A neural network approach for the solution of Van der Pol-Mathieu-Duffing oscillator model

Sahoo, Arup Kumar; Chakraverty, Snehashish

doi:10.1007/s12065-023-00835-1

Cited by 9 publications

(2 citation statements)

References 47 publications

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“…ANN is a branch of AI that mimics the training process of the human brain for predicting the patterns from the given historical data [23]. NN are processing devices of mathematical algorithms that can be implemented by computer programming.…”

Section: Preliminariesmentioning

confidence: 99%

Application of Physics-Informed Neural Networks for Simulating Mass-Spring-Damper Systems

Sahoo,

Kumar,

Chakraverty

2024

Preprint

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Dynamical problems are generally governed by a set of linear/non-linear differential equations (DEs). A large amount of prior physical information in the form of DEs plays an important role in simulation of dynamical systems. However, the traditional data-hungry machine learning models fail to express insightful scientific information from the data. Most of the implementations of neural networks are to perform non-linear mapping from input space to target space. However, Physics-informed neural networks (PINNs) can bridge the gap between scientific computing and data-hungry models. This paper exploits a new application of PINNs for approximating the behaviour of mass-spring-damper systems, showcasing how PINNs can effectively blend scientific principles with data-driven modeling. In this regard, we present solutions of two realistic application problems using PINNs. The accuracy of the predicted displacements of objects is established through results from literatures.

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Section: Preliminariesmentioning

confidence: 99%

Application of Physics-Informed Neural Networks for Simulating Mass-Spring-Damper Systems

Sahoo,

Kumar,

Chakraverty

2024

Preprint

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“…This study sought to provide useful information for choosing the best modeling approaches to determine poverty levels in the Indian setting by examining their performance and precision. Sahoo and Chakraverty [42] proposed a symplectic artificial neural network to handle nonlinear systems arising in dusty plasma models. They presented the dynamics of Van der Pol-Mathieu-Duffing oscillator problems for different excitation functions using the proposed method, and numerical simulations and graphical representations were carried out to establish the accuracy of the presented algorithm.…”

Section: Introductionmentioning

confidence: 99%

The Numerical Solution of Nonlinear Fractional Lienard and Duffing Equations Using Orthogonal Perceptron

Verma,

Sumelka,

Yadav

2023

Symmetry

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This paper proposes an approximation algorithm based on the Legendre and Chebyshev artificial neural network to explore the approximate solution of fractional Lienard and Duffing equations with a Caputo fractional derivative. These equations show the oscillating circuit and generalize the spring–mass device equation. The proposed approach transforms the given nonlinear fractional differential equation (FDE) into an unconstrained minimization problem. The simulated annealing (SA) algorithm minimizes the mean square error. The proposed techniques examine various non-integer order problems to verify the theoretical results. The numerical results show that the proposed approach yields better results than existing methods.

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Approximation error estimates by noise‐injected neural networks

Akiyama

2024

Math Methods in App Sciences

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One‐hidden‐layer feedforward neural networks are described as functions having many real‐valued parameters. Approximation properties of neural networks are established (universal approximation property), and the approximation error is related to the number of parameters in the network. The essentially optimal order of approximation error bounds was already derived in 1996. We focused on the numerical experiment that indicates the neural networks whose parameters contain stochastic perturbations gain better performance than ordinary neural networks and explored the approximation property of neural networks with stochastic perturbations. In this paper, we derived the quantitative order of variance of stochastic perturbations to achieve the essentially optimal approximation order and verified the justifiability of our theory by numerical experiments.

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A neural network approach for the solution of Van der Pol-Mathieu-Duffing oscillator model

Cited by 9 publications

References 47 publications

Application of Physics-Informed Neural Networks for Simulating Mass-Spring-Damper Systems

Application of Physics-Informed Neural Networks for Simulating Mass-Spring-Damper Systems

The Numerical Solution of Nonlinear Fractional Lienard and Duffing Equations Using Orthogonal Perceptron

Approximation error estimates by noise‐injected neural networks

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