Weakly Supervised Learning Technique for Solving Partial Differential Equations; Case Study of 1-D Reaction-Diffusion Equation

Zakeri, Behzad; Monsefi, Amin Karimi; Samsam, Sanaz; Monsefi, Bahareh Karimi

doi:10.1007/978-3-030-33495-6_28

Cited by 5 publications

(2 citation statements)

References 25 publications

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“…Coefficients, variables, boundary conditions type and dimensions of the RDE are highly dependent on the case which is studying, and based on the way that they are chosen, proper technique must be taken. All techniques aim to represent a precise solution (C(X, t)) of the RDE which describe diffusive property concentration in each time and position [21].…”

Section: Introductionmentioning

confidence: 99%

Solving partial differential equations by a supervised learning technique, applied for the reaction–diffusion equation

et al. 2019

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Deep learning is a crucial point of valuable intelligence resources to deal with complicated mathematical problems. The effectiveness of deep learning in solving differential equations has been considered over the past few years. Supervision of the learning process requires significant information to be marked in order to train the network. Nevertheless, this approach could not be a helpful strategy in case of unknown differential equations that we have no identified data. In order to address this problem, a new method for solving differential equations will be introduced in this paper using only the boundary and initial conditions. As an efficient method, inadequate monitoring can provide an ideal bed to fix boundary and initial value issues. For verification of the proposed method, a reaction-diffusion equation was performed. This equation has a variety of applications in engineering and science.

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Section: Introductionmentioning

confidence: 99%

Solving partial differential equations by a supervised learning technique, applied for the reaction–diffusion equation

et al. 2019

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“…Partial Differential Equations (PDEs) have always played a significant role in mathematical modeling and simulation, which are widely used in physics, engineering and economics [1], [2]. A wide range of physical phenomena are modelled by second-order PDEs with constant coefficients, and representing precise solutions for these kinds of equations is an important part of applied mathematics.…”

Section: Introductionmentioning

confidence: 99%

Solving the Reaction-Diffusion equation based on analytical methods and deep learning algorithm; the Case study of sulfate attack to concrete

Monsefi¹,

Bakhtiyarzade²

2019

Preprint

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The reaction-diffusion equation is one of the cornerstones equations in applied science and engineering. In the present study, a deep neural network has been trained in order to predict the solution of the equation with different coefficients using the numerical solution of this equation and the utility of deep learning. Analytical solution of the Reaction-Diffusion equation also has been conducted by taking advantage of Danckwerts method. The accuracy of deep learning results was compared with the analytical solutions. In order to decrease the learning time and to find out similar equations solutions, such as pure diffusion and pure reaction, dimensional analysis technique has been performed. It was demonstrated that deep learning can accurately estimate the Partial Differential Equations solution in the case of the reaction-diffusion equation with a constant coefficient.

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Least squares support vector regression for solving Volterra integral equations

Parand

Razzaghi

Sahleh

et al. 2020

Engineering with Computers

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Weakly Supervised Learning Technique for Solving Partial Differential Equations; Case Study of 1-D Reaction-Diffusion Equation

Cited by 5 publications

References 25 publications

Solving partial differential equations by a supervised learning technique, applied for the reaction–diffusion equation

Solving partial differential equations by a supervised learning technique, applied for the reaction–diffusion equation

Solving the Reaction-Diffusion equation based on analytical methods and deep learning algorithm; the Case study of sulfate attack to concrete

Least squares support vector regression for solving Volterra integral equations

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