh: A Low-Cost Inkjet-Printed Vanishing Gradient Tolerant Activation Function." Journal of Low Power Electronics and Applications 15, no. 2 (2025): 27. https://doi.org/10.3390/jlpea15020027.

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Inkjet-printed circuits on flexible substrates are rapidly emerging as a key technology in flexible electronics, driven by their minimal fabrication process, cost-effectiveness, and environmental sustainability. Recent advancements in inkjet-printed devices and circuits have broadened their applications in both sensing and computing. Building on this progress, this work has developed a nonlinear computational element coined as mTanh to serve as an activation function in neural networks. Activation functions are essential in neural networks as they introduce nonlinearity, enabling machine learn

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18

Wang, Ting, Wing W. Y. Ng, Wendi Li, and Sam Kwong. "Broad Autoencoder Features Learning for Classification Problem." International Journal of Cognitive Informatics and Natural Intelligence 15, no. 4 (2021): 1–15. http://dx.doi.org/10.4018/ijcini.20211001.oa23.

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Activation functions such as Tanh and Sigmoid functions are widely used in Deep Neural Networks (DNNs) and pattern classification problems. To take advantages of different activation functions, the Broad Autoencoder Features (BAF) is proposed in this work. The BAF consists of four parallel-connected Stacked Autoencoders (SAEs) and each of them uses a different activation function, including Sigmoid, Tanh, ReLU, and Softplus. The final learned features can merge such features by various nonlinear mappings from original input features with such a broad setting. This helps to excavate more inform

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Omer, Siraj Osman, Muhammad Aamir, Muhammad Bilal, Khalil Ullah, and Abbas Qadir. "A study of coefficient-related problems for symmetric starlike functions connected with a tan hyperbolic function." VFAST Transactions on Mathematics 12, no. 2 (2024): 99–113. https://doi.org/10.21015/vtm.v12i2.1945.

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The article aims to determine the sharp bounds of coefficients, Fekete-Szegö, Zalcman inequalities for the family SS∗ tanh of starlike function with respect to symmetric points linked with tan hyperbolic function. We also estimate determinant of |H2,2 (f)| is also obtained for the same class. Further, we study the logarithmic and inverse coefficients for the same class.

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Gao, Lihui, Chunxiao Guo, Yanfeng Guo, and Donglong Li. "Exact Solutions and Non-Traveling Wave Solutions of the (2+1)-Dimensional Boussinesq Equation." Mathematics 10, no. 14 (2022): 2522. http://dx.doi.org/10.3390/math10142522.

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By the extended (G′G) method and the improved tanh function method, the exact solutions of the (2+1) dimensional Boussinesq equation are studied. Firstly, with the help of the solutions of the nonlinear ordinary differential equation, we obtain the new traveling wave exact solutions of the equation by the homogeneous equilibrium principle and the extended (G′G) method. Secondly, by constructing the new ansatz solutions and applying the improved tanh function method, many non-traveling wave exact solutions of the equation are given. The solutions mainly include hyperbolic, trigonometric and rat

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Alamsyah, Nur, Titan Parama Yoga, and Budiman Budiman. "IMPROVING TRAFFIC DENSITY PREDICTION USING LSTM WITH PARAMETRIC ReLU (PReLU) ACTIVATION." JITK (Jurnal Ilmu Pengetahuan dan Teknologi Komputer) 9, no. 2 (2024): 154–60. http://dx.doi.org/10.33480/jitk.v9i2.5046.

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In the presence of complex traffic flow patterns, this research responds to the challenge by proposing the application of the Long Short-Term Memory (LSTM) model and comparing four different activation functions, namely tanh, ReLU, sigmoid, and PReLU. This research aims to improve the accuracy of traffic flow prediction through LSTM model by finding the best activation function among tanh, relu, sigmoid, and PReLU. The method used starts from the collection of traffic flow datasets covering the period 2015-2017 used to train and evaluate the LSTM model with the four activation functions. Tests

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22

Bezabeh, Belete Biazen, and Abrham Debasu Mengistu. "The effects of multiple layers feed-forward neural network transfer function in digital based Ethiopian soil classification and moisture prediction." International Journal of Electrical and Computer Engineering (IJECE) 10, no. 4 (2020): 4073. http://dx.doi.org/10.11591/ijece.v10i4.pp4073-4079.

