Deep Neural Network-Based Simulation of Sel’kov Model in Glycolysis: A Comprehensive Analysis

Rahman, Jamshaid Ul; Danish, Sana; Lu, Dianchen

doi:10.3390/math11143216

Cited by 6 publications

(1 citation statement)

References 34 publications

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“…There is a special place for dynamical systems [1], as well as for the identification of dynamical systems [2], in assessing physical phenomena in the realm of experimental science. Although many methods are used to model, simulate, and solve dynamical systems [3] and to discuss their stability [4], neural network-based techniques [5,6] to approximate the solution of DEs occurring in various systems [7] have, however, garnered a reputation in recent years. Other analytical methods for ordinary DEs [8] and partial DEs [9], semi-analytical methods [10], including the Variational Iteration Method (VIM) by using the Laplace Transform [11], and numerical methods have their own shortcomings in terms of convergence, precision, processing time, and computational complexity.…”

Section: Introductionmentioning

confidence: 99%

Oscillator Simulation with Deep Neural Networks

Rahman,

Danish,

2024

Mathematics

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The motivation behind this study is to overcome the complex mathematical formulation and time-consuming nature of traditional numerical methods used in solving differential equations. It seeks an alternative approach for more efficient and simplified solutions. A Deep Neural Network (DNN) is utilized to understand the intricate correlations between the oscillator’s variables and to precisely capture their dynamics by being trained on a dataset of known oscillator behaviors. In this work, we discuss the main challenge of predicting the behavior of oscillators without depending on complex strategies or time-consuming simulations. The present work proposes a favorable modified form of neural structure to improve the strategy for simulating linear and nonlinear harmonic oscillators from mechanical systems by formulating an ANN as a DNN via an appropriate oscillating activation function. The proposed methodology provides the solutions of linear and nonlinear differential equations (DEs) in differentiable form and is a more accurate approximation as compared to the traditional numerical method. The Van der Pol equation with parametric damping and the Mathieu equation are adopted as illustrations. Experimental analysis shows that our proposed scheme outperforms other numerical methods in terms of accuracy and computational cost. We provide a comparative analysis of the outcomes obtained through our proposed approach and those derived from the LSODA algorithm, utilizing numerical techniques, Adams–Bashforth, and the Backward Differentiation Formula (BDF). The results of this research provide insightful information for engineering applications, facilitating improvements in energy efficiency, and scientific innovation.

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Section: Introductionmentioning

confidence: 99%

Oscillator Simulation with Deep Neural Networks

Rahman,

Danish,

2024

Mathematics

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Modelling of Marburg virus transmission dynamics: a deep learning-driven approach with the effect of quarantine and health awareness interventions

Mustafa,

Rahman,

Omame

2024

Model. Earth Syst. Environ.

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An efficient deep neural network with amplifying sine unit for nonlinear oscillatory systems

Faiza,

Jamshaid,

Naveed

2024

JME

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Nonlinear differential equations play a pivotal role in modeling various physical phenomena, capturing their oscillatory behaviors. Numerous analytic and numerical methods have been developed to obtain precise or approximate solutions for nonlinear dynamics. This study introduces a novel approach utilizing neural network strategies, known for their computational flexibility. This study proposed a novel architecture for deep neural networks that is intended to simulate the nonlinear oscillations of two systems. It has been modified to include an oscillatory activation function called the amplifying sine unit. This study compares the results from our customized neural networks with those from the conventional stable and reliable numerical technique of the Runge-Kutta method of order four. Remarkably, there is striking agreement between the outcomes of the two methods, highlighting the ability of deep neural networks to identify nonlinear dynamical behaviors without requiring explicit conversion of mathematical models into an equation system.

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Deep Neural Network-Based Simulation of Sel’kov Model in Glycolysis: A Comprehensive Analysis

Cited by 6 publications

References 34 publications

Oscillator Simulation with Deep Neural Networks

Oscillator Simulation with Deep Neural Networks

Modelling of Marburg virus transmission dynamics: a deep learning-driven approach with the effect of quarantine and health awareness interventions

An efficient deep neural network with amplifying sine unit for nonlinear oscillatory systems

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