Numerical solution of unsteady advection dispersion equation arising in contaminant transport through porous media using neural networks

Yadav, Neha; Yadav, Anupam; Kim, Joong Hoon

doi:10.1016/j.camwa.2016.06.014

Cited by 27 publications

(16 citation statements)

References 35 publications

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“…The set of trained weights optimized through HHO-IPA, respectively for cases C 2 , C 3 and C 4 with fitness values 3.6962 × 10 −10 , 1.8650 × 10 −10 and 2.0357 × 10 −10 are graphically represented in figure (13). Using these weights the derived solutions for cases C 2 , C 3 and C 4 are mathematically defined as follows:…”

Section: A Problem-1: Vdp Dynamic Heartbeat Model In the Absence Of Forcing Termmentioning

confidence: 99%

“…Best solution ofx c 1 in the present scenario andx c 1 in previous scenario are similar. We got our results based on the inputs in the interval [0, 2] with h = 0.1 taken as step size and the AE in our solutions and reference numerical solutions are given in figure (13). It is evident that the accuracy of the order between 10 −11 − 10 −07 is achieved by our designed technique.…”

Section: A Problem-1: Vdp Dynamic Heartbeat Model In the Absence Of Forcing Termmentioning

confidence: 99%

“…Reference solutions by Adam's technique are used for calculating errors in our results. The set of trained weights optimized through HHO-IPA, respectively for cases C 2 , C 3 , and C 4 are shown in figure (13). We have plotted our solutions in figure (12a).…”

Section: Problem-ii Scenario-iimentioning

confidence: 99%

“…Artificial intelligence techniques are considered effective, accurate and reliable for the solution of many unconstrained and constrained optimization problems arising in different fields [13]- [15]. Some recent artificial intelligence methodologies based on artificial neural networks (ANNs) appeared with different applications [16], [17].…”

Section: Introductionmentioning

confidence: 99%

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Analysis of Oscillatory Behavior of Heart by Using a Novel Neuroevolutionary Approach

et al. 2020

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This paper aims at the analysis of the VdP heartbeat mathematical model. We have analysed the conditionality of a mathematical model which represents the oscillatory behaviour of the heart. A novel neuroevolutionary approach is chosen to analyse the mathematical model. The characteristics of the cardiac pulse of the heart are examined by considering two major scenarios with sixteen different cases. Artificial neural networks (ANNs) are constructed to obtain the best solutions for the heartbeat model. Unknown weights are finely tuned by a combination of a global search technique the Harris Hawks Optimizer (HHO) and a local search technique the Interior Point Algorithm (IPA). Stable behaviour of solutions obtained by considering different cases demonstrates that the model under consideration is well-conditioned. The accuracy of our novel procedure is established by getting the lowest residual errors in our solution for all cases. Graphical and statistical analysis are added to further elaborate the accuracy of our approach. INDEX TERMSCardiac pulse model, hybridized soft computing, artificial neural networks, non-linear ordinary differential equations, heuristics, interior-point algorithm, Harris Hawks optimizer. Ph.D. degree in software engineering from De Montfort University, in 2015. From 2004 to 2007, he worked in the Software Development Industry, where he implemented several systems and solutions for a National Academic Institution. His research interests include algorithms, semantic web, and optimization techniques. He focuses on enhancing real-world matching systems using machine learning and data analytics in the context of supporting decision-making.

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Section: A Problem-1: Vdp Dynamic Heartbeat Model In the Absence Of Forcing Termmentioning

confidence: 99%

Section: A Problem-1: Vdp Dynamic Heartbeat Model In the Absence Of Forcing Termmentioning

confidence: 99%

Section: Problem-ii Scenario-iimentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Analysis of Oscillatory Behavior of Heart by Using a Novel Neuroevolutionary Approach

et al. 2020

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“…Equation 1is a generalization of Eq. (4), therefore, the researchers have a big chance for modeling many problems in various areas of science such as anomalous diffusion, biology problems, petroleum engineering, heat transfer, physical problems, and others [3,4,33,37]. The fractional-order advection-dispersion equation is solved numerically through different approximation methods (see, for instance, [8,14,15,21,23,29]).…”

Section: Introductionmentioning

confidence: 99%

Vieta–Lucas polynomials for solving a fractional-order mathematical physics model

Agarwal

El‐Sayed

2020

Adv Differ Equ

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In this article, a fractional-order mathematical physics model, advection–dispersion equation (FADE), will be solved numerically through a new approximative technique. Shifted Vieta–Lucas orthogonal polynomials will be considered as the main base for the desired numerical solution. These polynomials are used for transforming the FADE into an ordinary differential equations system (ODES). The nonstandard finite difference method coincidence with the spectral collocation method will be used for converting the ODES into an equivalence system of algebraic equations that can be solved numerically. The Caputo fractional derivative will be used. Moreover, the error analysis and the upper bound of the derived formula error will be investigated. Lastly, the accuracy and efficiency of the proposed method will be demonstrated through some numerical applications.

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Deep learning‐based method for solving seepage equation under unsteady boundary

Li,

Shen,

Zha

et al. 2023

Numerical Methods in Fluids

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Deep learning‐based methods for solving partial differential equations have become a research hotspot. The approach builds on the previous work of applying deep learning methods to partial differential equations, which avoid the need for meshing and linearization. However, deep learning‐based methods face difficulties in effectively solving complex turbulent systems without using labeled data. Moreover, issues such as failure to converge and unstable solution are frequently encountered. In light of this objective, this paper presents an approximation‐correction model designed for solving the seepage equation featuring unsteady boundaries. The model consists of two neural networks. The first network acts as an asymptotic block, estimating the progression of the solution based on its asymptotic form. The second network serves to fine‐tune any errors identified in the asymptotic block. The solution to the unsteady boundary problem is achieved by superimposing these progressive blocks. In numerical experiments, both a constant flow scenario and a three‐stage flow scenario in reservoir exploitation are considered. The obtained results show the method's effectiveness when compared to numerical solutions. Furthermore, the error analysis reveals that this method exhibits superior solution accuracy compared to other baseline methods.

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Numerical solution of unsteady advection dispersion equation arising in contaminant transport through porous media using neural networks

Cited by 27 publications

References 35 publications

Analysis of Oscillatory Behavior of Heart by Using a Novel Neuroevolutionary Approach

Analysis of Oscillatory Behavior of Heart by Using a Novel Neuroevolutionary Approach

Vieta–Lucas polynomials for solving a fractional-order mathematical physics model

Deep learning‐based method for solving seepage equation under unsteady boundary

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