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In the area of machine learning performance analysis is the major task in order to get a better performance both in training and testing model. In addition, performance analysis of machine learning techniques helps to identify how the machine is performing on the given input and also to find any improvements needed to make on the learning model. Feed-forward neural network (FFNN) has different area of applications, but the epoch convergences of the network differs from the usage of transfer function. In this study, to build the model for classification and moisture prediction of soil, rectifie

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23

Priatna, Edvin, Rukmi Sari Hartati, Ida Bagus Gede Manuaba, I. Made Oka Widyantara, and Nurul Hiron. "Chattering Analysis of an Optimized Model Free Sliding Mode Controller for a DC Motor Speed Control." Journal of Advanced Research in Applied Sciences and Engineering Technology 51, no. 1 (2024): 229–44. http://dx.doi.org/10.37934/araset.51.1.229244.

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The purpose of this study is to examine the chattering phenomenon in DC motor speed control technique using Model Free Sliding Mode Controller (MFSMC). The method used is to manipulate the swithing tnah function and swithing sign function in the Grey Wolf Optimizer (GWO) model and Velocity Aided Grey Wolf Optimizer (VAGWO) algorithm. The model is analysed by MATLAB and SIMULINK programs through control model and DC motor model. The study results show that chattering of DC motor speed control is greatly eliminated by using the hyperbolic tangent function (tanh) instead of the signum function. T

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Abuelma’atti, Muhammad Taher, and Saad Radhi Al-Abbas. "A New Multi-tanh-Based Non-linear Function Synthesiser." International Journal of Electronics 103, no. 11 (2016): 1788–803. http://dx.doi.org/10.1080/00207217.2016.1138532.

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Abdel-All, Nassar Hassan, Mohamed Abd-Allah Abdel-Razek, and Abd-Allah Kamel Seddeek. "Expanding the Tanh-Function Method for Solving Nonlinear Equations." Applied Mathematics 02, no. 09 (2011): 1096–104. http://dx.doi.org/10.4236/am.2011.29151.

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Takacs, Jeno. "Approximations for Brillouin and its reverse function." COMPEL - The international journal for computation and mathematics in electrical and electronic engineering 35, no. 6 (2016): 2095–99. http://dx.doi.org/10.1108/compel-06-2016-0278.

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Purpose The mathematical complexity of the BJ(x) Brillouin function makes it unsuitable for most calculations and its application difficult for computer programming in magnetism. Here, its approximation with the tanh function is proposed to ease the mathematical operations for most cases. The approximation works with good accuracy, acceptable in practical calculations. This approximation has already formed the foundation of the “hyperbolic model” in magnetism for the study of hysteretic phenomena. The reversal of the Brillouin function is an important but difficult mathematical problem for pra

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27

Fan, Engui. "Travelling Wave Solutions for Two Generalized Hirota-Satsuma Coupled KdV Systems." Zeitschrift für Naturforschung A 56, no. 3-4 (2001): 312–18. http://dx.doi.org/10.1515/zna-2001-0314.

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Abstract In this paper we present an extended tanh method that utilizes symbolic computations to obtain more travelling wave solutions for two generalized Hirota-Satsuma coupled KdV systems in a unified way. The key idea of this method is to take full advantage of a Riccati equation involving a parameter and use its solutions to replace the tanh-function by the tanh method. It is quite interesting that the numbers and types of the traveling wave solutions can be judged from the sign of the parameter. In this paper we investigate the two generalized Hirota-Satsuma coupled KdV systems

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Syarif, Ahmad, Mahdhivan Syafwan, and Admi Nazra. "A SIMPLE JUSTIFICATION OF TANH METHOD FOR DISCRETE SOLITARY WAVE SOLUTIONS." Jurnal Lebesgue : Jurnal Ilmiah Pendidikan Matematika, Matematika dan Statistika 5, no. 2 (2024): 1060–65. http://dx.doi.org/10.46306/lb.v5i2.646.

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The tanh method is known as an effective method for solving partial differential equations and obtaining traveling wave solutions. While well-used in continuous systems, its application to discrete systems (nonlinear difference-differential equations, DDEs) is still less explored. This paper revisits the tanh method for discrete systems, providing a simple justification for the method to produce discrete solitary wave solutions, including pulse-type and (anti)kink-type. By transforming DDEs into nonlinear ordinary differential equations (ODEs) and using polynomial forms in terms of the tanh fu

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Elwakil, S. A., S. K. El-labany, M. A. Zahran, and R. Sabry. "Two New Applications of the Modified Extended Tanh-Function Method." Zeitschrift für Naturforschung A 58, no. 1 (2003): 39–44. http://dx.doi.org/10.1515/zna-2003-0106.

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Based on a modified extended tanh-function method and symbolic computation, new exact solutions are found for a soliton breaking equation and coupled kdv system. The obtained solutions include rational, soliton, singular and periodical solutions.

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Abourabia, Aly M., and Rabab A. Shahein. "Shock pattern solutions for viscous-collisional plasma ion acoustic waves in view of the linear theory of the non-equilibrium thermodynamics." Canadian Journal of Physics 89, no. 6 (2011): 673–87. http://dx.doi.org/10.1139/p11-037.

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In the framework of irreversible thermodynamics, we study nonlinear ion-acoustic waves (IAWs) in viscous and collisional plasmas. Electrons, which form the background, are assumed to be nonthermal. On account of ion viscosity and ion-electron collisions, we investigate using ion fluid equations. We study the effects of the nonthermally distributed electrons β and the temperature ratio σ (= Ti/Te) on the stability, where the stability for Burger’s equation is analyzed by two methods: the phase portrait method and irreversible thermodynamics relations at different values of σ and β. We usa a red

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Muis, Abdul, Elviawaty Muisa Zamzami, and Erna Budhiarti Nababan. "Convolutional Neural Network Activation Function Performance on Image Recognition of The Batak Script." Sinkron 9, no. 1 (2024): 182–95. http://dx.doi.org/10.33395/sinkron.v9i1.13192.

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Deep Learning is a sub-set of Machine learning, Deep Learning is widely used to solve problems in various fields. One of the popular deep learning architectures is The Convolutional Neural Network (CNN), CNN has a layer that transforms feature extraction automatically so it is widely used in image recognition. However, CNN's performance using the tanh function is still relatively low, therefore it is necessary to select the right activation function to improve accuracy performance. This study analyzes the use of the activation function in image recognition of the Batak script. The result of th

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Kareem MIHSIN, Bassim. "STUDY ON NEW SUBFAMILY OF CONVEX FUNCTIONS ATTACHED SQUEAKY COEFFICIENT BOUNDS WITH TANH FUNCTION." MINAR International Journal of Applied Sciences and Technology 05, no. 04 (2023): 219–34. http://dx.doi.org/10.47832/2717-8234.17.16.

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We are emplying tanh function of family D_ϱ^ε of convex functions in Ʋ be introduced and investigated. The major support of this paper deals the derivations of squeaky inequalities which involve Taylor- Maclaurin cofficients for functions that attributed to class〖 D〗_ϱ^ε of convex function in Ʋ. In private, the bounds of first three coefficients of Taylor- Maclaurin series and the estimates of second-and third-order Hankel determinant say, HD_2,2 (f) and HD_3,1 (f) respectively and the estimates of the Fekete-Szegӧ functionals are the major aim for our study in this paper.

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Yahya, Ibtihag, Razan Atif, Lina Ahmed, Tahleel Salah Eldeen, Akram Omara, and Megdi Eltayeb. "Polymeric Nanoparticles as Drug Delivery Systems for Controlled Release." Advanced Science, Engineering and Medicine 12, no. 2 (2020): 263–70. http://dx.doi.org/10.1166/asem.2020.2495.

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This study focuses on providing a comparative mathematical analysis of drug release from polymeric nanoparticle with different structures to allow in silico prediction of the appropriate and optimal model that applies to the whole drug release and not limited to a part of the process. The drug release data from nanoparticles have been applied using MATLAB software to apply mathematical models such as Zero-order, First-order, Higuchi, Hixson–Crowell, Korsmeyer-Peppas models besides a proposed model called Tanh function. This study results highlight the usefulness of mathematical models, key fin

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S. O., Essang,, Ante, J. E., Otobi, A. O., et al. "Optimizing Neural Networks with Convex Hybrid Activations for Improved Gradient Flow." Advanced Journal of Science, Technology and Engineering 5, no. 1 (2025): 10–26. https://doi.org/10.52589/ajste-uobyfv1b.

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This paper introduces a novel hybrid activation function by combining five popular activation functions (Sigmoid, ReLU, Tanh, Leaky ReLU, and ELU) with adjustable coefficients. This integrated approach aims to mitigate the limitations of individual functions, such as vanishing gradients and inactive neurons. Our analysis, including mathematical derivations and simulations, demonstrates that the hybrid function enhances gradient flow in deeper layers, accelerates convergence, and improves generalization compared to individual functions. This work highlights the potential of mixed activation fun

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Purnawansyah, Purnawansyah, Haviluddin Haviluddin, Herdianti Darwis, Huzain Azis, and Yulita Salim. "Backpropagation Neural Network with Combination of Activation Functions for Inbound Traffic Prediction." Knowledge Engineering and Data Science 4, no. 1 (2021): 14. http://dx.doi.org/10.17977/um018v4i12021p14-28.

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Predicting network traffic is crucial for preventing congestion and gaining superior quality of network services. This research aims to use backpropagation to predict the inbound level to understand and determine internet usage. The architecture consists of one input layer, two hidden layers, and one output layer. The study compares three activation functions: sigmoid, rectified linear unit (ReLU), and hyperbolic Tangent (tanh). Three learning rates: 0.1, 0.5, and 0.9 represent low, moderate, and high rates, respectively. Based on the result, in terms of a single form of activation function, a

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Hingu, Chanakya, Xingang Fu, Taofiki Saliyu, Rui Hu, and Ramkrishna Mishan. "Power-Optimized Field-Programmable Gate Array Implementation of Neural Activation Functions Using Continued Fractions for AI/ML Workloads." Electronics 13, no. 24 (2024): 5026. https://doi.org/10.3390/electronics13245026.

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The increasing demand for energy-efficient hardware platforms to support artificial intelligence (AI) and machine learning (ML) algorithms in edge computing has driven the adoption of system-on-chip (SoC) architectures. Implementing neural network (NN) activation functions, such as the hyperbolic tangent (tanh), on hardware presents challenges due to computational complexity, high resource requirements, and power consumption. This paper aims to optimize the hardware implementation of the tanh function using continued fraction and polynomial approximations to minimize resource consumption and p

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Takács, J. "Equivalent Analytical Functions of Sums of Sigmoid like Transcendental Functions." Applied Mathematics and Nonlinear Sciences 3, no. 2 (2018): 403–8. http://dx.doi.org/10.21042/amns.2018.2.00030.

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AbstractThere is no mathematical solution to adding up transcendental functions other than numerical process. This paper put forward analytical method to model the sum of sigmoid like functions with an equivalent function. The Brillouin and Langevin as well as the error function, the tanh, sigmoid and the tan-1 functions are investigated, their equivalent functions are calculated for four components and the error between the numerical (computer assisted) result and the equivalent function is tested for accuracy. The best modelling function, the most useful to include into mathematical operatio

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Zhang, Sheng, Wei Wang, and Jing-Lin Tong. "The Exp-function Method for the Riccati Equation and Exact Solutions of Dispersive Long Wave Equations." Zeitschrift für Naturforschung A 63, no. 10-11 (2008): 663–70. http://dx.doi.org/10.1515/zna-2008-10-1101.

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In this paper, the Exp-function method is used to seek new generalized solitonary solutions of the Riccati equation. Based on the Riccati equation and one of its generalized solitonary solutions, new exact solutions with three arbitrary functions of the (2+1)-dimensional dispersive long wave equations are obtained. Compared with the tanh-function method and its extensions, the proposed method is more powerful. It is shown that the Exp-function method provides a straightforward and important mathematical tool for solving nonlinear evolution equations in mathematical physics.

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Lv, Shixia, Zenggui Wang, and Guiying Chen. "MODIFIED EXTENDED TANH-FUNCTION METHOD TO GENERALIZED NONLINEAR DISPERSIVE EQUATION." Journal of Mathematical Sciences: Advances and Applications 53, no. 1 (2018): 41–56. http://dx.doi.org/10.18642/jmsaa_7100121997.

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Cheng-Lin, Bai, and Zhao Hong. "A New Modified Extended Tanh-Function Method and Its Application." Communications in Theoretical Physics 42, no. 2 (2004): 189–94. http://dx.doi.org/10.1088/0253-6102/42/2/189.

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Fan, Engui. "Extended tanh-function method and its applications to nonlinear equations." Physics Letters A 277, no. 4-5 (2000): 212–18. http://dx.doi.org/10.1016/s0375-9601(00)00725-8.

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Chun-Ping, Liu. "( G ′/ G )-Expansion Method Equivalent to Extended Tanh Function Method." Communications in Theoretical Physics 51, no. 6 (2009): 985–88. http://dx.doi.org/10.1088/0253-6102/51/6/05.

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Zdravković, Slobodan, Louis Kavitha, Miljko V. Satarić, Slobodan Zeković, and Jovana Petrović. "Modified extended tanh-function method and nonlinear dynamics of microtubules." Chaos, Solitons & Fractals 45, no. 11 (2012): 1378–86. http://dx.doi.org/10.1016/j.chaos.2012.07.009.

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Chang, Jing, Xin Zhao, Li Huan Liu, and Xin Liang. "The Traveling Wave Solutions of Nonlinear Beam Equations by Tanh-Function Method." Advanced Materials Research 889-890 (February 2014): 628–32. http://dx.doi.org/10.4028/www.scientific.net/amr.889-890.628.

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The nonlinear beam equation are real physical models, most of physical phenomena is described by nonlinear partial differential equations. In this work, we employ the tanh-function method to obtain new travelling wave solutions of nonlinear Beam equations.

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Akram, A., S. Ahmad, A. Rehman Jami, M. Sufyan, and U. Zahid. "Variations in the expansion and shear scalars for dissipative fluids." Modern Physics Letters A 33, no. 13 (2018): 1850076. http://dx.doi.org/10.1142/s0217732318500761.

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This work is devoted to the study of some dynamical features of spherical relativistic locally anisotropic stellar geometry in f(R) gravity. In this paper, a specific configuration of tanh f(R) cosmic model has been taken into account. The mass function through technique introduced by Misner–Sharp has been formulated and with the help of it, various fruitful relations are derived. After orthogonal decomposition of the Riemann tensor, the tanh modified structure scalars are calculated. The role of these tanh modified structure scalars (MSS) has been discussed through shear, expansion as well as

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Tian, Bo, KeYi Zhao, and Yi-Tian Gao. "Notiz: Modification of the Generalized tanh Method with sech Function for Generalized Hamiltonian Equations." Zeitschrift für Naturforschung A 52, no. 4 (1997): 372. http://dx.doi.org/10.1515/zna-1997-0413.

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Barus, Ertina Sabarita, Muhammad Zarlis, Zulkifli Nasution, and Sutarman Sutarman. "Development of machine learning for forecasting optimization implemented in morphology plant growth." Eastern-European Journal of Enterprise Technologies 3, no. 2 (135) (2025): 42–53. https://doi.org/10.15587/1729-4061.2025.331745.

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The object of the study is the forecasting and optimizing the plant growth rather. The data distribution at each iteration in the continuous optimization process tends to produce premature convergence because the optimum points are found at the beginning of the iteration, so that the actual optimum condition cannot be achieved. For this reason, a method is needed to see the optimum points at each iteration in the continuous optimization process. A multi-linear regression approach is used to predict the variables generated at each iteration, and then optimized using a neural network method appr

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Budiman, Budimann, Nur Alamsyah, and R. Yadi Rakhman Alamsyah. "ACTIVATION FUNCTION IN LSTM FOR IMPROVED FORECASTING OF CLOSING NATURAL GAS STOCK PRICES." JITK (Jurnal Ilmu Pengetahuan dan Teknologi Komputer) 10, no. 1 (2024): 100–107. http://dx.doi.org/10.33480/jitk.v10i1.5258.

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The closing price of natural gas stocks greatly influences investment decisions and the energy industry. Predicting prices correctly can greatly help investors, market participants, and all parties involved, as it allows for making better decisions and optimizing investment portfolios. By using deep learning methods to role model various LSTM activation functions, such as Sigmoid, ReLU, and Tanh, this exploration will hopefully help understand complex patterns in time series data. By finding an appropriate forecasting method, all parties involved can reduce the environmental impact. The experi

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Chen, Jun-Lang, and Chao-Qing Dai. "New Variable Separation Solutions of the (2+1)-Dimensional Generalized Broer-Kaup System." Zeitschrift für Naturforschung A 62, no. 12 (2007): 677–84. http://dx.doi.org/10.1515/zna-2007-1201.

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Using symbolic and algebra computation, the extended tanh-function method (ETM) based on the mapping method is further extended. New variable separation solutions of the (2+1)-dimensional generalized Broer-Kaup (GBK) system are derived. From the periodic wave solution and by selecting appropriate functions, the evolutional behaviours of dromions in the background of Jacobian elliptic wave and their interaction behaviours are investigated.

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Yingna, Zhong, Kauthar Mohd Daud, Kohbalan Moorthy, and Ain Najiha Mohamad Nor. "Filtering Approaches and Mish Activation Function Applied on Handwritten Chinese Character Recognition." ADCAIJ: Advances in Distributed Computing and Artificial Intelligence Journal 13 (November 1, 2024): e31218. https://doi.org/10.14201/adcaij.31218.

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Handwritten Chinese Characters (HCC) have recently received much attention as a global means of exchanging information and knowledge. The start of the information age has increased the number of paper documents that must be electronically saved and shared. The recognition accuracy of online handwritten Chinese characters has reached its limit as online characters are more straightforward than offline characters. Furthermore, online character recognition enables stronger involvement and flexibility than offline characters. Deep learning techniques, such as convolutional neural networks (CNN), h

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